WO2025259028A1

WO2025259028A1 - Methods and systems for decoding received signals in multiple-input multiple-output communication systems

Info

Publication number: WO2025259028A1
Application number: PCT/KR2025/008058
Authority: WO
Inventors: Krishna Kumar; Bharath S; Hari Krishna Boddapati; Ashok Kumar Reddy CHAVVA; Sandesh Rao M
Original assignee: Samsung Electronics Co Ltd
Current assignee: Samsung Electronics Co Ltd
Priority date: 2024-06-12
Filing date: 2025-06-12
Publication date: 2025-12-18
Anticipated expiration: 2026-12-12

Abstract

The disclosure relates to a 5G communication system or a 6G communication system for supporting higher data rates beyond a 4G communication system such as long term evolution (LTE). Disclosed herein is a method for decoding received signal that includes obtaining an input parameter from the received signal, obtaining a tree structure based on matrix factorization of the channel matrix, pre-processing of the received signal, obtaining an initial linear solution, determining a neighbour of the linear solution based on the modulation order for a layer and a pre-defined number of the neighbour in the layer, creating a search space by pruning the tree structure, applying a decoding technique on the search space, computing a decision metric, determining a likelihood-based metric based on the decision metric, and decoding the received signal by feeding the likelihood-based metric for the at least one bit to a channel decoder.

Description

METHODS AND SYSTEMS FOR DECODING RECEIVED SIGNALS IN MULTIPLE-INPUT MULTIPLE-OUTPUT COMMUNICATION SYSTEMS

The disclosure relates to the field of mobile communications, and particularly, to methods and systems for decoding received signals in a multiple-input multiple-output (MIMO) communication system.

Considering the development of wireless communication from generation to generation, the technologies have been developed mainly for services targeting humans, such as voice calls, multimedia services, and data services. Following the commercialization of 5G (5th-generation) communication systems, it is expected that the number of connected devices will exponentially grow. Increasingly, these will be connected to communication networks. Examples of connected things may include vehicles, robots, drones, home appliances, displays, smart sensors connected to various infrastructures, construction machines, and factory equipment. Mobile devices are expected to evolve in various form-factors, such as augmented reality glasses, virtual reality headsets, and hologram devices. In order to provide various services by connecting hundreds of billions of devices and things in the 6G (6th-generation) era, there have been ongoing efforts to develop improved 6G communication systems. For these reasons, 6G communication systems are referred to as beyond-5G systems.

6G communication systems, which are expected to be commercialized around 2030, will have a peak data rate of tera (1,000 giga)-level bps and a radio latency less than 100μsec, and thus will be 50 times as fast as 5G communication systems and have the 1/10 radio latency thereof.

In order to accomplish such a high data rate and an ultra-low latency, it has been considered to implement 6G communication systems in a terahertz band (for example, 95GHz to 3THz bands). It is expected that, due to severer path loss and atmospheric absorption in the terahertz bands than those in mmWave bands introduced in 5G, technologies capable of securing the signal transmission distance (that is, coverage) will become more crucial. It is necessary to develop, as major technologies for securing the coverage, radio frequency (RF) elements, antennas, novel waveforms having a better coverage than orthogonal frequency division multiplexing (OFDM), beamforming and massive multiple input multiple output (MIMO), full dimensional MIMO (FD-MIMO), array antennas, and multiantenna transmission technologies such as large-scale antennas. In addition, there has been ongoing discussion on new technologies for improving the coverage of terahertz-band signals, such as metamaterial-based lenses and antennas, orbital angular momentum (OAM), and reconfigurable intelligent surface (RIS).

Moreover, in order to improve the spectral efficiency and the overall network performances, the following technologies have been developed for 6G communication systems: a full-duplex technology for enabling an uplink transmission and a downlink transmission to simultaneously use the same frequency resource at the same time; a network technology for utilizing satellites, high-altitude platform stations (HAPS), and the like in an integrated manner; an improved network structure for supporting mobile base stations and the like and enabling network operation optimization and automation and the like; a dynamic spectrum sharing technology via collison avoidance based on a prediction of spectrum usage; an use of artificial intelligence (AI) in wireless communication for improvement of overall network operation by utilizing AI from a designing phase for developing 6G and internalizing end-to-end AI support functions; and a next-generation distributed computing technology for overcoming the limit of UE computing ability through reachable super-high-performance communication and computing resources (such as mobile edge computing (MEC), clouds, and the like) over the network. In addition, through designing new protocols to be used in 6G communication systems, developing mecahnisms for implementing a hardware-based security environment and safe use of data, and developing technologies for maintaining privacy, attempts to strengthen the connectivity between devices, optimize the network, promote softwarization of network entities, and increase the openness of wireless communications are continuing.

It is expected that research and development of 6G communication systems in hyper-connectivity, including person to machine (P2M) as well as machine to machine (M2M), will allow the next hyper-connected experience. Particularly, it is expected that services such as truly immersive extended reality (XR), high-fidelity mobile hologram, and digital replica could be provided through 6G communication systems. In addition, services such as remote surgery for security and reliability enhancement, industrial automation, and emergency response will be provided through the 6G communication system such that the technologies could be applied in various fields such as industry, medical care, automobiles, and home appliances.

In a first aspect of the disclosure, provided herein is a method for decoding received signal in a multiple-input multiple-output (MIMO) communication system, the method comprising: obtaining an input parameter from the received signal, wherein the input parameter includes at least one of a signal vector, a noise variance, a modulation order, and a channel matrix; obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signal; obtaining an initial linear solution based on the received signal, the channel matrix, and the noise variance; determining a neighbour of the linear solution for a layer of the tree structure based on the modulation order for the layer and a pre-defined number of the neighbour in the layer, of the tree structure; creating a search space by pruning the tree structure based on the neighbour for the layer of the tree structure; applying a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising at least one bit; computing a decision metric for the at least one bit of the decoded signal vector; determining a likelihood-based metric for the at least one bit of the decoded signal vector based on the decision metric; and decoding the received signal by feeding the likelihood-based metric for the at least one bit to a channel decoder.

In a second aspect of the disclosure, provided herein is a system for decoding received signal in a multiple-input multiple-output (MIMO) communication system, the system comprising: at least one processor; and a memory coupled with the at least one processor, wherein the at least one processor is configured to: obtain an input parameter from the received signal, wherein the input parameter includes at least one of a signal vector, a noise variance, a modulation order, and a channel matrix; obtain a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signal; obtain an initial linear solution based on the received signal, the channel matrix, and the noise variance; determine a neighbour of the linear solution for a layer of the tree structure based on the modulation order for the layer and a pre-defined number of the neighbour in the layer, of the tree structure; create a search space by pruning the tree structure based on the neighbour for the layer of the tree structure; apply a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising at least one bit; compute a decision metric for the at least one bit of the decoded signal vector; determine a likelihood-based metric for the at least one bit of the decoded signal vector based on the decision metric; and decode the received signal by feeding the likelihood-based metric for the at least one bit to a channel decoder.

These and other features, aspects, and advantages of the disclosure will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:

Figures 1a and 1b illustrates performance analysis of sphere decoding depicting corresponding block error rate (BLER) and computational complexity under four Transmit (Tx) layers and 16-Quadrature Amplitude Modulation (16-QAM), according to an embodiment of the disclosure;

Figure 2 illustrates an environment implementing a system for decoding received signals in a multiple-input multiple-output (MIMO) communication system, according to an embodiment of the disclosure;

Figure 3 illustrates a Maximum Likelihood Detection (MLD) modelled as tree search for K=3 layers and Binary Phase Shift Keying (BPSK) modulation, according to an embodiment of the disclosure;

Figure 4 illustrates a Sphere Decoder for pruning of the tree, according to an embodiment of the disclosure;

Figure 5 illustrates a block diagram of the system for decoding received signals, according to an embodiment of the disclosure;

Figure 6 illustrates an exemplary search space obtained during decoding received signals using a neighborhood-based tree pruning, according to an embodiment of the disclosure;

Figure 7a illustrates an exemplary structure of a decision tree, according to an embodiment of the disclosure;

Figure 7b illustrates an exemplary structure of the decision tree after the neighbourhood-based tree pruning, according to an embodiment of the disclosure;

Figure 8 illustrates a schematic workflow of a method depicting the neighbourhood-based tree pruning (NTP) based sphere decoding, according to an embodiment of the disclosure;

Figure 9a illustrates a comparative analysis of block error rate (BLER) of the sphere decoding using the NTP mechanism, according to an embodiment of the disclosure;

Figure 9b illustrates a comparative analysis of the computational complexity of the sphere decoding using the NTP mechanism, according to an embodiment of the disclosure;

Figure 10 illustrates a schematic workflow of a method depicting node limiting (NL) mechanism based sphere decoding, according to an embodiment of the disclosure;

Figure 11a illustrates a comparative analysis of the BLER of the sphere decoding using the NL mechanism, according to an embodiment of the disclosure;

Figure 11b illustrates a comparative analysis of the computational complexity of the sphere decoding using the NL mechanism, according to an embodiment of the disclosure;

Figure 12 illustrates a schematic workflow of a method depicting a combined approach of the NTP and the NL mechanism sphere decoding, according to an embodiment of the disclosure;

Figure 13a illustrates a comparative analysis of the BLER of the sphere decoding using the combination of the NTP mechanism and the NL mechanism, according to an embodiment of the disclosure;

Figure 13b illustrates a comparative analysis of the computational complexity of the sphere decoding using the combination of the NTP mechanism and the NL mechanism, according to an embodiment of the disclosure;

Figures 14a and 14b illustrate a process flow of a method for decoding received signals in MIMO communication system using the NTP mechanism, according to an embodiment of the disclosure;

Figures 15a and 15b illustrate a process flow of a method for decoding received signals in MIMO communication system using the NL mechanism, according to an embodiment of the disclosure; and

Figures 16a and 16b illustrate a process flow of a method for decoding received signals in MIMO communication system using the NTP and NL mechanism, according to an embodiment of the disclosure.

Further, skilled artisans will appreciate that elements in the drawings are illustrated for simplicity and may not have necessarily been drawn to scale. For example, the flow charts illustrate the method in terms of the most prominent steps involved to help improve understanding of aspects of the disclosure. Furthermore, in terms of the construction of the device, one or more components of the device may have been represented in the drawings by conventional symbols, and the drawings may show only those specific details that are pertinent to understanding the embodiments of the disclosure so as not to obscure the drawings with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein.

For the purpose of promoting an understanding of the principles of the disclosure, reference will now be made to the various embodiments and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the disclosure is thereby intended, such alterations and further modifications in the illustrated system, and such further applications of the principles of the disclosure as illustrated therein being contemplated as would normally occur to one skilled in the art to which the disclosure relates.

It will be understood by those skilled in the art that the foregoing general description and the following detailed description are explanatory of the disclosure and are not intended to be restrictive thereof.

Reference throughout this specification to "an aspect," "another aspect" or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosure. Thus, appearances of the phrase "in an embodiment", "in another embodiment" and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.

The terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process or method that comprises a list of steps does not include only those steps but may include other steps not expressly listed or inherent to such process or method. Similarly, one or more devices or sub-systems or elements or structures or components proceeded by "comprises... a" does not, without more constraints, preclude the existence of other devices or other sub-systems or other elements or other structures or other components or additional devices or additional sub-systems or additional elements or additional structures or additional components.

In modern mobile communication systems, particularly in 5th Generation (5G) and beyond, multiple-input multiple-output (MIMO) technology has played a crucial role in enhancing both data rates and energy efficiency. The MIMO technology leverages multiple antennas at both transmitter end and receiver end to enable simultaneous transmission of multiple data streams over same time-frequency resources. The MIMO technology significantly increases network capacity and spectral efficiency by exploiting spatial multiplexing, thereby making the technology indispensable for advanced wireless systems. The effectiveness of the MIMO technology, however, hinges on accurate detection and recovery of the transmitted data streams.

One of the theoretically optimal methods for signal recovery is Maximum Likelihood Detection (MLD), which ensures minimal error probability. However, the implementation of MLD in practical systems is highly challenging due to computational complexity associated with the MLD, which grows exponentially with number of transmit antennas and modulation order. As a result, simpler detection techniques are typically employed. To mitigate complexity issues while achieving reliable performance, linear equalization methods, such as Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE) equalizers are commonly used in practical MIMO communication systems. Further, the MMSE equalizer performs remarkably well when number of receive (Rx) streams, represented by N_r, is significantly higher than number of transmit (Tx) layers, represented by N_t, (i.e., when N_r >> N_t). However, the performance of the MMSE equalizer severely deteriorates considerably when the number of Rx streams is comparable to the number of Tx layers (i.e., N_r N_t), leading to increased detection errors. Such degradation becomes especially relevant in centralized radio access network (cRAN) and virtualized radio access network (vRAN) architectures, where port reduction strategies are frequently adopted to minimize fronthaul overhead. In such scenarios, a challenge of ensuring high detection accuracy while maintaining system efficiency becomes pronounced, necessitating advanced signal processing techniques and optimized equalization strategies to enhance robustness of MIMO communication systems.

There are existing MIMO detectors that are primarily designed to achieve high performance when N_r is significantly larger than N_t. Although the existing MIMO detectors leverage advanced signal processing techniques, however, they tend to fail in scenarios where N_r is approximately equal to N_t, leading to degraded signal recovery. To overcome such limitation, tree search-based approaches have been explored, which are known to provide near-optimal performance even when N_r N_t. Among these methods, two well-recognized prior techniques are a Sphere Decoder and a QR decomposition-based M-algorithm (QRDM). While the Sphere Decoder has the capability to attain exact the MLD performance, the QRDM offers a more flexible balance between error performance and computational complexity. However, both the Sphere Decoder and the QRDM still suffer from significantly higher complexity as compared to simpler detectors, such as, the MMSE detector.

To address higher complexity concerns of the Sphere Decoder and the QRDM, various techniques were developed to refine the tree search detectors further to reduce computational demands. However, these efforts often lead to a trade-off, where reducing complexity results in compromised error performance. The decline in detection accuracy translates to diminished energy efficiency when compared to the theoretically optimal MLD. The energy consumption is a critical factor in modern wireless systems, particularly for base stations and user devices, these limitations pose significant challenges in practical deployments.

Further, International Mobile Telecommunications (IMT) 2030, particularly 6^th Generation systems, emphasize on enhanced coverage and higher data rates beyond those of 5G systems. Thus, it becomes a necessity for innovative MIMO detection techniques to strike balance between performance, complexity, and energy efficiency. To fulfilling the requirements of the IMT 2030, the receivers are required to achieve close to a Maximum Likelihood (ML) detector performance while maintaining the computational complexity similar to the MMSE detection. To elaborate, the near-ML detector may require considerably lower energy to attain a given block error rate (BLER) target, directly improving energy efficiency. The near-MLD may enhance communication system longevity by minimizing energy required for signal detection, while ensuring reliable performance, which may reduce operational costs. Additionally, superior signal recovery using near-MLD may extend coverage by enabling users or base stations to detect transmitted signals at longer distances compared to the current MMSE-based systems. The inherent advantage of the near-MLD is the ability to achieve high detection accuracy with significantly lower energy expenditure than the MMSE based systems, making the near-ML detector ideal for large-scale deployments where maintaining seamless connectivity across vast areas is critical. The near-MLD also support higher data throughput. With increased detection accuracy, the transmitters can utilize higher-order modulation schemes, leading to improved spectral efficiency. Since the near-ML detectors can more precisely recover complex modulated signals compared to MMSE detectors, the near-ML detectors enable wireless networks to transmit data at higher rates without sacrificing reliability.

Figures 1a and 1b illustrates the performance analysis of the Sphere Decoder depicting the corresponding BLER and computational complexity under four Transmit (Tx) layers and 16-Quadrature Amplitude Modulation (16-QAM), according to an embodiment of the disclosure. For comparison, the BLER and complexity metrics of the QRDM, the MMSE, and a MMSE Successive Interference Cancellation (MMSE-SIC) are also depicted. Analysis reveals that while the Sphere Decoder delivers superior BLER performance among all detection methods, the computational complexity surpasses that of other detectors. Such a high computational load limits the feasibility of the Sphere Decoder for real-time implementations where efficiency and processing speed are critical.

It is revealed that the Sphere Decoder may be widely used for achieving the near-MLD performance in the MIMO communication systems, making the Sphere Decoder an attractive choice for improving signal recovery accuracy. Unlike linear detection techniques such as the MMSE, which trade off accuracy for reduced computational complexity, the Sphere Decoder approaches optimal detection by efficiently searching most probable transmitted signal within a constrained search space. Such capability allows Sphere Decoder to provide a significant improvement in error performance compared to conventional detection methods.

However, despite several advantages, none of the existing Sphere Decoders achieve near-MLD performance while maintaining a computational complexity close to the MMSE, particularly in challenging scenarios where N_r N_t.

Another critical drawback associated with the existing Sphere Decoder is reliance on uniform modulation, where all transmit layers carry symbols from same modulation alphabet. While such assumption may simplify detection, however, such assumption does not align with practical wireless communication scenarios. In real-world deployments, base stations often schedule different users or transmit layers with varying modulation orders based on their individual channel conditions, leading to a Mixed Modulation Scenario. Such adaptation allows users with strong channel conditions to operate at higher-order modulation schemes while users with weaker links utilize lower-order modulation, thereby optimizing spectral efficiency. However, the existing Sphere Decoders are not designed to handle mixed modulation effectively, making them unsuitable for realistic system configurations. The inability to accommodate mixed modulation further limits their applicability in the advanced MIMO communication systems such as those envisioned for 6G networks.

Although the sphere decoding offers a reduction in complexity of MLD, however, the computational demand of the sphere decoding remains significantly high for practical implementations. The challenge arises due to the large tree size, particularly under higher-order modulation schemes and when utilizing more than two Transmit (Tx) layers, making the Sphere Decoder impractical for real-time applications.

Therefore, there lies a need for an improved solution that can address the above-mentioned issues and the limitations of the existing systems and methods.

It is provided to introduce a selection of concepts, in a simplified format, that are further described in the detailed description of the disclosure. It is neither intended to identify essential inventive concepts of the disclosure nor is it intended for determining the scope of the disclosure.

According to an embodiment of the disclosure, a method for decoding received signals in a multiple-input multiple-output (MIMO) communication system is disclosed. The method includes obtaining one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters may include one or more signal vectors received over the one or more channels in the MIMO communication system, a corresponding noise variance across the one or more channels in the MIMO communication system, a modulation order, and a channel matrix of the received signals. The method further includes obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. The method includes obtaining an initial linear solution based on the received signals, the channel matrix, and the corresponding noise variance. Furthermore, the method includes determining one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and a pre-defined number of neighbours in each layer, of the tree structure. The method includes creating a search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure. Moreover, the method includes applying a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising one or more bits. The method includes computing decision metrics for each bit of the decoded signal vector. Additionally, the method includes determining a likelihood-based metrics for each bit of the decoded signal vector based on the decision metrics. The method includes decoding the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

According to an embodiment of the disclosure, a method for decoding received signals in a multiple-input multiple-output (MIMO) communication system is disclosed. The method includes obtaining one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters include one or more signal vectors received over the one or more channels in the MIMO communication system, a corresponding noise variance across the one or more channels in the MIMO communication system, a modulation order, and a channel matrix of the received signals. The method includes obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. The method includes initializing a number of leaf nodes visited to zero in the tree structure. Further, the method includes applying a tree-based decoding search on the tree structure, starting from a path in the tree structure with an initial radius to obtain a decoded signal vector comprising one or more bits. The method includes incrementing the number of leaf nodes visited in the tree structure by one each time a leaf node is visited along a path, during the tree-based decoding search. Furthermore, the method includes computing decision metrics for each bit of the decoded signal vector at end of each path during the tree-based decoding search. Moreover, the method includes determining if the number of leaf nodes visited is equal to a pre-defined maximum number of leaf nodes to visit. Upon determining that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, the method further includes terminating the tree-based decoding search and determining a likelihood-based metrics for each bit of the decoded signal vector based on current estimate of decision metrics. Additionally, the method further includes decoding the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

According to an embodiment of the disclosure, a method for decoding received signals in a multiple-input multiple-output (MIMO) communication system is disclosed. The method includes obtaining one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters include one or more signal vectors received over the one or more channels in the MIMO communication system, a corresponding noise variance across the one or more channels in the MIMO communication system, a modulation order, and a channel matrix of the received signals. The method includes obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. Further, the method includes obtaining an initial linear solution based on the received signals, the channel matrix, and the corresponding noise variance. The method includes determining one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and a pre-defined number of neighbours in each layer, of the tree structure. Furthermore, the method includes creating a search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure. The method includes initializing a number of leaf nodes visited to zero in the search space. Moreover, the method includes applying a decoding technique on the search space, starting from a path to obtain a decoded signal vector comprising one or more bits. The method includes incrementing the number of leaf nodes visited in the search space by one each time a leaf node is visited along a path during the decoding technique. Additionally, the method includes computing decision metrics for each bit of the decoded signal vector at end of each path in the search space during the decoding technique. The method includes determining if the number of leaf nodes visited is equal to a pre-defined maximum number of leaf nodes to visit. Upon determining that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, the method includes terminating the decoding technique in the search space and determining a likelihood-based metrics based for each bit of the decoded signal vector based on current estimate of decision metrics. The method includes decoding the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

According to an embodiment of the disclosure, a system for decoding received signals in a multiple-input multiple-output (MIMO) communication system is disclosed. The system comprising one or more processors and a memory coupled with the one or more processors. The one or more processors are configured to obtain one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters include one or more signal vectors received over the one or more channels in the MIMO communication system, a corresponding noise variance across the one or more channels in the MIMO communication system, a modulation order, and a channel matrix of the received signals. The one or more processors are configured to obtain a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. Further, the one or more processors are configured to obtain an initial linear solution based on the received signals, the channel matrix, and the corresponding noise variance. The one or more processors are configured to determine one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and a pre-defined number of neighbours in each layer, of the tree structure. Furthermore, the one or more processors are configured to create a search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure. The one or more processors are configured to apply a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising one or more bits. Moreover, the one or more processors are configured to compute decision metrics for each bit of the decoded signal vector. The one or more processors are configured to determine a likelihood-based metrics for each bit of the decoded signal vector based on the decision metrics. Additionally, the one or more processors are configured to decode the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

According to an embodiment of the disclosure, a system for decoding received signals in a multiple-input multiple-output (MIMO) communication system is disclosed. The system comprising one or more processors and a memory coupled with the one or more processors. The one or more processors are configured to obtain one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters include one or more signal vectors received over the one or more channels in the MIMO communication system, a corresponding noise variance across the one or more channels in the MIMO communication system, a modulation order, and a channel matrix of the received signals. The one or more processors are configured to obtain a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. Further, the one or more processors are configured to initialize a number of leaf nodes visited to zero in the tree structure. The one or more processors are configured to apply a tree-based decoding search on the tree structure, starting from a path in the tree structure with an initial radius to obtain a decoded signal vector comprising one or more bits. Furthermore, the one or more processors are configured to increment the number of leaf nodes visited in the tree structure by one each time a leaf node is visited along a path, during the tree-based decoding search. The one or more processors are configured to compute decision metrics for each bit of the decoded signal vector at end of each path during the tree-based decoding search. Moreover, the one or more processors are configured to determine if the number of leaf nodes visited is equal to a pre-defined maximum number of leaf nodes to visit. Upon determination that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, the one or more processors are configured to terminate the tree-based decoding search and determine a likelihood-based metrics for each bit of the decoded signal vector based on current estimate of decision metrics. Additionally, the one or more processors are configured to decode the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

According to an embodiment of the disclosure, a system for decoding received signals in a multiple-input multiple-output (MIMO) communication system is disclosed. The system comprising one or more processors and a memory coupled with the one or more processors. The one or more processors are configured to obtain one or more input parameters from the received signals over one or more channels in the MIMO communication system, wherein the one or more input parameters include one or more signal vectors received over the one or more channels in the MIMO communication system, a corresponding noise variance across the one or more channels in the MIMO communication system, a modulation order, and a channel matrix of the received signals. Further, the one or more processors are configured to obtain a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. The one or more processors are configured to obtain an initial linear solution based on the received signals, the channel matrix, and the corresponding noise variance. Furthermore, the one or more processors are configured to determine one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and a pre-defined number of neighbours in each layer, of the tree structure. The one or more processors are configured to create a search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure. Moreover, the one or more processors are configured to initialize a number of leaf nodes visited to zero in the search space. The one or more processors are configured to apply a decoding technique on the search space, starting from a path to obtain a decoded signal vector comprising one or more bits. Further, the one or more processors are configured to increment the number of leaf nodes visited in the search space by one each time a leaf node is visited along a path during the decoding technique. Additionally, the one or more processors are configured to compute decision metrics for each bit of the decoded signal vector at end of each path in the search space during the decoding technique. Further, the one or more processors are configured to determine if the number of leaf nodes visited is equal to a pre-defined maximum number of leaf nodes to visit. Upon determination that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, the one or more processors are configured to terminate the decoding technique in the search space and determine a likelihood-based metrics based for each bit of the decoded signal vector based on current estimate of decision metrics. Additionally, the one or more processors are configured to decode the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

To further clarify the advantages and features of the disclosure, a more particular description of the disclosure will be rendered by reference to specific embodiments thereof, which are illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the disclsoure and are therefore not to be considered limiting of its scope. The disclosure will be described and explained with additional specificity and detail in the accompanying drawings.

The disclosure is directed towards optimization decoding techniques for tree search, for instance, a sphere decoder, and significantly reducing complexity while maintaining a high Block Error Rate (BLER) performance. The disclosure is directed towards enhancing practicality of the sphere decoder in modern communication systems, ensuring an improved balance between error performance and computational efficiency.

In particular, the disclosure addresses limitations of existing Sphere Decoding techniques and provides methods and systems that may achieve near-Maximum Likelihood detection (MLD) at Minimum Mean Squared Error (MMSE)-like complexity while also supporting mixed modulation scenarios. Furthermore, the disclosure may significantly enhance energy efficiency, extend coverage, and enable higher data throughput, ultimately contributing to fulfilment of International Mobile Telecommunications (IMT) 2030 requirements for next-generation communication systems.

Figure 2 illustrates an environment implementing a system 220 for decoding received signals in a multiple-input multiple-output (MIMO) communication system, according to an embodiment of the disclosure.

According to an embodiment of the disclosure, the environment 200 of MIMO communication system may be a wireless communication network, which includes a plurality of antennas 204a and 204b at a transmitter 202 and a receiver 208, respectively, to enhance data transmission efficiency, reliability, and capacity. In a non-limiting example, in the MIMO communication system, the transmitter 202 may transmit a signal over a set of transmitter antennas 204a. The transmitted signal may include a plurality of data stream transmitted, simultaneously, by the transmitter 202. At the receiver 208, the transmitted signal from the transmitter 202 may be received by a set of receiver antennas 204b, via one or more communication channels 206 (alternatively referred hereinafter as the communication channel 206). At the receiver 208, an advanced signal processing techniques such as, but not limited to, spatial multiplexing, beamforming, and decoding may be performed for separating and optimizing the received signal, to reduce interference and improve reliability. In an implementation, a system 220 may be used for decoding the received signal in the MIMO communication system. In a non-limiting example, the system 220 may be a part of the receiver 208 or may be in communication with the receiver 208.

According to an embodiment of the disclosure, for an uplink communication scenario, K users (not shown in Figure 2) may transmit a signal from the transmitter 202, equipped with a plurality of antennas 204a, to the receiver 208, equipped with M set of receiver antennas 204b. In a non-limiting example, the receiver 208 may be a Base Station (BS). The transmitted signal may be a data stream. Each user may transmit the data stream over a plurality of Orthogonal Frequency-Division Multiplexing (OFDM) subcarriers, where (k, ) may represent a subcarrier index k and the corresponding OFDM symbol index . The transmitted signals from all K users may be concatenated, as shown in equation (1):

(1)

where each user's transmitted symbol may be chosen from a specific modulation alphabet (), where , such as Quadrature Amplitude Modulation (QAM) or Phase Shift Keying (PSK).

If all the users employ same modulation scheme, then . Further, the communication channel 206 between the each user's transmitter 202 and the receiver 208 may be represented by equation (2):

(2)

where may denote the channel response for the user j. At the receiver 208, the received signal across the M set of transmitter antennas 204a may be combined as shown in equation (3):

(3) representing the signals received from all the M set of receiver antennas 204b at the receiver 208.

Thus, the received signal y at the receiver 208 is given by equation (4) and (5):

(4)

(5)

where, may represent an Additive White Gaussian Noise (AWGN), which may introduce a random interference in the MIMO communication system.

For further simplification, indices may be omitted, leading to a compact model of the MIMO communication system represented by equation (6):

(6)

where may represent a channel matrix, may represent the transmitted symbol vector, and may represent the estimated signal.

The MIMO uplink communication includes multiple users that may transmit data from the transmitter 202 to the receiver 208 over the communication channel 206. The receiver 208 may employ signal processing techniques such as, but not limited to, MMSE filtering, Successive Interference Cancellation (SIC), or Sphere Decoding to accurately separate and recover the transmitted signals from different users while mitigating interference and noise.

In an implementation, a Maximum Likelihood (ML) Detector may identify the transmitted signal that best matches the received signal. The Maximum Likelihood (ML) Detector may operate by searching over all possible signal vectors within the MIMO signal set , which may be formed by the modulation alphabets corresponding to the each transmitting user. The ML Detector may find the signal vector that may minimize the error between the received signal and the estimated signal . Mathematically, the signal may be represented by equation (7):

(7)

The ML Detector may calculate an Euclidean distance between the received vector and every possible transmitted vector and may also select one amongst these vectors with the least deviation. However, the number of possible MIMO vectors in set may grow exponentially with both the modulation order and the number of MIMO layers, making exhaustive ML Detector computationally prohibitive for the MIMO communication system with more than two layers or higher-order modulation schemes.

Therefore, to address the complexity discussed above, the Sphere Decoder may reformulate the MLD computation into a structured decision tree search. Instead of evaluating all possible vectors exhaustively, the Sphere Decoder may represent a cost function as a tree structure and searches for the signal vector with the minimum cost using a tree search technique. Before implementing the sphere decoding, a QR Decomposition (QRD) of the channel matrix may be performed to transform the equation (6) for the compact model of the MIMO communication system into a simplified form. The decomposition expresses as shown in equation (8):

(8)

where may represent an orthonormal matrix, and may be defined as given below in equation (9):

(9)

with as an upper triangular matrix, as shown in equation (10):

(10)

The decomposition of may simplify the detection process, allowing the Sphere Decoder to systematically search the tree structure for an optimal solution rather than evaluating all possible signal vectors exhaustively. Such solution may reduce computational complexity while preserving error performance of traditional MLD. In an advantageous aspect, the use of QRD in MIMO detection may make sphere decoding more practical for high-dimensional communication systems, such as 5^th Generation (5G), Long-Term Evolution (LTE), and advanced wireless standards, where efficient signal processing is critical.

According to an embodiment of the disclosure, during the MIMO signal detection, pre-processing may be applied to the received signal vector using the QR decomposition, which may transform the equation (6) of the compact model into a more structured form for efficient computation. Specifically, pre-multiplying the received vector with a Hermitian transpose () of the orthonormal matrix may be represented by equation (11):

(11)

where may indicate a transformed received vector and may indicate a transformed noise vector. Since is the orthonormal matrix, the Euclidean norm remains unchanged, which may be represented by equation (12):

(12)

The transformation may simplify the detection process by converting the original equation (6) into a triangular system, reducing the computational complexity. Because is the upper triangular matrix, cost computation may be decomposed and represented by equation (13):

(13)

where each function may represent a cost term that may depend on different subsets of symbols. The may be represented by equation (14):

(14)

The decomposition may reveal that a first term only depends on one symbol , a second term on two symbols (), and so on. Such hierarchical dependency may enable the tree search technique for computing the optimal detection solution, as employed in the sphere decoding. Instead of exhaustively searching all possible vectors , tree search techniques may leverage the tree structure to find most likely transmitted signal efficiently, making the MIMO detection computationally feasible even for the MIMO communication systems with high modulation order and multiple antennas.

A detailed explanation of the system 220 is explained in conjunction with the Figure 5.

Figure 3 illustrates a Maximum Likelihood Detection (MLD) modelled as tree search for K=3 layers and Binary Phase Shift Keying (BPSK) modulation, according to an embodiment of the disclosure.

According to an embodiment of the disclosure, while modelling the MLD as Tree Search, the detection process may be structured hierarchically, where the number of stages in the tree may correspond to the number of the MIMO layers. For instance, in the MIMO communication system with three layers, the tree structure may consist of three levels, with a root node representing an initial detection phase and successive levels corresponding to different MIMO layers. The stage immediately below the root node may represent a topmost layer = , referred to as a highest layer in the MIMO communication system. As the search progresses downward, each node may correspond to a lower layer, with one or more leaf nodes representing a final layer = 1, where symbol decisions may be finalized. At each stage in the tree, the number of branches emerging from each node may be determined by the size of the modulation alphabet used in that specific layer. If every layer in the MIMO communication system employs Binary Phase Shift Keying (BPSK) modulation, then each node may have two branches, corresponding to two possible symbols (0 or 1) in the BPSK constellation. In an implementation, for a given layer , each branch may correspond to a particular symbol , selected from the modulation alphabet , where . The MIMO communication system may assign a branch metric to each branch, representing likelihood or cost associated with selecting that symbol within the tree structure. Such a branch metric may be derived from the received signal and may account for a cumulative detection cost across layers. In an implementation, by structuring the MLD as the tree search problem, the MIMO communication system may avoid exhaustive search across all possible transmission combinations, instead leveraging the hierarchical approach to systematically evaluate symbol probabilities while reducing computational complexity. Such an approach of structuring the MLD may be beneficial for high-order modulation and large-scale MIMO communication systems, where exhaustive detection methods may become impractical due to exponential growth in the search space. Furthermore, the sphere decoding may utilize the tree search technique to efficiently identify the most likely transmitted signal while minimizing error rates.

In an implementation, during the MIMO detection, each node at layer in the MLD tree may be associated with an accumulated cost, denoted as . The accumulated cost may represent the sum of all branch metrics encountered while traversing from the root node down to a given node in layer . Mathematically, the accumulated cost may be represented as shown in equation (15):

(15)

where may represent the individual cost contribution at layer , influenced by modulation symbols chosen from the modulation alphabet . Each path from the root node to the leaf node may correspond to the unique MIMO signal vector , representing a potential transmitted signal. For example, the leftmost path of the tree structure, as referred to in Figure 4, from the root node to the leaf node may form the vector , such that each transmitted symbol may be selected sequentially as the tree is traversed downward. The MLD method may require evaluating all possible paths in the tree to determine the optimal transmitted signal that may minimize detection cost. The evaluation may involve traversing all nodes from the leftmost path to the rightmost path, such that every possible signal combination must be checked. However, such an exhaustive search may become computationally impractical for higher-order QAM, such as 64-QAM or 256-QAM, and when the multiple MIMO layers are involved. Due to the exponential growth in complexity, the MLD may be infeasible for real-time implementation in practical communication systems. Therefore, to address such challenge, the Sphere Decoder may refine tree traversal by employing intelligent pruning mechanisms. Rather than examining every possible signal vector, the Sphere Decoder may systematically eliminate the branches that do not contribute to an optimal solution. The Sphere Decoder may dramatically reduce computational complexity while maintaining near-optimal detection performance by prioritizing paths with lower accumulated costs early in the search process. Further, the system implementing pruning of the Sphere Decoder is explained in detail in the forthcoming paragraphs while explaining Figure 5.

Figure 4 illustrates a Sphere Decoder for pruning of the tree, according to an embodiment of the disclosure.

According to an embodiment of the disclosure, the Sphere Decoder may be used in the MIMO signal detection to efficiently determine the transmitted signal vector with the least cost. The Sphere Decoder may be used to identify the MIMO vector that may minimize the detection error while significantly reducing computational complexity compared to the MLD. Instead of exhaustively searching all possible signal combinations, the Sphere Decoder may narrow down the search space using the tree search structure. In an implementation, the Sphere Decoder may be initialized. Before initiating the tree search, the Sphere Decoder may define an initial search radius, denoted as . The defining the initial search radius as , signifies that a cost threshold may be set to an infinitely large value. As the tree search progresses, the cost threshold may be dynamically updated whenever a new signal vector is encountered with a lower error cost, ensuring that only best candidate solutions may be retained. Furthermore, a process of tree search may be followed. The tree structure may organize the detection process in the hierarchical layers corresponding to the number of MIMO antennas. During the search process, a left-most path traversal may be followed, such that the searching may initiate from the left-most branch of the tree, traversing downwards until reaching the leaf node. Upon arriving at the first leaf node, the Sphere Decoder may evaluate the cost function , which may measure the Euclidean distance between the received signal and the estimated signal under the given channel matrix (). If this cost is lower than the initial threshold , the radius is updated, for example, as shown in Figure 4, the minimum cost is revised to = 7. Once the first path is evaluated, the tree search may systematically explore the next possible paths one by one to perform traversal and update the cost. The second path, third path, and subsequent branches may be evaluated in sequence. At each step, the Sphere Decoder may check if a new signal vector may produce a cost lower than the current minimum cost. If a better candidate is found, the cost may be further reduced, ensuring that only the most efficient solution is retained. Unlike the existing exhaustive MLD, which requires traversing all possible paths in the tree from the left-most path to the right-most path, the sphere decoding may eliminate unnecessary computations by pruning the branches that exceed the current cost threshold.

According to an embodiment of the disclosure, the pruning in the Sphere Decoding may reduce the computational complexity while maintaining the accuracy of signal detection. The pruning of the tree may be based on the observation that once a node with the cost higher than the current minimum cost () is encountered during the traversal, further exploration of a sub-tree originating from the node may be unnecessary. Further, since no lower-cost solution may emerge from that branch, the entire sub-tree originating from that node may be eliminated, thereby optimizing the search process and improving efficiency compared to the MLD, which may exhaustively evaluate all possible vectors.

In a non-limiting example, the sphere decoding initiated with the search radius may be set to , such that all possible signal vectors may be initially considered. As tree traversal progresses, the search may be initiated by following the left-most path, reaching the leaf node. Upon reaching the leaf node, the Sphere Decoder may compute the total accumulated cost. In a non-limiting example, if the cost is lower than , the minimum cost may be updated as shown in Figure 4. Further, the second path may be traversed to the leaf node, and the minimum cost may be updated to = 4. Furthermore, subsequent paths, that is third and fourth path, may be explored. However, the subsequent paths may not lead to an improvement in the minimum cost. When a fifth path may be explored, the Sphere Decoder may encounter a node with cost 5. Since 5 > , the entire sub-tree from that node may be pruned, such that the entire sub-tree from that node may be excluded from further search. The optimal signal vector may be determined to be , corresponding to the second path.

According to an embodiment of the disclosure, in the MIMO communication systems, the signal detection may be accompanied by a Log-Likelihood Ratio (LLR) computation to facilitate error correction in the receiver 208. The LLR values may quantify the confidence level of each received bit and may be subsequently fed into a channel decoder, which may employ techniques such as, but not limited to, Turbo Coding, Low-Density Parity-Check (LDPC) decoding, and like, for enhanced reliability. A soft-output MLD may provide the LLR values based on the Euclidean distance between the received signal and the possible transmitted signals , under the given channel matrix (). The LLR value of the b-th bit of the j-th symbol/layer is given by equation (15):

(15)

where may represent the LLR value of the b-th bit within the j-th symbol/layer. Further, and may represent disjoint sets containing the MIMO signal vectors, where the b-th bit of the j-th symbol may be 0 or 1, respectively. The union of these two sets may encompasses all possible symbol vectors , i.e., that . Furthermore, may represent a noise variance, ensuring normalization of the LLR values. In an implementation, minor modification in the Sphere Decoder may allow efficient computation of the LLR values, integrating soft-output detection capabilities. To detect the soft-output, the ML solution may be determined using the sphere decoding, as shown in equation (16) below:

(16)

where, the vector may represent the signal estimate that minimizes the detection error. The corresponding bit sequence () associated with the vector may be identified. The minimum cost associated with the ML solution may be computed as shown in equation (17) below:

(17)

To compute the LLR values, the minimum cost among alternative symbol vectors where the b-th bit of the j-th symbol may be flipped through bit complement of ML bit, which may be determined as shown in equation (18) below:

(18)

where may represent the set of vectors where the b-th bit of the j-th symbol may differ from the ML estimate. Thus, by implementing the sphere decoding with the LLR extraction, the MIMO communication systems may achieve efficient soft-output detection, improving the BER performance. In an advantageous aspect the sphere decoding with the LLR extraction may enable robust error correction using Turbo Decoders, LDPC Codes, and other Forward Error Correction (FEC) methods.

According to an embodiment of the disclosure, mathematically, the LLR for the b-th bit of the j-th symbol/layer may expressed as shown in equation (19):

(19)

where, may represent the cost corresponding to the current ML solution. Further, may represent the bit sequence associated with the current ML solution. Furthermore, may represent the costs corresponding to counter hypothesis for each bit. Thus, unlike the traditional hard-output ML detection, which generally selects only the best signal estimate, the soft-output sphere decoding may compute and maintain the LLR values throughout the tree search. Specifically, the soft-output SD keeps track of the , , and .

According to an embodiment of the disclosure, the pruning in the soft-output sphere decoding may be initiated when all cost values may be set to infinity (∞), ensuring that every possible solution may be initially considered. Therefore, the cost corresponding to the current ML solution may be represented by equation (20):

(20)

for all . The tree search process may be initiated by exploring the left-most path, leading to the first update of detection costs upon reaching the leaf node. As the search may progresses, the each newly evaluated path may update and the LLR values if the lower-cost solution is found. The paths that may not lead to further cost reduction may be eliminated. Therefore, the pruning criteria may involve stopping the tree search midway along the path if the search is clear that no further cost updates may be occurring. For instance, if the accumulated cost at a node exceeds and for all j, b, the entire subtree originating from that node may be pruned.

Further, the system 220 of Figure 2 is explained in detail in the forthcoming paragraphs while explaining Figure 5.

According to an embodiment of the disclosure, while the sphere decoding achieves MLD performance, the complexity remains prohibitively high, particularly for practical implementations involving the higher-order QAM schemes like the 64-QAM and 256-QAM, or MIMO communication systems with more than two layers. However, the fundamental challenge with the sphere decoding may stem from the exponential growth in search space as the modulation order and the number of MIMO layers increase. Although the tree pruning may help mitigate such issues, the number of possible symbol combinations may still make the sphere decoding computationally intensive. Therefore, one approach to reducing the search space may be to refine the initial radius of the sphere decoding. Instead of beginning with the infinite search radius ( = ∞), the initial radius may be set to , where k may represent a positive integer and may represent the noise variance. By carefully selecting k, the vectors that may be significantly distant from the optimal solution may be immediately discarded, thereby reducing the number of computations required. Such refinement may decrease the likelihood of excessive tree exploration and accelerate the convergence toward the optimal detection result.

Figure 5 illustrates a block diagram of the system for decoding received signals, according to an embodiment of the disclosure.

According to an embodiment of the disclosure, the system 220 may include at least a processor 502, a memory 504, a data unit 506, and a plurality of modules 508. The plurality of modules 508 may be configured to decode the received signals in the MIMO communication system. According to an embodiment of the disclosure, the at least one processor 502 may be in communication with the memory 504. The at least one processor 502 may be configured to initiate or stop one or more routines or a process based on the signals received from the transmitter 202. The at least one processor 502 may be a single processing unit or several units, all of which could include multiple computing units. The at least one processor 502 may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the at least one processor 502 may be configured to fetch and execute computer-readable instructions and data stored in the memory 504.

According to an embodiment of the disclosure, the memory 504 may include any non-transitory computer-readable medium known in the art including, for example, volatile memory, such as static random-access memory (SRAM) and dynamic random-access memory (DRAM), and/or non-volatile memory, such as read-only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes.

According to an embodiment of the disclosure, the data unit 506 amongst other things, includes routines, programs, objects, components, data structures, and like, which perform particular tasks or implement data types. The data unit 506 may also be implemented as signal processor(s), state machine(s), logic circuitries, and/or any other device or component that manipulates signals based on operational instructions. Further, the data unit 506 may be implemented in hardware, instructions executed by a processing unit, or by a combination thereof. The processing unit may comprise a processor, such as the at least one processor 502, a state machine, a logic array, or any other suitable devices capable of processing instructions. The processing unit may be a general-purpose processor which executes instructions to cause the general-purpose processor to perform the required tasks or, the processing unit can be dedicated to performing the required functions. According to an embodiment of the disclosure, the data unit 506 may be machine-readable instructions (software) that, when executed by the processor 502, perform any of the described functionalities.

In one implementation, the system 220 may perform neighborhood-based tree pruning (NTP) to eliminate branches dynamically based on proximity to the most likely solution, thereby reducing unnecessary computations. The NTP may help in minimizing the complexity of the sphere decoding by leveraging an initial linear solution, such as MMSE, to restrict the set of candidate vectors considered during the tree search process. Such an approach may effectively narrow the search space, reducing computational overhead while maintaining detection accuracy.

According to an embodiment of the disclosure, the at least one processor 502, of the system 220, in communication with the memory 504, may be configured to obtain one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters may include one or more signal vectors received over the one or more channels in the MIMO communication system. For instance, the one or more signal vectors may include within the MIMO signal set . The one or more input parameters may include corresponding noise variance across the one or more channels in the MIMO communication system, the modulation order, and the channel matrix of the received signals. In an implementation, the one or more signal vectors may indicate the received signals at each of the set of receiver antennas 204b of the MIMO communication system. Further, the corresponding noise variance may indicate level of background noise in the received signals. Furthermore, the modulation order may indicate the number of bits per symbol used in the modulation scheme. Furthermore, the pre-defined number of neighbours in each layer may indicate the count of nearby points considered for the decoding technique, and the channel matrix may indicate channel coefficients obtained between the set of transmitter antennas 204a and the set of receiver antennas 204b.

According to an embodiment of the disclosure, the processor 502 may be further configured to obtain a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. The processor 502 may be further configured to obtain the initial linear solution based on the received signals, the channel matrix , and the corresponding noise variance (). The processor 502 may be further configured to determine one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and the pre-defined number of neighbours in each layer, of the tree structure. In an implementation, the initial linear solution may be selected since the effects of channel fading and noise are well-structured. In an advantageous aspect, the detection process may become computationally more efficient while maintaining near-optimal performance by focusing the sphere decoding search space within the neighbourhood of the initial linear solution. Instead of performing an exhaustive tree search across all possible modulation symbol vectors, the system of the disclosure limit the search to signal candidates that may be most likely to be the correct solution.

In an implementation, the processor 502 may determine the initial linear solution, denoted as , using the MMSE equalizer. The initial linear solution may be represented by equation (21):

(21)

where, may represent a Hermitian (conjugate transpose) of the channel matrix , may represent the noise variance, accounting for interference in the system 220, and the may represent an identity matrix, ensuring matrix inversion stability. Once the initial linear solution () is computed, the processor 502 may leverage the neighboring candidates to selectively prune the search tree. Therefore, instead of evaluating all possible vectors , only signal vectors within the restricted region around the initial linear solution () may be considered. Such refinement may remove unnecessary paths early in the tree traversal, significantly reducing computational complexity while preserving detection accuracy.

According to an embodiment of the disclosure, the processor 502 may be configured to create a search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure. The processor 502 may be configured to apply a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising one or more bits. In an implementation, the decoding technique may include a soft-output sphere decoding. Furthermore, decision metrics for each bit of the decoded signal vector may be computed, and a likelihood-based metrics for each bit of the decoded signal vector may be determined based on the decision metrics. In an implementation, the decision metrics may indicate a quantitative measure for determining most probable transmitted data, and the likelihood-based metrics include log-likelihood ratios. Furthermore, the received signals may be decoded by the processor 502 by feeding the likelihood-based metrics for each bit to the channel decoder. Therefore, instead of exploring all possible branches, i.e., all symbols of modulation alphabet in the given layer, only those branches that correspond to a few neighbours of initial solution may be explored. Further, the rest of the branches may be pruned.

Further, another implementation of the system 220 is explained in detail in the forthcoming paragraphs.

In another implementation, the system 220 may implement a Node Limiting (NL) mechanism for decoding the received signals. The NL mechanism may set an upper bound on the number of nodes explored per stage, ensuring controlled search complexity. According to an embodiment of the disclosure, the computational complexity of the Sphere Decoder may vary significantly depending on the channel conditions and SNR. At low SNR, the detection process requires an extensive search through the decision tree, leading to high computational burden. As the SNR increases, the search space may reduce naturally because transmitted signals are more distinguishable from the noise, thereby lowering the complexity of the Sphere Decoder. However, real-world implementations may often necessitate a fixed upper bound on complexity, ensuring that processing time and resource usage remain predictable. Since the traditional Sphere Decoder may not guarantee an upper complexity limit, which may be impractical for deployment in the high-speed wireless communication systems. Therefore, to address such issue, the NL mechanism may be utilized.

According to an embodiment of the disclosure, the one or more processors 502 of the system 220 may be configured to obtain one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more processors 502 may be configured to obtain the tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. Further, a number of leaf nodes visited to zero in the tree structure may be initialized by the processor 502. Furthermore, the one or more processors 502 may be configured to apply the tree-based decoding search on the tree structure, starting from the path in the tree structure with the initial radius to obtain the decoded signal vector comprising one or more bits. The one or more signal vectors may indicate the received signals at each of a set of receiver antennas 204b of the MIMO communication system. Further, the corresponding noise variance may indicate level of background noise in the received signals. Further, the modulation order may indicate the number of bits per symbol used in the modulation scheme, and the channel matrix indicates channel coefficients obtained between a set of transmitter antennas 204a and the set of receiver antennas 204b. The one or more processors 502 may be configured to increment the number of leaf nodes visited in the tree structure by one each time a leaf node is visited along a path, during the tree-based decoding search. In an implementation, the leaf node may indicate the end point of the path in the search space that may originate from the root node. In another implementation, the likelihood-based metrics may include log-likelihood ratios. Further, the tree-based decoding search may comprise the sphere decoding search and the decision metrics may indicate a quantitative measure for determining most probable transmitted data. The one or more processors 502 may be configured to compute decision metrics for each bit of the decoded signal vector at end of each path during the tree-based decoding search. The one or more processors 502 may be configured to determine if the number of leaf nodes visited is equal to a pre-defined maximum number of leaf nodes to visit. Upon determination that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, one or more processors 502 may be configured to terminate the tree-based decoding search and determine a likelihood-based metrics for each bit of the decoded signal vector based on current estimate of decision metrics. In an implementation, upon determination that the number of leaf nodes visited is less than the pre-defined maximum number of leaf nodes to visit, the one or more processors may be configured to continue the tree-based decoding search along a subsequent path in the tree structure until the maximum number of leaf nodes to be visited is reached. Furthermore, the one or more processors 502 may be configured to decode the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

In an implementation, the number of leaf nodes visited during sphere decoding may be continuously monitored using a variable . When the number of the visited leaf nodes reaches a predefined maximum threshold , the tree search may be immediately terminated, preventing further exploration of additional paths. In an advantageous aspect, the processor 502 may implement the NL mechanism during the sphere decoding for achieving low complexity, making the system 220 viable for real-time applications where processing constraints may be strictly maintained. Additionally, the NL mechanism may provide a significant performance gain which may be widely used in practical systems. In another advantageous aspect, the refinement may ensure that high-order modulation schemes, such as the 64-QAM and the 256-QAM, and large-scale MIMO configurations, may remain computationally feasible while delivering superior signal detection accuracy.

In an implementation, the system 220 based on the NTP mechanism may significantly reduce the computational complexity at the SNR. However, the complexity remains relatively high in the low SNR scenarios, where extensive tree search may be required to compensate for increased noise interference. While the MIMO communication systems may not typically operate under such low SNR conditions, occasional fluctuations or adverse transmission environments may lead to temporary low SNR occurrences. In such cases, a detection mechanism with a predefined maximum complexity threshold may be required, ensuring that decoding latency remains within acceptable limits even under unfavourable conditions. To address such an issue, a combined approach may be implemented where both the mechanisms, that is, the NTP mechanism, and the NL mechanism may be employed into the Sphere Decoder. The combined approach may ensure that the search space remains limited, even in low SNR scenarios, by enforcing an upper bound on the number of visited leaf nodes during the tree traversal. In an implementation, the NTP mechanism may minimize the search space by restricting tree exploration to the neighboring symbols, while the NL mechanism may further control the complexity by halting the search once the predefined maximum number of nodes are evaluated.

According to an embodiment of the disclosure, the system 220 may implement a combination of the NTP mechanism and the NL mechanism for decoding the received signals for improving the performance and minimizing the complexity. The one or more processors 502 of the system 220 may be configured to obtain one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters may include one or more signal vectors () received over the one or more channels in the MIMO communication system. The one or more input parameters may further include the corresponding noise variance () across the one or more channels in the MIMO communication system, the modulation order, and the channel matrix () of the received signals. The one or more processors 502 may be configured to obtain a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals. The one or more processors 502 may be configured to obtain the initial linear solution based on the received signals, the channel matrix (), and the corresponding noise variance (). Further, the one or more processors 502 may be configured to determine one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and the pre-defined number of neighbours in each layer, of the tree structure. Furthermore, the one or more processors 502 may be configured to create a search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure. The one or more processors 502 may be further configured to initialize a number of leaf nodes visited to zero in the search space and apply the decoding technique on the search space, starting from the path to obtain the decoded signal vector comprising one or more bits. The one or more processors 502 may be further configured to increment the number of leaf nodes visited in the search space by one each time a leaf node is visited along a path during the decoding technique. The one or more processors 502 may be further configured to compute decision metrics for each bit of the decoded signal vector at end of each path in the search space during the decoding technique. Furthermore, the one or more processors 502 may be configured to determine if the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit. Upon determination that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, the one or more processors 502 may be further configured to terminate the decoding technique in the search space and determine the likelihood-based metrics for each bit of the decoded signal vector based on current estimate of decision metrics, and decode the received signals by feeding the likelihood-based metrics for each bit to a channel decoder. In an advantageous aspect, by incorporating the combined approach of the NTP and the NL mechanism, the MIMO system may achieve consistent low-latency detection while benefiting from the several dB of SNR gain compared to conventional MMSE detection, which may be commonly used in the practical MIMO communication systems.

Figure 6 illustrates an exemplary search space obtained during decoding received signals using a neighborhood-based tree pruning, according to an embodiment of the disclosure.

According to an embodiment of the disclosure, referring to Figure 6, to illustrate the concept of the NTP, a two Transmit (Tx) layer MIMO communication system may be considered, where each layer may employ 16-QAM. The NTP may use the initial linear solution as a reference point to define the restricted search space, reducing the computational complexity of sphere decoding while maintaining the accurate signal detection. In an implementation, the initial linear solution may be obtained based on one of zero forcing (ZF) equalizer and the MMSE equalizer.

Let the initial linear solution be represented as given below in equation (22):

(22)

where may correspond to a first layer and to a second layer. Instead of searching across all possible transmitted symbols in the 16-QAM constellation, the processor 502 may restrict the search space by selecting only a predefined number of neighbours closest to the initial solution. For instance, in the first layer, four closest neighbours of may be visually represented within a circular region, forming the set , which may be mathematically denoted as shown in equation (23) below:

(23)

where may represent the four closest neighbouring signal points surrounding the initial MMSE-based solution for the first layer. In general, for any layer , the closest neighbours of the initial linear solution may be represented by . Furthermore, to efficiently implement the NTP, the predefined number of neighbours () may be selected for each MIMO layer. The decision tree used in the sphere decoding may be constructed using only the neighbourhood symbols instead of considering all possible symbols in the modulation alphabet . Therefore, by employing the NTP, the processor 502 may achieve near-MLD performance without suffering from the exponential search space expansion that generally occur in the traditional Sphere Decoder.

Figure 7a illustrates an exemplary structure of a decision tree, according to an embodiment of the disclosure. According to an embodiment of the disclosure, referring to Figure 7a, each decision tree node may represent a possible transmitted symbol, and each branch emanating from a node may correspond to a distinct symbol from the 16-QAM alphabet. Since 16-QAM consists of 16 unique symbols, each node in both Layer 1 and Layer 2 may have 16 branches, such that the search space may rapidly expand as the tree grows. Further, as the modulation order increases, such as, but not limited to, 64-QAM or 256-QAM, the number of branches per node may also significantly rise. For instance, in the 64-QAM, each node may have 64 branches, and in the 256-QAM, each node may have 256 branches, leading to an exponential increase in the number of root-to-leaf paths that may be explored. Such a vast search space may make the sphere decoding computationally prohibitive, as an exhaustive search over such the large tree may require immense processing power and memory, making the entire process impractical for real-time implementation. Therefore, to overcome such challenge, the system 220 of the disclosure implements the NTP to limit the search space by focusing on symbols closest to the initial linear solution.

Figure 7b illustrates an exemplary structure of the decision tree after the neighbourhood-based tree pruning, according to an embodiment of the disclosure. According to an embodiment of the disclosure, in the system 220, the decision tree may be selectively pruned by the processor 502 to reduce computational complexity during the sphere decoding. Instead of searching across all possible transmitted symbol vectors, the processor 502 may only consider a limited set of neighboring candidates, which may significantly narrow the search space. In a non-limiting example, the pruned tree may be constructed by selecting the = 5 closest neighbors of the initial linear solution () in Layer 2, which may be represented as , and the = 4 closest neighbors of the initial solution () in Layer 1, which may be represented as . All other branches corresponding to non-neighbouring symbols may be eliminated, ensuring that the tree search is confined within a high-quality subset of potential solutions. Once the processor 502 completes the process of defining the pruned tree, the sphere decoding may be operated exclusively within the restricted search space, significantly reducing computational complexity compared to the original full tree.

Figure 8 illustrates a schematic workflow of a method depicting the NTP based sphere decoding, according to an embodiment of the disclosure.

Referring to Figure 8, at step, 802, the receiver 208 may obtain the one or more input parameters from the received signals. The received one or more input parameters may include, the receive (Rx) stream vector (), the estimated channel (), the noise variance , the modulation order for each layer (), the initial radius (), the number of neighbours in each layer .

At step 804, the initial linear solution () may be calculated, using methods like MMSE equalization, based on at least on the receive (Rx) stream vector (), the estimated channel (), the noise variance .

At step 806, the neighbours of the initial solution in each layer may be calculated based on the number of neighbours in each layer and the modulation order for each layer ().

At step 808, the soft-output sphere decoding may be performed on the pruned tree formed by the neighbours of initial solution starting from initial radius to obtain least cost and for each bit.

At step 810, the LLR values may be computed for each bit using the and the , as shown in equation (19) and equation (20).

At step 812, the LLR values may be fed into the channel decoder to obtain the decoded bits, ensuring accurate data recovery in the MIMO communication system.

Figure 9a illustrates a comparative analysis of the BLER of the sphere decoding using the NTP mechanism and Figure 9b illustrates a comparative analysis of the computational complexity of the sphere decoding using the NTP mechanism, according to an embodiment of the disclosure.

Referring to Figure 9a and 9b, the comparative analysis depicts the BLER and the computational complexity of the NTP mechanism based sphere decoding across varying SNR conditions in the MIMO communication system setup with 4 User Equipments (UEs), 1 transmit antenna (204a), 4 receive antennas (204b), 15kHz subcarrier spacing, 6 Resource Blocks (RBs), a TDL-C channel model, and Modulation and Coding Scheme (MCS) 19 using 64-QAM (rate 873/1024). The Figures 9a and 9b compare the NTP mechanism based sphere decoding against the existing detection methods, including the MMSE, the QR Decomposition with M-algorithm (QRDM), the QR Decomposition with Quadratic Likelihood Detection (QRD-QLD), and the QRDM with Reliability-Based Adjustment (QRDM-RA), highlighting the performance advantages in BLER reduction and complexity optimization. Figures 9a and 9b depicts that at 10% BLER, which may be a typical target performance, the NTP mechanism based Sphere Decoder achieves an 8 dB SNR gain over the MMSE while maintaining a complexity of only 10× MMSE. Additionally, the NTP mechanism based Sphere Decoder offers the highest SNR gain with the lowest complexity among existing arts. While the QRDM and the QRD-QLD exhibit excessively high complexity, QRDM-RA provides lower SNR improvement, making NTP-SD the most efficient detection approach for practical systems.

Table 1

Table 1, mentioned above, depicts the performance and complexity of the system 220 implementing NTP mechanism, based on the comparative analysis of the SNR gain and complexity of the NTP mechanism based Sphere Decoder and other prior-arts is at 10% BLER.

Figure 10 illustrates a schematic workflow of a method depicting NL mechanism based sphere decoding, according to an embodiment of the disclosure.

Referring to Figure 10, at step 1002, the receiver 208 may obtain the one or more input parameters from the received signals. The received one or more input parameters may include, the receive (Rx) stream vector (y), the estimated channel (), the noise variance , the modulation order for each layer (), the initial radius (), and the maximum number of leaf nodes to visit .

At step 1004, the number of leaf nodes visited to =0 may be initialized.

At step 1006, the Sphere Decoder tree search may be initiated from the left most path of the tree with the initial radius .

At step 1008, may be incremented by 1, (), each time when the leaf node is visited.

At step 1010, a condition may be checked whether (). If the becomes equal to , the process may proceed to step 1012, else step 1014 may be followed.

At 1012, if the condition in step 1010 is satisfied, the tree search may be stopped and the LLR values may be calculated based on the current estimate of and .

At step 1016, once the current estimate of and are calculated, the LLR values may be fed into the channel decoder to obtain the decoded bits.

At step 1014, if the condition in step 1010 is satisfied, the tree search may continue for the next path, and the step 1008 may reiterate.

Figure 11a illustrates a comparative analysis of the BLER of the sphere decoding using the NL mechanism and Figure 11b illustrates a comparative analysis of the computational complexity of the sphere decoding using the NL mechanism, according to an embodiment of the disclosure.

Referring to Figure 11a and 11b, the comparative analysis depicts the comparative analysis by evaluating the BLER and the computational complexity for the NL mechanism based Sphere Decoder. The MIMO communication system includes a 4 User Equipment (UE) MIMO system with 1 transmit antenna 204a, 4 receive antennas 204b, 15kHz subcarrier spacing, 6 Resource Blocks (RBs), TDL-C channel model, and Modulation and Coding Scheme (MCS) 19 using 64-QAM (rate 873/1024). The comparative analysis focuses on limiting the leaf node visits is limited to 500, compared to the total tree size of 16777216 nodes (64⁴). For comparison, the existing arts, such as the QRD-QLD and the QRDM-RA are also analyzed, with results summarized in Table 2. At 10% BLER target, the NL mechanism based Sphere Decoder may achieve the highest 6 dB SNR gain over the MMSE while maintaining the lowest complexity among all detectors. Unlike the existing arts, which reach 100×MMSE complexity in low SNR conditions, the NL mechanism based Sphere Decoder may be capped at 50×MMSE, and may be further optimized by reducing the maximum visited nodes while still delivering several dB of gain over MMSE.

Table 2

Figure 12 illustrates a schematic workflow of a method depicting a combined approach of the NTP and the NL mechanism sphere decoding, according to an embodiment of the disclosure.Referring to Figure 12, at step 1202, the receiver 208 may obtain the one or more input parameters from the received signals. The received one or more input parameters may include, the receive (Rx) stream vector (y), the estimated channel (), the noise variance , the modulation order for each layer (), the initial radius (), the number of neighbours in each layer , and the maximum number of leaf nodes to visit .

At step 1204, the initial linear solution () may be calculated based on the receive (Rx) stream vector (), the estimated channel (), the noise variance .

At step 1206, the neighbours of initial solution in each layer may be calculated based on the modulation order for each layer (), and the number of neighbours in each layer .

At step 1208, the number of leaf nodes visited to =0 may be initialized.

At step 1210, the soft-output sphere decoder may start from the left most path of the pruned tree formed by the neighbours of the initial solution.

At 1212, may be incremented by 1, (), each time when the leaf node is visited.

At step 1214, a condition may be checked whether (). If the becomes equal to the process may proceed to step 1216, else step 1218 may be followed.

At step 1216, if the condition in step 1210 is satisfied, the tree search may be stopped and the LLR values may be calculated based on the current estimate of and .

At step 1216, once the current estimate of and are calculated, the LLR values may be fed into the channel decoder to obtain the decoded bits.

At step 1214, if the condition in step 1210 is satisfied, the tree search may continue for the next path, and the step 1218 may reiterate.

Figure 13a illustrates a comparative analysis of the BLER of the sphere decoding using the combination of the NTP mechanism and the NL mechanism and Figure 13b illustrates a comparative analysis of the computational complexity of the sphere decoding using the combination of the NTP mechanism and the NL mechanism, according to an embodiment of the disclosure.

Referring to Figure 13a and 13b, the comparative analysis based on evaluation of the BLER and the computational complexity for the combination of the NTP mechanism and the NL mechanism based Sphere Decoder. The MIMO communication system includes a 4 User Equipment (UE) MIMO system with 1 transmit antenna 204a, 4 receive antennas 204b, 15kHz subcarrier spacing, 6 Resource Blocks (RBs), TDL-C channel model, and Modulation and Coding Scheme (MCS) 19 using 64-QAM (rate 873/1024). The comparative analysis focuses on the BLER performance and the computational complexity of the combination of the NTP mechanism and the NL mechanism based Sphere Decoder for a 4×4 MIMO system under 64-QAM modulation. The setup considers 20 neighboring symbols per layer for NTP and limits the tree traversal to 200 leaf nodes for NL. For comparison, the NTP mechanism based Sphere Decoder and NL mechanism based Sphere Decoder results are also presented, with key findings. At 10% BLER, the combination of the NTP mechanism and the NL mechanism based Sphere Decoder achieves a 7 dB gain while maintaining a low complexity of 7× MMSE. Additionally, the maximum complexity of the combination of the NTP mechanism and the NL mechanism based Sphere Decoder is limited to 20× MMSE, demonstrating an effective trade-off between performance and computational efficiency.

Therefore, the NL mechanism is most effective when combined with the NTP mechanism in the Sphere Decoder. In an advantageous aspect, the combined approach ensures that high-performance MIMO detection may remain computationally feasible, making such an approach particularly beneficial for high-order modulation schemes and real-time wireless communication systems. Thus, the combination of the NTP mechanism and the NL mechanism based Sphere Decoder may achieve several dBs of SNR gain compared to the existing systems that use the MMSE, with only marginal increase in complexity.

Figures 14a and 14b illustrate a process flow of a method 1400 for decoding received signals in MIMO communication system using the NTP mechanism, according to an embodiment of the disclosure.

Referring to Figure 14, at step 1402, the method 1400 may include obtaining one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters may include one or more signal vectors received over the one or more channels in the MIMO communication system, the corresponding noise variance across the one or more channels in the MIMO communication system, the modulation order, and the channel matrix of the received signals.

At step 1404, the method 1400 may include obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals.

At step 1406, the method 1400 may include obtaining an initial linear solution based on the received signals, the channel matrix, and the corresponding noise variance. In an implementation, the initial linear solution may be obtained based on one of zero forcing (ZF) equalizer and the MMSE equalizer.

At step 1408, the method 1400 may include determining one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and a pre-defined number of neighbours in each layer, of the tree structure.

At step 1410, the method 1400 may include creating a search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure.

At step 1412, the method 1400 may include applying a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising one or more bits. In an implementation, the decoding technique may incorporate the soft-output sphere decoding, which may refine signal detection by evaluating multiple possible transmitted data vectors. The decision metrics may provide a quantitative framework for identifying the most probable transmitted signals, ensuring accurate retrieval of information. Additionally, the likelihood-based metrics, such as the LLRs, may quantify confidence levels in detected bits, aiding in error correction and improving overall communication reliability.

At step 1414, the method 1400 may include computing decision metrics for each bit of the decoded signal vector. In an implementation, the signal vectors may include the noise variance that may quantify the level of background interference affecting the signals. Further, the signal vectors may include the modulation order that may define the number of bits mapped per symbol in the modulation scheme, influencing data transmission efficiency. The signal vectors may include the predefined neighbor count per layer that may specify the number of nearby constellation points considered in the decoding process to refine detection accuracy. Furthermore, the signal vectors may include the channel matrix that may characterizes the signal propagation conditions by mapping the channel coefficients between the transmitter antennas and receiver antennas.

At step 1416, the method 1400 may include determining a likelihood-based metrics for each bit of the decoded signal vector based on the decision metrics.

At step 1418, the method 1400 may include decoding the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

Figures 15a and 15b illustrate a process flow of a method 1500 for decoding received signals in MIMO communication system using the NL mechanism, according to an embodiment of the disclosure.

Referring to Figures 15a and 15b, at step 1502, the method 1500 may include obtaining one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters include one or more signal vectors received over the one or more channels in the MIMO communication system, the corresponding noise variance across the one or more channels in the MIMO communication system, the modulation order, and the channel matrix of the received signals.

At step 1504, the method 1500 may include obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals.

At step 1506, the method 1500 may include initializing a number of leaf nodes visited to zero in the tree structure.

At step 1508, the method 1500 may include applying a tree-based decoding search on the tree structure, starting from a path in the tree structure with an initial radius to obtain a decoded signal vector comprising one or more bits. In an implementation, the one or more signal vectors may indicate the received signals at each of the set of receiver antennas of the MIMO communication system. The one or more signal vectors may indicate corresponding noise variance indicates level of background noise in the received signals. The one or more signal vectors may further indicate the modulation order indicates a number of bits per symbol used in a modulation scheme. The one or more signal vectors may further indicate and the channel matrix indicates channel coefficients obtained between a set of transmitter antennas and the set of receiver antennas.

At step 1510, the method 1500 may include incrementing the number of leaf nodes visited in the tree structure by one each time a leaf node is visited along a path, during the tree-based decoding search.

At step 1512, the method 1500 may include computing decision metrics for each bit of the decoded signal vector at end of each path during the tree-based decoding search.

At step 1514, the method 1500 may include determining if the number of leaf nodes visited is equal to a pre-defined maximum number of leaf nodes to visit. In an implementation, the leaf node may indicate the end point of the path in the search space that originates from the root node, the likelihood-based metrics include log-likelihood ratios, the tree-based decoding search comprises the sphere decoding search and the decision metrics indicate a quantitative measure for determining most probable transmitted data.

At step 1516, the method 1500 may include upon determining that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, terminating the tree-based decoding search and determining a likelihood-based metrics for each bit of the decoded signal vector based on current estimate of decision metrics. In an implementation, if the count of visited leaf nodes remains below the predefined maximum limit, the tree-based decoding process may proceed along the next available path within the tree structure until the set threshold for the leaf node visits is fully reached.

At step 1518, the method 1500 may include decoding the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

Figures 16a and 16b illustrate a process flow of a method 1600 for decoding received signals in MIMO communication system using the NTP and NL mechanism, according to an embodiment of the disclosure.

Referring to Figures 16a and 16b, at step 1602, the method 1600 may include obtaining one or more input parameters from the received signals over one or more channels in the MIMO communication system. The one or more input parameters include one or more signal vectors received over the one or more channels in the MIMO communication system, the corresponding noise variance across the one or more channels in the MIMO communication system, the modulation order, and the channel matrix of the received signals.

At step 1604, the method 1600 may include obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signals.

At step 1606, the method 1600 may include obtaining an initial linear solution based on the received signals, the channel matrix, and the corresponding noise variance.

At step 1608, the method 1600 may include determining one or more neighbours of the linear solution for each layer of the tree structure based on the modulation order for each layer and the pre-defined number of neighbours in each layer, of the tree structure.

At step 1610, the method 1600 may include creating the search space by pruning the tree structure based on the one or more neighbours for each layer of the tree structure.

At step 1612, the method 1600 may include initializing the number of leaf nodes visited to zero in the search space.

At step 1614, the method 1600 may include applying the decoding technique on the search space, starting from the path to obtain the decoded signal vector comprising one or more bits.

At step 1616, the method 1600 may include incrementing the number of leaf nodes visited in the search space by one each time the leaf node is visited along the path during the decoding technique.

At step 1618, the method 1600 may include computing decision metrics for each bit of the decoded signal vector at end of each path in the search space during the decoding technique.

At step 1620, the method 1600 may include determining if the number of leaf nodes visited is equal to a pre-defined maximum number of leaf nodes to visit.

At step 1622, the method 1600 may include upon determining that the number of leaf nodes visited is equal to the pre-defined maximum number of leaf nodes to visit, terminating the decoding technique in the search space and determining the likelihood-based metrics based for each bit of the decoded signal vector based on current estimate of decision metrics.

At step 1624, the method 1600 may include decoding the received signals by feeding the likelihood-based metrics for each bit to a channel decoder.

In an advantageous aspect, the disclosure introduces methods and systems to reduce the complexity of the Sphere Decoder tree search for the MIMO detection, using the neighbourhood-based tree pruning (NTP) mechanism and the node limiting (NL) mechanism, and the combination of the two. Under NTP mechanism, the disclosed system and method shows that, computing tree branches for only a few neighbours of initial linear solution in each MIMO layer, instead of all modulation symbols, reduces the complexity significantly. Further, under the NL mechanism, restricting the maximum number of leaf nodes visited by the Sphere Decoder tree search allows achieving flexible trade-off between performance and complexity. Furthermore, using the NTP mechanism and the NL mechanism jointly in the Sphere Decoder tree search improves performance while having a complexity close to linear detectors such as MMSE.

While specific language has been used to describe the disclosure, any limitations arising on account of the same are not intended. As would be apparent to a person in the art, various working modifications may be made to the method in order to implement the inventive concept as taught herein.

The drawings and the forgoing description give examples of embodiments. Those skilled in the art will appreciate that one or more of the described elements may well be combined into a single functional element. Alternatively, certain elements may be split into multiple functional elements. Elements from one embodiment may be added to another embodiment. For example, orders of processes described herein may be changed and are not limited to the manner described herein.

Claims

A method for decoding received signal in a multiple-input multiple-output (MIMO) communication system, the method comprising:

obtaining an input parameter from the received signal, wherein the input parameter includes at least one of a signal vector, a noise variance, a modulation order, and a channel matrix;

obtaining a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signal;

obtaining an initial linear solution based on the received signal, the channel matrix, and the noise variance;

determining a neighbour of the linear solution for a layer of the tree structure based on the modulation order for the layer and a pre-defined number of the neighbour in the layer, of the tree structure;

creating a search space by pruning the tree structure based on the neighbour for the layer of the tree structure;

applying a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising at least one bit;

computing a decision metric for the at least one bit of the decoded signal vector;

determining a likelihood-based metric for the at least one bit of the decoded signal vector based on the decision metric; and

decoding the received signal by feeding the likelihood-based metric for the at least one bit to a channel decoder.
The method of claim 1, wherein the signal vector indicates the received signal at a receiver antenna, the noise variance indicates a level of background noise in the received signal, the modulation order indicates a number of bit per symbol used in a modulation scheme, the pre-defined number of the neighbour in the layer indicates a count of nearby points considered for the decoding technique, and the channel matrix indicates a channel coefficient obtained between a transmitter antenna and the receiver antenna.
The method of claim 1, wherein the decoding technique includes a soft-output sphere decoding, the decision metric indicates a quantitative measure for determining most probable transmitted data, and the likelihood-based metric includes a log-likelihood ratio.
The method of claim 1, further comprising:

initializing a number of a leaf node visited to zero in the tree structure;

applying a tree-based decoding search on the tree structure, starting from a path in the tree structure with the initial radius to obtain the decoded signal vector comprising the at least one bit;

incrementing the number of the leaf node visited in the tree structure by one each time the leaf node is visited along the path, during the tree-based decoding search;

computing the decision metric for the at least one bit of the decoded signal vector at an end of the path during the tree-based decoding search;

determining if the number of the leaf node visited is equal to a pre-defined maximum number of the leaf node to visit;

upon determining that the number of the leaf node visited is equal to the pre-defined maximum number of the leaf node to visit, terminating the tree-based decoding search; and

determining the likelihood-based metric for the at least one bit of the decoded signal vector based on a current estimate of the decision metric.
The method of claim 4, further comprising:

upon determining that the number of the leaf node visited is less than the pre-defined maximum number of the leaf node to visit, continuing the tree-based decoding search along a subsequent path in the tree structure until the maximum number of the leaf node to be visited is reached.
The method of claim 4, wherein the leaf node indicates an end point of the path in the search space that originates from a root node, and the tree-based decoding search comprises a sphere decoding search.
The method of claim 1, further comprising:

initializing a number of a leaf node visited to zero in the search space;

applying the decoding technique on the search space, starting from a path to obtain the decoded signal vector comprising the at least one bit;

incrementing the number of the leaf node visited in the search space by one each time the leaf node is visited along the path during the decoding technique;

computing the decision metric for the at least one bit of the decoded signal vector at an end of the path in the search space during the decoding technique;

determining if the number of the leaf node visited is equal to a pre-defined maximum number of the leaf node to visit;

upon determining that the number of the leaf node visited is equal to the pre-defined maximum number of the leaf node to visit, terminating the decoding technique in the search space; and

determining the likelihood-based metric for the at least one bit of the decoded signal vector based on current estimate of the decision metric.
A system for decoding received signal in a multiple-input multiple-output (MIMO) communication system, the system comprising:

at least one processor; and

a memory coupled with the at least one processor, wherein the at least one processor is configured to:

obtain an input parameter from the received signal, wherein the input parameter includes at least one of a signal vector, a noise variance, a modulation order, and a channel matrix;

obtain a tree structure based on matrix factorization of the channel matrix and pre-processing of the received signal;

obtain an initial linear solution based on the received signal, the channel matrix, and the noise variance;

determine a neighbour of the linear solution for a layer of the tree structure based on the modulation order for the layer and a pre-defined number of the neighbour in the layer, of the tree structure;

create a search space by pruning the tree structure based on the neighbour for the layer of the tree structure;

apply a decoding technique on the search space, starting from an initial radius to obtain a decoded signal vector comprising at least one bit;

compute a decision metric for the at least one bit of the decoded signal vector;

determine a likelihood-based metric for the at least one bit of the decoded signal vector based on the decision metric; and

decode the received signal by feeding the likelihood-based metric for the at least one bit to a channel decoder.
The system of claim 8, wherein the initial linear solution is obtained based on one of a zero forcing (ZF) equalizer and a minimum mean squared error (MMSE) equalizer.
The system of claim 8, wherein the signal vector indicates the received signal at a receiver antenna, the noise variance indicates a level of background noise in the received signal, the modulation order indicates a number of bit per symbol used in a modulation scheme, the pre-defined number of the neighbour in the layer indicates a count of nearby points considered for the decoding technique, and the channel matrix indicates a channel coefficient obtained between a transmitter antenna and the receiver antenna.
The system of claim 8, wherein the decoding technique includes a soft-output sphere decoding, the decision metric indicates a quantitative measure for determining most probable transmitted data, and the likelihood-based metric includes a log-likelihood ratio.
The system of claim 8, wherein the at least one processor is further configured to:

initialize a number of a leaf node visited to zero in the tree structure;

apply a tree-based decoding search on the tree structure, starting from a path in the tree structure with the initial radius to obtain the decoded signal vector comprising the at least one bit;

increment the number of the leaf node visited in the tree structure by one each time the leaf node is visited along the path, during the tree-based decoding search;

compute the decision metric for the at least one bit of the decoded signal vector at an end of the path during the tree-based decoding search;

determine if the number of the leaf node visited is equal to a pre-defined maximum number of the leaf node to visit;

upon determination that the number of the leaf node visited is equal to the pre-defined maximum number of the leaf node to visit, terminate the tree-based decoding search; and

determine the likelihood-based metric for the at least one bit of the decoded signal vector based on a current estimate of the decision metric.
The system of claim 12, wherein the at least one processor is further configured to:

upon determination that the number of the leaf node visited is less than the pre-defined maximum number of the leaf node to visit, continue the tree-based decoding search along a subsequent path in the tree structure until the maximum number of the leaf node to be visited is reached.
The system of claim 12, wherein the leaf node indicates an end point of the path in the search space that originates from a root node, and the tree-based decoding search comprises a sphere decoding search.
The system of claim 8, wherein the at least one processor is further configured to:

initialize a number of a leaf node visited to zero in the search space;

apply the decoding technique on the search space, starting from a path to obtain the decoded signal vector comprising the at least one bit;

increment the number of the leaf node visited in the search space by one each time the leaf node is visited along the path during the decoding technique;

compute the decision metric for the at least one bit of the decoded signal vector at an end of the path in the search space during the decoding technique;

determine if the number of the leaf node visited is equal to a pre-defined maximum number of the leaf node to visit;

upon determination that the number of the leaf node visited is equal to the pre-defined maximum number of the leaf node to visit, terminate the decoding technique in the search space; and

determine the likelihood-based metric for the at least one bit of the decoded signal vector based on current estimate of the decision metric.