WO2024007299A1

WO2024007299A1 - A signal processing device and method for a non-stationary dynamic environment

Info

Publication number: WO2024007299A1
Application number: PCT/CN2022/104621
Authority: WO
Inventors: Alexandr Kuzminskiy; Pei XIAO; Rahim Tafazolli; Fan Wang
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2022-07-08
Filing date: 2022-07-08
Publication date: 2024-01-11

Abstract

A receiver (200) for a wireless network, devices (100,110) for the receiver (200) and the receiver (200) including the devices (100,110) are disclosed. The devices (100,110) are configured to obtain a received signal (101) and one or more pilot symbols (102), which are received by the receiver (200) over a channel. A first device (100) is configured to determine a data-regularized covariance matrix (103) based on both the received signal (101) and the one or more pilot symbols (102). A second device (110) is configured to train a machine learning model (111) based on the one or more pilot symbols (102). The first device (100) is then configured to determine an estimate(104) of the received signal (101) based on the received signal (101) and the data-regularized covariance matrix (103), while the second devices (110) is configured to determine the estimate (104) of the received signal (101) by applying the trained machine learning model (111) to the received signal (101).

Description

A SIGNAL PROCESSING DEVICE AND METHOD FOR A NON-STATIONARY DYNAMIC ENVIRONMENT

TECHNICAL FIELD

The present disclosure relates to a receiver for a wireless network. The disclosure presents devices for the receiver, and the receiver respectively including the devices. The devices may perform a signal processing on a received signal, which is received by the receiver over a channel, based on pilot symbols. The devices are specifically designed for compensating channel and hardware impairments in a non-stationary environment.

BACKGROUND

The main limiting factor for existing and future wireless networks is the harsh and generally uncontrollable interference in a dynamic non-stationary environment. One example of such a dynamic non-stationary environment is the uplink from a 5 ^th generation (5G) wireless network to a low earth orbit (LEO) satellite network with high residual Doppler shift. Possibly, the uplink is also affected by hardware impairments such as IQ imbalance (IQI) , because of limited satellite resources. Another example is spectrum sharing in an unlicensed spectrum, wherein asynchronous interference may have a different time or frequency format compared to the desired signals.

In such dynamic non-stationary environments, interference mitigation becomes a pivotal technology. Interference mitigation by means of antenna arrays is of special interest, because (massive) multiple input multiple output (MIMO) is deemed as one of the key enablers for existing and future wireless networks. Interference rejection combining (IRC) based on the minimum mean square error (MMSE) criterion is a simple antenna array interference mitigation technology that uses linear beamforming at the receiver based on estimated second order statistics (SOS) , which can be applied in different wireless network configurations such as single user (SU) and multiple user (MU) MIMO (SU/MU-MIMO) systems.

On the other hand, channel and hardware impairments, such as IQ imbalance, phase noise, frequency offset, etc., may render the transmitted signal improper, but may introduce additional useful information (in the pseudo-autocorrelation matrix) , which can be advantageously utilized to improve the system performance. For a complex random signal vector, the SOS are completely characterized by its autocorrelation matrix as well as pseudo-autocorrelation matrix. However, the conventional satellite transmitter or receiver only utilizes the autocorrelation of the signal, leading to suboptimal performance.

The main feature of the above-described non-stationary scenarios is that different symbols in the desired signal data slot may be received under different propagation and/or interference conditions. Conventional space-time-frequency equalization and interference rejection techniques in wireless communications exploit known pilot symbols (also referred to as training symbols) to estimate the weight vector of an antenna array using the estimated propagation channel of the desired signal and space-time-frequency parameters of the interference. The underlying assumption for this kind of techniques is, that the training data is reliable since the co-channel interference (CCI) completely overlaps with the training symbols of the desired signal. Normally, this is the case in slowly varying environment for synchronous CCI, which has the same time-frequency structure as the desired user.

However, a non-stationary dynamic environment, asynchronous cells, a packed intermittent transmission, inter-system interference of different time/frequency formats in an unlicensed spectrum, and other techniques may lead to more complicated scenarios. The main difficulty with these scenarios is that potentially a different content of CCI sources may be observed over the training and data intervals. Under these conditions, adaptive beamformers designed over the training interval, which is occupied by the known training sequences, become inefficient for interference mitigation over the data interval, due to a possibility of the presence of interference signals absent over the training interval. Directly using the estimate of the covariance matrix averaged over the data interval does not result in an efficient useful signal extraction, due to the useful signal presence in the data used for covariance matrix estimation, leading to the possibility of rejection of both the desired signal and interference depending on the available degrees of freedom (antenna elements) .

The conventional pilot-based and data-based IRC solutions are defined in various 3GPP documents. Moreover, a widely linear or augmented (for orthogonal frequency division multiplexing (OFDM) ) linear IRC (AIRC) was proposed. However, the adaptive AIRC based on iterative least mean square (LMS) or recursive least squares (RLS) algorithms may not be suitable for modern slot based wireless networks.

There is an issue, that in a non-stationary dynamic environment the conventional pilot-based solutions may lose their efficiency, because the interference content at the pilot symbols used for estimation of the interference plus noise covariance matrix may be different compared to the interference content at the data symbols of the desired signal slot.

In addition, in the non-stationary dynamic environment also the conventional data-based solutions may lose their efficiency, because the interference plus noise covariance matrix estimated over data symbols or the whole data slot contains the desired signal and interference leading distortion of the desired signal together with interference rejection.

SUMMARY

In view of the above, this disclosure aims to improve the conventional data-based and pilot-based solutions. That is, to overcome the drawbacks of the conventional pilot-based and data-based solutions is an objective An objective is generally to develop a more robust signal processing at the receiver for the non-stationary dynamic environment. Another objective is to take into account SOS for exploiting information inherent in improper signals.

These and other objectives are achieved by the solution of this disclosure as described in the independent claims. Advantageous implementations are further defined in the dependent claims.

A first aspect of this disclosure provides a device for a receiver, the device being configured to: obtain a received signal and one or more pilot symbols, which are received by the receiver over a channel; determine a data-regularized covariance matrix based on both the received signal and the one or more pilot symbols; and determine an estimate of the received signal based on the received signal and the data-regularized covariance matrix.

The device of the first aspect is able to overcome the drawbacks of the conventional pilot-based and data-based solutions, because both the signal (data symbols) and pilot symbols are used to determine the covariance matrix. Thus, a more robust signal processing is obtained, which can be implemented at the receiver. Thus, the receiver is improved especially for non-stationary dynamic environments.

In an implementation form of the first aspect, the device is configured to: determine a channel estimate of the channel based on the received signal and the one or more pilot symbols; determine a pilot-based covariance matrix based on the one or more pilot symbols and the channel estimate; determine a data-based covariance matrix based on the received signal; and determine the data-regularized covariance matrix by weighting the pilot-based covariance matrix and the data-based covariance matrix, respectively, based on one or more receiver parameters of the receiver.

In this way, the pilot-based approach and the data-based approach are combined to create a more robust solution, which is also receiver-adapted.

In an implementation form of the first aspect, the device is configured to: calculate a weight vector based on the channel estimate and the data-regularized covariance matrix; and determine the estimate of the received signal by linearly combining the weight vector and the received signal.

In an implementation form of the first aspect, the one or more receiver parameters comprise at least one of a number of antennas of the receiver, a number of user signals in the received signal in case of a multi-user received signal, and a signal to noise ratio of the received signal.

In an implementation form of the first aspect, the device is configured to: determine one or more scenario parameters based on the received signal; and determine the channel estimate based on the received signal, the one or more pilot symbols, and the one or more scenario parameters.

In an implementation form of the first aspect, the one or more scenario parameters comprises at least one of a delay spread of the received signal and a Doppler shift of the received signal.

Thus, characteristics of the actual non-stationary dynamic environment can be taken into account.

In an implementation form of the first aspect, the device is configured to: calculate a mixing factor based on the one or more receiver parameters; and weight the pilot-based covariance matrix and the data-based covariance matrix, respectively, according to the mixing factor.

The optimal mixing factor may lead to a further improved estimate of the received signal, for example, reflected in a lower bit error rate.

In an implementation form of the first aspect, the device is configured to calculate the mixing factor based on the one or more receiver parameters and the one or more scenario parameters.

Thus, characteristics of the specific non-stationary dynamic environment and characteristics of the receiver can be taken into account.

In an implementation form of the first aspect, the device comprises a trained model configured to calculate the mixing factor based on the one or more receiver parameters.

In an implementation form of the first aspect, the trained model is a trained neural network.

In an implementation form of the first aspect, the received signal is an OFDM, signal.

In an implementation form of the first aspect, the received signal is a MU signal or a SU signal.

A second aspect of this disclosure provides a device for a receiver, the device being configured to: obtain a received signal and one or more pilot symbols, which are received by the receiver over a channel; train a machine learning model based on the one or more pilot symbols; and determine an estimate of the received signal by applying the trained machine learning model to the received signal.

The device of the second aspect is able to overcome the drawbacks of the conventional pilot-based and data-based approaches, as it is able to take into account SOS to exploit information inherent in improper signals. The machine learning model may be trained using the pilot symbols. Since the device of the second aspect may have the information of the received pilot symbols, and the machine learning is trained at that device (e.g., in the receiver) , the device can obtain a more accurate estimate of the received signal.

In an implementation form of the second aspect, the trained machine learning model is an augmented complex extreme learning machine (A-CELM) , wherein the A-CELM has only one hidden layer comprising hidden nodes and the complex conjugate of the hidden nodes.

A third aspect of this disclosure provides a receiver comprising: one or more antennas; and the device according to the first aspect or any of its implementation forms, wherein the receiver is configured to receive the received signal and the one or more pilot symbols over the channel with the plurality of antennas and to provide them as input into the device, and the device is configured to determine the estimate of the received signal based on the input.

Since the receiver includes the device of the first or the second aspect, it enjoys the same advantages as described above.

A fourth aspect of this disclosure provides a method for a receiver, the method comprising: obtaining a received signal and one or more pilot symbols, which are received by the receiver over a channel; wherein the method further comprises: determining a data-regularized covariance matrix based on both the received signal and the one or more pilot symbols; and determining an estimate of the received signal based on the received signal and the data-regularized covariance matrix; or wherein the method further comprises: training a machine learning model based on the one or more pilot symbols; and determining an estimate of the received signal by applying the trained machine learning model to the received signal.

In an implementation form of the fourth aspect, the method comprises: determining a channel estimate of the channel based on the received signal and the one or more pilot symbols; determining a pilot-based covariance matrix based on the one or more pilot symbols and the channel estimate; determining a data-based covariance matrix based on the received signal; and determining the data-regularized covariance matrix by weighting the pilot-based covariance matrix and the data-based covariance matrix, respectively, based on one or more receiver parameters of the receiver.

The method of the fourth aspect may have further implementation forms according to the steps performed by the device of the first aspect and the device of the second aspect and their implementation forms, respectively. Accordingly, the method of the fourth aspect achieves the same respective advantages as described above.

A fifth aspect of this disclosure provides a computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform the method according to the fourth aspect or any implementation form thereof.

A sixth aspect of this disclosure provides a storage medium storing executable program code which, when executed by a processor, causes the method according to the fourth aspect or any of its implementation forms to be performed.

In view of the above aspects and implementation forms, for example, this disclosure proposes using a data-based regularization of a pilot-based estimate of the interference plus noise covariance matrix, in order to introduce a controllable by means of a mixing factor balance between interference mitigation that is not presented at the training interval and signal distortions because of the presence of the received signal components in the data-based estimate of the interference plus noise covariance matrix. Assuming the availability of a high number of degrees of freedom (e.g., antennas) at the receiver (modern trend for, e.g., gNB design) , this data-regularized estimate of the interference plus noise covariance matrix allows effective rejection of all interference components presented in the data slot for appropriate selection of the mixing factor. The disclosure also proposes an adaptive selection of the mixing factor using a neural network (NN) function approximation with off-line training in the typical scenarios for the given network configuration. The proposed solution may be extended to widely (augmented) linear processing to address scenarios with hardware impairments, which is especially important for LEO satellite application.

To remedy drawbacks of CELM, e.g., being unable to exploit signal impropriety, thus leading to suboptimal performance, in addition this disclosure proposes applying an A-CELM (compare, e.g., ‘H. Zhang, et al. “The augmented complex-valued extreme learning machine” , Neurocomputing, 311, pp. 363-372, 2018’ ) , which is capable of fully capturing the SOS for the maximum performance improvement under hardware impairments.

It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

BRIEF DESCRIPTION OF DRAWINGS

The above described aspects and implementation forms will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

FIG. 1 shows different devices according to this disclosure

FIG. 2 shows a receiver according to this disclosure, the receiver comprising a device according to this disclosure.

FIG. 3 illustrates an exemplary device according to this disclosure.

FIG. 4 shows details of the exemplary device of FIG. 3.

FIG. 5 illustrates another exemplary device according to this disclosure.

FIG. 6 shows simulation results for an exemplary device of this disclosure similar to that of FIG. 3.

FIG. 7 shows further simulation results for the exemplary device of FIG. 6.

FIG. 8 shows simulation results for an exemplary device of this disclosure similar

to that of FIG. 5.

FIG. 9 shows further simulation results for the exemplary device of FIG. 8.

FIG. 10 shows further simulation results for the exemplary device of FIG. 8.

FIG. 11 shows a flow-diagram of a method according to this disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 shows two

devices

100 and 110 according to this disclosure. The device 100 is shown in (a) , and the device 110 is shown in (b) . Both

devices

100, 110 can be used in a receiver, for instance, a receiver 200 as shown in FIG. 2, which will be explained below. Both

devices

110, 110 may perform signal processing in the receiver 200, in order to compensate channel and hardware impairments in especially a non-stationary environment.

The device 100 is configured to obtain a received signal 101 and to obtain one or more pilot symbols 102. Both the received signal 101 and the pilot symbols 102 are received by the receiver 200 over a channel, which may be an impaired channel. The receiver 200 may input the received signal 101 and the pilot symbols 102 into the device 100. The received signal 101 and the pilot symbols 102 may be received, for instance, in separate time intervals, or time slots, or other time and/or frequency resources. The received signal 101 may contain data symbols, and may be received in a dedicated data interval. The pilot symbols may be received in a training interval. However, data symbols and pilot symbols may also be received together.

The device 100 is configured to determine a data-regularized covariance matrix 103 based on both the received signal 101 and the one or more pilot symbols 102 (e.g., in a first optional processing block as indicated with the dashed box) . The device 100 may accordingly use data symbols and pilot symbols 102 to obtain the covariance matrix 103. Further, the device 100 is configured to determine an estimate 104 of the received signal 101 based on the received signal 101 and the data-regularized covariance matrix 103 (e.g., in a second optional processing block as indicated with the dashed box) . The estimate 104 of the signal may be compensated for channel and/or hardware impairments that have affected the (transmission of the) received signal 101.

Also the device 110 is configured to obtain a received signal 101 and one or more pilot symbols 102, which are received by the receiver 200 over a channel, in a similar manner as described above for the device 100.

The device 110 is further configured to train a machine learning model 111 based on the one or more pilot symbols 102 (e.g., in a first optional processing block as indicated with the dashed box) , and to determine an estimate 104 of the received signal 101 by applying the trained machine learning model 111 to the received signal 101 (e.g., in a second optional processing block as indicated with the dashed box) . The estimate 104 of the signal may again be compensated for channel and/or hardware impairments that have affected the (transmission of the) received signal 101.

The device 100 and/or 110 may comprise a processor or processing circuitry configured to perform, conduct or initiate the various operations of the device 100 and/or 110 described herein. The processing circuitry may comprise hardware and/or the processing circuitry may be controlled by software. In particular, the processing circuitry may comprise or form the optional processing blocks indicated with the dashed boxed in FIG. 1.The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs) , field-programmable arrays (FPGAs) , digital signal processors (DSPs) , or multi-purpose processors. The device 100 and/or 110 may further comprise memory circuitry, which stores one or more instruction (s) that can be executed by the processor or by the processing circuitry, in particular under control of the software. For instance, the memory circuitry may comprise a non-transitory storage medium storing executable software code which, when executed by the processor or the processing circuitry, causes the various operations of the device 100 and/or 110 to be performed. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the device 100 and/or 110 to perform, conduct or initiate the operations or methods described herein.

FIG. 2 shows a receiver 200 according to this disclosure. The receiver 200 comprises one or more antennas 201, for instance, it may comprise an antenna array. The antennas 201 may be configured for MIMO and/or OFDM. The receiver 200 is configured to receive the received signal 101 and the one or more pilot symbols 102 (as described above) over a channel with the plurality of antennas 201. There may be channel and/or hardware impairments that affect the received signal 101. The receiver 200 may be configured for OFDM and/or SU/MU-MIMO reception.

The receiver 200 further comprises either the device 100 or the device 110, as shown in FIG. 1, and is configured to provide the received signal 101 and the received pilot symbols 102 as input (s) into the

device

100, 110. The

device

100, 110 is then configured, as described above, to determine the estimate 104 of the signal, and the receiver 200 may use this estimate 104 for optional further signal processing, for example, for decoding the signal or the like. Notably, the estimate 104 of the signal is intended to recover the signal that was transmitted by a transmitter to the receiver 200 over the channel, and which resulted –e.g. due to channel and/or hardware impairments –in the received signal 101 received by the receiver 200.

FIG. 3 shows a block diagram of an exemplary device 100, which builds on the device 100 shown in FIG. 1 (a) . Same elements are labelled with the same reference signs, and function likewise.

The device 100 shown in FIG. 3 is configured to obtain the received signal 100, e.g. received by the one or more antennas 201 of a receiver 200, and the one or more pilot symbols 102.

The device 100 may comprise a plurality of processing blocks, e.g., as illustrated. In particular, the device 100 may have a “channel estimation” processing block configured to determine a channel estimate 301 of the channel based on the received signal 101 and the one or more pilot symbols 102. Further, the device 100 may have a “pilot-based covariance matrix estimator” processing block configured to determine a pilot-based covariance matrix 302 based on the one or more pilot symbols 102 and the channel estimate 301. Further, the device 100 may have a “data-based covariance matrix estimator” processing block configured to determine a data-based covariance matrix 303 based on the received signal 101. Then, the device 100 may also have a “data-regularized covariance matrix calculator” processing block configured to determine the data-regularized covariance matrix 103 by weighting the pilot-based covariance matrix 302 and the data-based covariance matrix 303, respectively, based on one or more receiver parameters 305 of the receiver 200. The device 100 may receive the receiver parameters 305 as input from the receiver 200, or may be able to determine or calculate these receiver parameters 305. The device 100 may comprise further optional processing blocks as explained in the following.

As exemplarily shown in FIG. 3, the received signal 101 may arrive at a “scenario analyser” processing block, which may estimate one or more scenario parameters 307 based on the received signal 101. For instance, typical scenario parameters 307 may be a delay spread and/or a Doppler shift of the received signal 101. The received signal 101, and the one or more pilot symbols 102, and optionally the output of the scenario analyzer, i.e., the one or more scenario parameters 307, are further used at the “channel estimator” processing block for the estimation 301 of the propagation channel of the received signal 101. As mentioned above, the pilot-based covariance matrix 302 (interference plus noise covariance matrix) is estimated in the “pilot-based covariance matrix estimator” processing block, and the data-based covariance matrix 303 is estimated in the “data-based covariance matrix estimator” processing block.

These pilot-based and data-based

covariance matrices

302 and 303 may further be weighted according to a mixing factor 308 in the “data-regularized covariance matrix calculator” processing block, in order to determine the data-regularized covariance matrix 103. The mixing factor 308 may be calculated based on the one or more receiver parameters 305, particularly, in a “Data base (neural network) ” processing block 309 and using as the receiver parameters 305, for instance, the number of antennas 201 of the receiver 201, and/or a number of signals in the received signal 101, and/or a signal to noise ration of the received signal 101.

The data-regularized covariance matrix 103 and the channel estimate 301 may further be used to calculate a weight vector 306 in a “weight vector calculator” processing block. Then, a linear combination of the weight vector 306 and the received signal 101 may be performed in a “signal estimator” processing block 304, in order to determine the estimate 104 of the received signal 101.

FIG. 4 shows an implementation of the “Data base (neural network) ” processing block 309, which is shown in FIG. 3, and which is used in the device 100 to determine the mixing factor 308. In a training (off-line) mode of this processing block 309, the one or more receiver parameters 305 and/or the one or more scenario parameters 307 are used in a “scenario simulator” processing block to generate several realizations of the received signal 101 according to the device 100 shown in FIG. 3 (denoted as a Data regularized IRC (DRIRC) ) for a set of mixing factors 308 generated by a “mixing factor samples” processing block. A bit error rate (BER) is estimated at the output of the DRIRC for each mixing factor. Then, a “minimiser” processing block is configured to find an optimal mixing factor 308 that gives the minimum BER, which is used as the training NN output for the receiver parameters 305 and scenario parameters 307 as the NN training input leading to the NN parameters for on-line generation of the mixing factor 308 suitable for the given receiver and

scenario parameters

305, 307.

More details of the signals and processing blocks shown in FIG. 3 and FIG. 4 may be described as follows.

For the received signal 101, the following model of an OFDM signal received by the receiver 200 with K antennas 201 may be assumed for the n th symbol on thefth subcarrier:

x (f, n) =H (f, n) s (f, n) +z (f, n) , (1)

where x (f, n) ∈C ^K×1 is the received signal vector, H (f, n) = [h ₁, ..., h _M] ∈C ^K×M is the propagation channel matrix, where M＞1 is the number of useful signals for MU-MIMO and M=1 for SU-MIMO, z (f, m) ∈C ^K×1 is the interference plus noise vector. Signal estimation in a data slot containing L≥1 resource blocks (RBs) adjacent in the frequency domain may be assumed. Each data slot contains N _p pilot symbols and N _d data symbols at the known positions in the slot.

In the “scenario analyser” processing block, a typical estimation of delay spread and Doppler shift for interpolated channel estimation may be used, e.g., as in ‘Z. Sharif, A.Z. Sha’ameri, “Estimation of the Doppler spread and Time Delay Spread for the Wireless Communication Channel” in Proc. ICCAIE, Dec. 2010’ .

A pilot-based channel estimation with time/frequency interpolation, as defined in ‘P. Hoeher, S. Kaiser, P. Robertson, “Two-Dimensional Pilot-Symbol-Aided Channel Estimation by Wiener Filtering” in Proc. ICASSP, Apr. 1997’ may be used in the “channel estimation” processing block.

A pilot-based interference plus noise covariance matrix 302 may be estimated for the m th received signal 101 as follows in the “pilot-based covariance matrix estimator” processing block:

where (·) ^*is the conjugate transpose operation, f _pi, n _pi is the location of the ith pilot symbol 102 of the m th received signal in the data slot,

is the channel estimate 301 at the output the processing block, I _K is the K×K unit matrix, and β≥0 is the diagonal loading coefficient, which can be selected according to the field trials as in US 9,641,294 B2 or analytically as in ‘A.M. Kuzminskiy, P. Xiao, R. Tafazolli, “Uniform Expected Likelihood Solution for Interference Rejection Combining Regularization” in Proc. ICASSP, Mar. 2016’ .

In the “data-based covariance matrix estimator” block, the data-based covariance matrix 303 may be estimated as follows:

where f _di, n _di is the location of the ith data symbol in the data slot.

In the “data-regularized covariance matrix calculator” processing block, the data-regularized covariance matrix 103 may be calculated as follows:

where 0≤δ≤1 is the mixing factor 309.

Alternatively, the data-regularized covariance matrix 103 can be calculated as

This leads to another implementation of the weight vector 306 in the “weight vector calculator” processing block with simpler computation complexity.

In the “weight vector calculator” processing block, the weight vector 306 for the m th received signal may be calculated as follows:

for the data-regularized covariance matrix 103 defined in equation (4) , and

for the data-regularized covariance matrix 103 defined in equation (5) . The computational complexity of equation (7) is lower compared to equation (6) , because it needs only one matrix inversion per data slot.

For δ=0, the equations (6) and (7) represent the pilot-based 3GPP IRC, and for δ=1, the equation (6) represents the data-based 3GPP IRC (see Y. Ohwatari, N. Miki, T. Asai, T. Abe, H. Taoka, “Performance of Advanced Receiver Employing Interference Rejection Combining to Suppress Inter-cell Interference in LTE-Advanced Downlink” in Proc. VTC-Fall, Sept. 2011’ )

In the “signal estimator” processing block 304, the estimate 104 of the m th signal is calculated as follows:

The “scenario simulator” processing block of the processing block 309 may generate a received signal 101 for given scenario parameters 307 and receiver parameters 305 according to equation (1) using a conventional channel generation tools such as MALAB Communications Toolbox.

The DRIRC processing block is according to the device 100 shown in FIG. 3.

The mixing factor samples in the processing block 309 may contain predefined samples of the mixing factor 308, for example, 0: 0.02: 1.

The “minimizer” processing block in the processing block 309 may find the mixing factor 308 value that gives the minimum BER among the mixing factor 308 values generated by the “mixing factor samples” processing block.

The NN can be defined using MATLAB Deep Learning Toolbox, for example, with the “fitnet” routine for the given number of hidden nodes and the “net” routine for NN. NN training can be performed using MATLAB Deep Learning Toolbox with, for example, the “train” routine for the scenario parameters 307 and receiver parameters 304 as the NN input and the optimal mixing factor 308 at the output of the “minimizer” processing block as the NN output.

To obtain the widely (augmented) linear version of the data regularized AIRC (ADRIRC) suitable for networks with hardware impairments such as IQI, the received signal vector in (1) may be replaced with an extended received signal vector using the conjugate signal from the mirror OFDM subcarrier

where N _DFT is the dimension of discreet Fourier transform used in OFDM network, and (·) ^C is the complex conjugate operation. Then, dimension K for all variables in the description of DRIRC above is replaced with dimension 2K for ADRIRC.

FIG. 5 shows a block diagram of an exemplary device 110, which builds on the device 110 shown in FIG. 1. Same elements are labelled with the same reference signs, and function likewise.

FIG. 5 presents, as trained machine learning model 111 of the device 110, an improved version of CELM to exploit signal impropriety. Complex extreme learning machine is a fast single layer feedforward network, which performs random feature mapping with the unknown parameters being learned by linear parameter solving. The design of the device 110 or receiver 200 can be optimized with A-CELM, in which the covariance matrix and the pseudo-covariance matrix are both considered to completely capture the second-order statistics (SOS) of the received signal 101, which is improper and non-circular, due to hardware impairments.

The basic structure of the A-CELM is depicted in FIG. 5. In particular, the A-CELM has only one hidden layer 501 comprising hidden nodes 502 and the complex conjugate 503 of the hidden nodes 502.

Given is

which represents arbitrary distinct N samples. Here, x _k and t _k represent the received and transmitted signal vectors respectively. In the context of A-CELM, the former is the input to the A-CELM post-distorter and the latter denote the output target vectors, which are the pilot symbols 102. The hidden layer input weights and biases

are randomly generated instead of tuned selection and N _h is the number of hidden layer nodes 502. The randomly initialized hidden layer weights and biases project the received signal 101 vector to a random space with the non-linear mapping function f (·) . The hidden layer 501 output corresponding to hidden node i is given as

In A-CELM, to incorporate the SOS of the received signal 101 to the NN structure, the hidden layer 501 is modified by appending the complex conjugate of the hidden nodes 502. Corresponding to

anew set of hidden node outputs is obtained as

The output corresponding to the k-th input x _k is given by

where β _i and γ _i represent the weights of the output layer corresponding to the hidden layer 501 and the augmented conjugate hidden layer 501. If

there exist β _i, γ _i, w _i and b _i such that o _k=t _k for k=1, 2, …N. These N equations can be compactly represented in a matrix form. Let the input matrix contain all the received signal vectors

and the weight matrix

the bias vector

and the bias matrix obtained by stacking the bias vectors N times, i.e.,

The output hidden layer matrix corresponding to (1) is

where f (A) denotes the activation function to each element of matrix A, i.e.

Let H _a denotes the augmented hidden layer matrix incorporated with the complex conjugate of H as H _a= [H, H ^*] . If

and

the effective output layer weight matrix

corresponding to A-CELM is obtained as

If the N target vectors t _k are stacked in matrix T as

it is related to the hidden layer outputs and output layer weights as

The weights bias matrix are randomly generated from any continuous probability distribution. Given the target matrix T, the parameter to be calculated for the A-CELM is the output weight matrix

which is obtained by minimizing the cost function

which can be obtained by the least square algorithm as

where

denotes the Moore–Penrose generalized inverse of the matrix H _a. The cost function can be modified to avoid over-fitting as

The closed form solution to the above unconstrained optimization problem is obtained as

In the following, some performance evaluation is presented for the

devices

100 and 110 with respect to FIG. 6-10

For device 100, application of DRIRC and ADRIRC in the uplink LEO satellite MU-MIMO scenario with IQI is illustrated in FIG. 6 and FIG. 7 for the following simulation assumptions:

· 2 GHz carrier frequency

· 10 MHz bandwidth (N _DFT=1024)

· 15 kHz carrier spacing

· 16QAM signalling

· 1/2 convolutional code rate for (133, 171) code with constraint length of 7

· Whole band spectrum allocation

· Satellite multipath channel model according to 3GPP TR 38.811 V15.4.0

· 0.42 ppm maximum residual Doppler shift corresponding to 1200 km satellite altitude, 40 km beam footprint diameter, 1000 km/h UE velocity [1]

· Independent for different antennas IQI parameters uniformly distributed in 1, …, 3 dB and 0, …, 20 degrees for amplitude and phase imbalance correspondingly

· Typical UL RB with 12 subcarriers, 2 pilot and 12 data OFDM symbols

· L=5 adjacent in the frequency domain RBs in a data slot

· Uncorrelated channels for different receive antennas

· Pilots generated with MATLAB “ltePUSCHDRS” routine

· Channel estimation with 2D interpolation over 3 frequency sliding RBs

· Diagonal loading of half noise power

· BER averaging over 500 scenario realizations

The simulation results for M=4 and K=16 are shown in FIG. 6 for the high (a) and low (b) Doppler shift of 0.42 ppm and 0.0042 ppm correspondingly. One can see in Fig. 6b that zero mixing factor 308 is the optimal selection in the low Doppler shift scenario leading to the conventional IRC and AIRC, which means that data-based regularization is not needed for low Doppler shift. On the contrary, one can see a significant data regularization gain for higher Doppler shift in Fig. 6a for the correctly selected mixing factor 308.

Efficiency of the NN based selection of the mixing factor is illustrated in FIG. 7, which shows the simulation results for M=2 and K=16, and two additional co-channel interferences with 3 dB and 5 dB signal to interference ratios (SIR) for DRIRC and ADRIRC compared to the optimal (non-implementable) mixing factor value found by means a direct BER minimization for each scenario realization. The IRC and AIRC for δ=0 are also plotted in FIG. 7 for comparison. One can see that the NN based results are very close to the optimal ones.

To evaluate the performance of the device 110, one can randomly choose input weights and biases from a complex circular area with center at the origin and having uniform distribution. The complex inverse hyperbolic sine function is used as the activation function at the hidden layer. The hyper-parameter, i.e., the number of hidden nodes 502, has been adjusted by gradually increasing the number of hidden nodes and the optimum number of hidden nodes for both CELM and A-CELM is selected as 50 based on cross validation method.

FIG. 8a compares the BER versus SNR performance of the conventional CELM and A-CELM for different LEO satellite scenarios and numerologies under the effect of Doppler shift, phase noise, I/Q imbalance and HPA non-linearity at OBO = 0dB. The performance corresponding to two maximum residual Doppler shifts of f _d = 750 Hz and f _d = 1.5 kHz and maximum user equipment velocity of 1000 km/h, LEO satellite altitude, h = 600 km and beam footprint diameter, d = 20 km is shown in FIG. 8a. The AM/AM and AM/PM characteristics of a typical satellite TWTA provided by European Space Agency is used to represent nonlinearity. The model parameters for simulation of the amplitude and phase responses of the HPA are given in ‘A. Jayaprakash, H. Chen, P. Xiao, B.G. Evans, Y. Zhang, J.Y. Li, and A.B. Awoseyila, “Analysis of candidate waveforms for integrated satellite terrestrial 5G systems” in 2019 IEEE 2nd 5GWorld Forum (5GWF) , Sep. 2019, pp. 636–641 ‘. The phase noise is simulated using the S-band satellite phase noise mask parameters in ‘3GPP, “Key satellite parameters and simulation assumptions for NTN” 3 ^rd Generation Partnership Project (3GPP) , Discussion RAN1-96, 04 2019, R1-1905216 ‘. One can employ DFT-spread-OFDM waveform corresponding to FFT-size, N = 1024, subcarrier spacing 15 kHz and the cyclic prefix length 72 is modulated using 4-QAM. The C-ELM and A-CELM is trained using block pilots corresponding to one DFT-s-OFDM symbol. In order to facilitate comparison, the performance curve of an ideal pre-distorter which perfectly linearizes the power amplifier and without phase noise and I/Q imbalance is also included. It is clearly observed that the A-CELM, which utilizes the impropriety of the received signal, shows significant performance gain compared to CELM. The A-CELM also shows improved performance compared to the perfect pre-distorter, which infers that even though the non-linearity, phase noise and I/Q imbalance are absent for the ideal pre-distorter, the increase in BER compared to A-CELM is attributed to the distortion due to residual Doppler shift induced distortion. The A-CELM is more effective in combating the distortions due to non-linearity, phase noise, I/Q imbalance and Doppler shift.

The BER versus SNR performance comparison corresponding to maximum residual Doppler shifts of f _d = 1.5 kHz, in the presence of multipath propagation for LEO satellite elevation angle of 10° is shown in FIG. 8b and FIG 8c. The performance curves corresponding to an ideal pre-distorter (PD) , with zero-forcing (ZF) equalization assuming perfect channel knowledge, in the absence and presence of phase noise and IQ imbalance is also shown for comparison. The multipath channel is simulated using the TDL channel model recommended by 3GPP (see ‘3GPP. “Study on New Radio (NR) to support non-terrestrial networks” 3 ^rd Generation Partnership Project (3GPP) , Technical Report (TR) RAN-80, 09 2020, version 15.4.0’ ) for non-line-of-sight satellite to user link in sub-urban environment, which is used to generate the impulse response corresponding to each tap at LEO satellite elevation angle (EA) of 10°. A half-rate convolutional code with the constraint length equal to 7 is employed for channel coding. The BER versus SNR performance comparison for delay spread corresponding to 10 ns and 50 ns are shown in FIG. 8b and FIG. 8c, respectively. A-CELM and CELM are compared with ideal predistortion and zero forcing equalization assuming perfect channel knowledge for the following scenarios 1) with impairments (delay spread, Doppler, phase noise, nonlinearity, IQ imbalance) , 2) without impropriety (zero IQ imbalance) and 3) without impairments (zero Doppler, zero phase noise and zero IQ imbalance) . The superiority in performance of the A-CELM method is prominent in the case of coded systems and delivers significant performance gain compared to all the other benchmark schemes.

To demonstrate the robustness of A-CELM against impropriety of the received constellation, the BER performance comparison for different values of I/Q phase imbalance is illustrated in FIG. 9a for a coded system at the S-band, with the channel delay spread of 50 ns and maximum residual Doppler shift, f _d = 750 Hz at SNR = 10dB. The CELM suffers a degraded BER performance with increasing impropriety whereas the A-CELM exhibits strong resilience against the signal impropriety. The BER curves of ideal PD and ZF which are not varying with increased I/Q phase imbalance corresponding to the scenarios without impropriety.

In order to illustrate the robustness under different Doppler conditions, the BER versus residual Doppler shifts for a fixed delay spread and SNR = 10dB, is shown in FIG. 9b. Even though the ideal PD and ZF method in the absence of impairments perform better than CELM, the A-CELM still delivers much better performance.

To demonstrate the capability of A-CELM for combating the various impairments under different delay-Doppler conditions, we compare the performance with different delay and Doppler spreads at SNR = 10dB in FIG. 10. The superiority in the performance of A-CELM is again ascertained over CELM and the ideal PD and ZF for all the different combinations of delay spreads and Doppler shifts.

FIG. 11 shows a method 1100 according to this disclosure. The method 1100 may be performed by the device 100 or the device 110. Accordingly, the method 1100 may be performed by a receiver 200.

The method comprises a step 1101 of obtaining a received signal 101 and one or more pilot symbols 102, which are received by the receiver 200 over a channel. The method 1100 may further comprise, in a first alternative which may be carried out by the device 100, a step 1102 of determining a data-regularized covariance matrix 103 based on both the received signal 101 and the one or more pilot symbols 102, and a step 1103 of determining an estimate 104 of the received signal 101 based on the received signal 101 and the data-regularized covariance matrix 103. The method 1100 may also comprise, in a second alternative which may be carried out by the device 110, a step 1104 of training a machine learning model 111 based on the one or more pilot symbols 102, and a step 105 of determining the estimate 104 of the received signal 101 by applying the trained machine learning model 111 to the received signal 101.

The present disclosure has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed matter, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

A device (100) for a receiver (200) , the device (100) being configured to:

obtain a received signal (101) and one or more pilot symbols (102) , which are received by the receiver (200) over a channel;

determine a data-regularized covariance matrix (103) based on both the received signal (101) and the one or more pilot symbols (102) ; and

determine an estimate (104) of the received signal (101) based on the received signal (101) and the data-regularized covariance matrix (103) .
The device (100) according to claim 1 configured to:

determine a channel estimate (301) of the channel based on the received signal (101) and the one or more pilot symbols (102) ;

determine a pilot-based covariance matrix (302) based on the one or more pilot symbols (102) and the channel estimate (301) ;

determine a data-based covariance matrix (303) based on the received signal (101) ; and

determine the data-regularized covariance matrix (103) by weighting the pilot-based covariance matrix (302) and the data-based covariance matrix (303) , respectively, based on one or more receiver parameters (305) of the receiver (200) .
The device (100) according to claim 2, configured to:

calculate a weight vector (306) based on the channel estimate (301) and the data-regularized covariance matrix (103) ; and

determine the estimate (104) of the received signal (101) by linearly combining the weight vector (306) and the received signal (101) .
The device (100) according to claim 2 or 3, wherein the one or more receiver parameters (305) comprise at least one of a number of antennas (201) of the receiver (200) , a number of user signals in the received signal (101) in case of a multi-user received signal, and a signal to noise ratio of the received signal (101) .
The device (100) according to one of the claims 2 to 4, configured to:

determine one or more scenario parameters (307) based on the received signal (101) ; and

determine the channel estimate (301) based on the received signal (101) , the one or more pilot symbols (102) , and the one or more scenario parameters (307) .
The device (100) according to claim 5, wherein the one or more scenario parameters (307) comprises at least one of a delay spread of the received signal (101) and a Doppler shift of the received signal (101) .
The device (100) according to one of the claims 1 to 6, configured to:

calculate a mixing factor (308) based on the one or more receiver parameters (305) ; and

weight the pilot-based covariance matrix (302) and the data-based covariance matrix (303) , respectively, according to the mixing factor (308) .
The device (100) according to claim 3 or 4 and according to claim 6 or 7, configured to calculate the mixing factor (308) based on the one or more receiver parameters (305) and the one or more scenario parameters (307) .
The device (100) according to claim 7 or 8, comprising a trained model (309) configured to calculate the mixing factor (308) based on the one or more receiver parameters (305) .
The device (100) according to claim 9, wherein the trained model (309) is a trained neural network.
The device (100) according to one of the claims 1 to 10, wherein the received signal (101) is an orthogonal frequency-division multiplexing, OFDM, signal.
The device (100) according to one of the claims 1 to 11, wherein the received signal (101) is a multi-user signal or a single-user signal.
A device (110) for a receiver (200) , the device (110) being configured to:

obtain a received signal (101) and one or more pilot symbols (102) , which are received by the receiver (200) over a channel;

train a machine learning model (111) based on the one or more pilot symbols (102) ; and

determine an estimate (104) of the received signal (101) by applying the trained machine learning model (111) to the received signal (101) .
The device (110) according to claim 13, wherein the trained machine learning model (111) is an augmented complex extreme learning machine, A-CELM, wherein the A-CELM has only one hidden layer (501) comprising hidden nodes (502) and the complex conjugate (503) of the hidden nodes (502) .
A receiver (200) comprising:

one or more antennas (201) ; and

the device (100, 110) according to one of the claims 1 to 14;

wherein the receiver (200) is configured to receive the received signal (101) and the one or more pilot symbols (102) over the channel with the plurality of antennas (201) and to provide them as input into the device (100, 110) , and the device (100, 110) is configured to determine the estimate (104) of the received signal (101) based on the input.
A method (1100) for a receiver, the method comprising:

obtaining (1101) a received signal (101) and one or more pilot symbols (102) , which are received by the receiver (200) over a channel;

wherein the method (1100) further comprises:

determining (1102) a data-regularized covariance matrix (103) based on both the received signal (101) and the one or more pilot symbols (102) ; and

determining (1103) an estimate (104) of the received signal (101) based on the received signal (101) and the data-regularized covariance matrix (103) ;

or wherein the method (1100) further comprises:

training (1104) a machine learning model (111) based on the one or more pilot symbols (102) ; and

determining (1105) an estimate (104) of the received signal (101) by applying the trained machine learning model (111) to the received signal (101) .
The method (1100) according to claim 16, wherein the method (1100) comprises:

determining a channel estimate (301) of the channel based on the received signal (101) and the one or more pilot symbols (102) ;

determining a pilot-based covariance matrix (302) based on the one or more pilot symbols (102) and the channel estimate (301) ;

determining a data-based covariance matrix (303) based on the received signal (101) ; and

determining the data-regularized covariance matrix (103) by weighting the pilot-based covariance matrix (302) and the data-based covariance matrix (303) , respectively, based on one or more receiver parameters (305) of the receiver (200) .
A computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform the method (1100) according to claim 16 or 17.