WO2022053552A1 - Detection of single-tone frequency hopping random access preamble - Google Patents

Abstract

The invention provides a method and system for the efficient and low-complexity detection of a single-tone frequency hopping random access preamble in a received OFDM signal. It applies specifically to the identification of UEs in a Narrowband Internet-of-Things, NB-IoT, setup, wherein a base station needs to detect UEs with a low number of preamble repetitions, so as to reduce the number of retransmissions.

Description

DETECTION OF SINGLE-TONE FREQUENCY HOPPING RANDOM ACCESS PREAMBLE

Technical field

The invention lies in the field of telecommunications. In particular, the invention relates to a method and system for efficient preamble detection and time-of-arrival estimation for single-tone frequency hopping random access in Narrowband-Intemet-of-Things, NB-IoT, systems.

This work was supported by the Luxembourg National Research Fund, FNR, in the framework of the FNR- IPBG project ’’INSTRUCT: Integrated Satellite-Terrestrial Systems for Ubiquitous Beyond 5G Communications” .

Background of the invention

In known receivers of NB-IoT systems, it is difficult to efficiently and accurately conclude to the presence of a preamble and to achieve timing synchronization from a physical random access channel NPRACH waveform. The invention aims at resolving at least some of the drawbacks that arise in known methods and systems.

The main goal of the upcoming internet of things, loT, is to interconnect various kinds of devices in order to make existing systems more intelligent, responsive, and robust. It is envisioned that loT will have a considerable economic and societal impact. [1] reports that the number of loT connected devices expected to exceed 4.1 billion by 2024. This results in a variety of use cases with different requirements and methodologies leading to a necessity of tailored communication technology. Correspondingly, many technologies appeared in both licensed and unlicensed markets, cf. [2]— [4], and among them the Narrowband-IoT, NB-IoT, which is a recent cellular technology standardized by 3rd Generation Partnership Project, 3GPP, in 2016 [4], [5], It aims at providing connectivity to billions of loT devices, supporting low device cost, long battery lifetime, and wide coverage. NB-IoT inherits from the existing long term evolution, LTE, technology. The radio access is based on orthogonal frequency-division multiple access, OFDMA, for downlink and single-carrier frequency division multiple access, SC-FDMA, for uplink with 180 kHz system bandwidth. The reason for that was to allow a better co-existence with Legacy LTE, the reuse of existing infrastructures, and reduction of time-to-market. However, some changes have been introduced in NB-IoT compared to LTE to ensure the aforementioned objectives. In [6] and [7], these changes are summarized and discussed.

One of the differences between NB-IoT and LTE is in the so-called random access, RA, procedure. A new waveform is designed for the RA in NB-IoT compared to the traditional signaling using Zadoff-Chu sequences employed in LTE RA [8], This change has been introduced in order to reduce the peak-to- average power ratio, PAPR, thus improving the battery lifetime of the device and the coverage in the context of loT network. It is worth noting that high PAPR requires a large backoff for the power amplifier, PA, in general, which leads to a low efficiency of the PA and correspondingly a low battery lifetime. Moreover, high PA backoff reduces the radiated signal power and reduces the coverage. In contrast, the new NBIoT physical random access channel, NPRACH, waveform has very good PAPR properties. The NPRACH waveform is specified as a single-tone frequency hopping preamble [8], On the other hand, the new waveform is still compatible with the LTE SC-FDMA and OFDMA schemes, and it is typically treated as an OFDM signal with one sub-carrier [8], [9],

Similarly to the RA in LTE, the RA in NB-IoT manages the uplink synchronization and the requests of scheduling of data transmissions. In this context, the uplink synchronization means that the Base Station, BS, has to detect (and identify) all active user equipments, UEs, in the coverage area of the BS and estimate their Round-Trip Delays, RTDs. Through this, the delay between each UE and the BS is acquired, which represents a common timing reference. The acquired delay allows the B S to perform timing advance needed to keep the orthogonality among multiple UEs, which is typically required in SC-FDMA systems. The estimation of RTD refers to a Time-of-arrival, ToA, estimation, whereas the user detection refers to NPRACH preamble detection. It is worth noting that this operation is essential for a successful system operation. In fact, RA is the first phase of system operation and covers the first messages from each UE to the BS. Hence, a wrong detection and/or an erroneous ToA estimation would lead to increased latency and performance degradation for the system. In practice, when a user is not correctly detected, another round of RA procedure is started, which implies an increased power consumption as well as additional delays in data packet transmission. The latter is also responsible for a decrease of the overall system throughput. On the other hand, when the detection is correct and only the ToA is inaccurate, the timing synchronization might be lost, which may lead to an increased packet error rate. Furthermore, the performance degradation depends on the ToA error: large errors can completely damage the data exchange. In order to avoid this, 3GPP standard [10] provides the requirements for the maximum rate of wrong detections and for the maximum ToA error in NPRACH.

One of the challenges in any communication system is the presence of a random carrier frequency offset, CFO. It can be produced by imperfect local oscillators, LOs, Doppler shift, or downlink frequency synchronization errors in case of 3 GPP based communication.

For the ToA estimation in SC-FDMA system, the CFO contributes to the phase rotation of the received complex signal in a similar way as the timing offset. Correspondingly, it is difficult to separate the influence of CFO and ToA on the received signal, such that the accuracy of the ToA estimation is typically very low in presence of CFO. In this context, there are few works that addressed the NPRACH reception design. The first work in this domain [9] has been filed [11]. The proposed technique is based on a two- dimensional, 2D, Fast Fourier Transform, FFT, for a joint estimation of CFO and ToA. Then the preamble detection is performed comparing the metric used for the ToA estimate with a predefined threshold. The main drawback of this method is its computational complexity, which is extremely high due to the 2D- FFT, which makes this method impractical.

In [12], a low-complexity NPRACH receiver design has been proposed. It decouples the detection problem from the estimation problem. The detection is based on energy detection scheme and the collected signal energy is compared with the optimal threshold derived by the authors. The estimation is based on the CFO estimation and subsequent compensation. Then, the ToA is estimated from the phase of the received signal. In [12], the performance of the detection part was provided with the assumed absent CFO. This is not a realistic assumption for practical scenarios, where CFO is present and impacts the signal-to-noise ratio, SNR. Moreover, the method has a processing delay that increases with the number of preamble repetitions leading to a less efficient real-time system as pointed out in [13], Another relevant work that has been recently submitted for a publication is [13], The author provides a detailed and useful mathematical model for the NPRACH signals. However, the proposed method supports only small ToA values, i.e. ToA < 66.7 us (which is defined as format 0 in the 3GPP Standard). In this method, at first the CFO is estimated (with capability limitation, i.e. the maximum tolerated CFO is < 357 Hz) from the received signal and then compensated. After that, the ToA estimation is performed using one-dimensional, ID, FFT, which leads to lower computational complexity compared to [9], [11], The detection part is done by comparing the metric based on ToA estimate with a predefined threshold, which has been obtained experimentally. Unfortunately, this method has some weaknesses with respect to both performance and complexity. Firstly, it is limited to NPRACH format 0 (ToA < 66.7 us), such that users with larger ToA (e.g. NPRACH format 1) cannot be detected. Secondly, the estimation and the compensation of the CFO leads to a degradation of the ToA estimation performance in case of inaccurate CFO estimation and compensation. Furthermore, both CFO estimation and compensation contribute to the receiver complexity.

Based on this state-of-the-art analysis, it becomes apparent that all the existing techniques follow the classical way of dealing with a synchronization problem (i.e. either CFO estimation and compensation before timing estimation or joint frequency and timing estimation). Though this, the system performance in known solutions deteriorates in terms of energy efficiency, flexibility, and/or reliability.

Technical problem to be solved

It is an objective of the present invention to present a method and system which overcome at least some of the disadvantages of the prior art.

Summary of the invention

In accordance with a first aspect of the invention, a method for detecting a single-tone frequency hopping random access preamble at a receiver is provided. The method comprises the steps of receiving and demodulating, using receiving means, a signal on an OFDM data communication channel, the demodulated signal comprising a sequence of groups of symbols SGi, 0 < i < m, wherein each group SGi has at least one symbol, and wherein each group is received on one of a plurality of available channel sub-carriers; using data processing means, determining a frequency hop for each pair of symbol groups having consecutive indexes (SGi, SGi+1) in said sequence, and associating said frequency hop with the symbol group SGi having the lower index i; using data processing means, generating an all-zero one-dimensional indexed array A in a memory element, wherein the index spans all the determined frequency hops; - using data processing means, generating a differential symbol Zi,1 for each symbol group SGi, by multiplying a representative symbol of said group SGi with the conjugate of a representative symbol of symbol group SGi+1; - using data processing means, adding the resulting differential symbol Zi,1 to the position in said array A that corresponds to the expected frequency hop determined for said symbol group SGi; - using data processing means, performing a one-dimensional Fast Fourier Transform of the resulting array A and storing the coefficients in a corresponding FFT array FFT(A); - using data processing means, determining the presence of a preamble subject to the comparison of the maximum absolute value of said FFT(A) array with a predetermined threshold value. In accordance with an aspect of the invention, a method for detecting a single-tone frequency hopping random access preamble at a receiver is provided. The method comprises the following steps: a) receiving and demodulating , using receiving means, a signal on an orthogonal frequency-division multiplexing, OFDM, data communication channel, the demodulated signal comprising a sequence of groups of symbols SG_i , 0 ≤ i ≤ m, wherein each group of symbols SG_i has at least one symbol, and wherein each group of symbols SG_i is received on one of a plurality of available channel sub-carriers; b) using data processing means, generating a differential symbol Z_i,1 for each pair of groups of symbols (SG_i, SG_i+1), by multiplying a representative symbol of the first group of symbols SG_i with the conjugate of a representative symbol of the following group of symbols SG_i+1; c) using data processing means, determining an expected frequency hop between the groups of symbols of each pair of groups of symbols (SG_i, SG_i+1), having consecutive indexes in said sequence, and associating said expected frequency hop with the differential symbol Z_i,1 that corresponds to the groups of symbols (SG_i, SG_i+1); d) using data processing means, generating an all-zero one-dimensional array v in a memory element, the array v having a number of positions that spans a range comprising all the determined expected frequency hops; e) using data processing means, adding each differential symbol Z_i,1 to the value at the position in said array v that corresponds to the expected frequency hop, which is associated with the differential symbol Z_i,1; f) using data processing means, performing a one-dimensional Fast Fourier Transform, FFT, of the resulting array v and storing the coefficients in a corresponding FFT array FFT(v); g) using data processing means, determining the presence of a preamble subject to the comparison of the maximum absolute value of said FFT(v) array with a predetermined threshold value. Preferably m is an integer value corresponding the number of groups of symbols that are received. Preferably, the method may further comprise the step of: h) upon detection of a preamble, estimating, using data processing means, a transmission delay between the transmitter of said preamble and the receiver, based on the position of said maximum absolute value in said FFT(v) array. The method may preferably be a method of detecting the presence of a User Equipment that transmits said received signal, wherein the User Equipment is identified upon detection of said preamble. Preferably, step b) may further comprise: b1) generating at least one additional differential symbol Z_i,c for each pair of groups of symbols (SG_i, SG_i+c), having an index difference c (1<c≤cmax) in said sequence, by multiplying a representative symbol of the first group SG_i with the conjugate of a representative symbol of the group of symbols SG_i+c; and step c) may further comprise: c1) determining at least one additional expected frequency hop between the groups of symbols of each pair of group of symbols (SG_i, SG_i+c), (1<c≤cmax), multiplying the determined expected frequency hop by M/c, M being the Minimum Common Multiple of all c≤cmax, and associating the resulting frequency hop with the differential symbol Z_i,c to the groups of symbols (SG_i, SG_i+c); c2) updating the expected frequency hops determined at step c) by multiplying them with M, M being the Minimum Common Multiple of all c≤cmax; Further, step e) may preferably comprise the preliminary step of e1) multiplying the phases of the differential symbols Z_i,1 by M and multiplying the phases of the differential symbols Z_i,c by M/c, M being the Minimum Common Multiple of all c≤cmax, prior to adding the resulting differential symbols Z’_i,1, Z’_i,c to the respective values at the positions in said array v that correspond to the expected frequency hops that are associated with said differential symbols Z’_i,1, Z’_i,c. Said representative symbol of a groups of symbols SG_i may preferably be determined by summing up all the symbols of said group of symbols. Preferably, said representative symbol of a group of symbols SG_i may be any of the symbols received for said group. Preferably, said representative symbol of a group of symbols SG_i may be any but the first of the symbols received for said group. Said representative symbol of a group of symbols SG_i may preferably be determined by averaging all the symbols of said group. Preferably, each group of symbols may comprise a cyclic prefix followed by a sequence of preferably 5 symbols Preferably, a pattern of expected frequency hops may be pre-provided in a memory element to which the data processing means have read access. Preferably, said sequence of groups of symbols may comprise at least one repetition of a frequency hopping pattern. Preferably, each repetition of said frequency hopping pattern may start at a randomly or pseudo-randomly determined subcarrier frequency.

Preferably, the pattern of expected frequency hops may comprise at least one repetition of an expected frequency hopping pattern. Preferably, each repetition of said frequency hopping pattern may start at a randomly or pseudo-randomly determined subcarrier frequency.

Said signal may preferably be received on a Narrowband Internet of Things, NB-IoT, Physical Random Access channel, NPRACH.

Said array v may preferably have a size of 2h+l positions, wherein h is the largest frequency hop that has been determined, and wherein at the central position corresponds to a frequency hop equal to 0.

Preferably the value cmax providing the maximum distance, or reception time, between groups of symbols in the computation of differential symbols may be equal to 2.

Said predetermined threshold value may preferably correspond to a probability of at least 90% and preferably of at least 99% of said single-tone frequency hopping random access preamble being present in said received signal. Preferably the threshold value may correspond to a probability of 99,9% of said single-tone frequency hopping random access preamble being present in said received signal. The predetermined threshold value may preferably depend on the preamble that is to be detected.

In accordance with a further aspect of the invention, a system comprising data receiving means having at least one antenna, and a data processor if provided. The data processor is configured for implementing the steps in accordance with aspects of the invention.

In accordance with another aspect of the invention, a base station for a Narrowband-Internet of Things system is provided. The system complies with aspects of the invention and comprises data receiving means for receiving signals from User Equipment devices.

In accordance with yet another aspect of the invention, a computer program comprising computer readable code means is provided, which, when run on a computer, causes the computer to carry out the method according to aspects of the invention.

In accordance with a final aspect of the invention, a computer program product comprising a computer readable medium on which the computer program according to aspects of the invention is stored. In order to mitigate the aforementioned weaknesses, the aspects in accordance with the present invention propose a novel efficient NPRACH reception and signal processing technique, which is resistant to the presence of frequency errors. The main contributions may be summarized as follows:

1) Design of an efficient NPRACH reception method that allows to detect the NPRACH preamble and to estimate the ToA. The technique can address all NPRACH formats, and it is designed in a way that the CFO present in the received signal is perfectly eliminated. Hence, no estimation and compensation of the CFO are required. This allows not only to reduce the computational complexity, but also to avoid ToA errors coming from an imperfect CFO estimation and compensation. An extension of the method is also provided as a generalization of the proposed method to further improve the performance;

2) The obtained results demonstrate a large margin compared to 3 GPP requirements and the superiority of the proposed method compared to known solutions. Furthermore, these interesting results are obtained with less complexity compared to the complexity of known solutions. The comparison shows 50% of complexity reduction compared to [13], This high performance can be supposedly exploited in order to reduce the overhead (e.g. the NPRACH preamble length) leading to increased spectral and energy efficiencies, which are crucial in the context of loT systems.

Brief description of the drawings

Several embodiments of the present invention are illustrated by way of figures, which do not limit the scope of the invention, wherein:

Figure 1 provides a workflow illustrating the main steps of a method in accordance with a preferred embodiment of the invention;

Figure 2 provides a schematic illustration of a receiving system in accordance with a preferred embodiment of the invention;

Figure 3 illustrates received groups of symbols at their respective channel subcarriers;

Figure 4 illustrates frequency hop patterns for twelve transmitters transmitting concurrently on a shared time/frequency resource in accordance to predetermined preamble patterns;

Figure 5 illustrates a cumulative probability density function used to determine a predetermined threshold value in accordance with a preferred embodiment of the invention;

Figure 6 illustrates an interpolation step used in a method in accordance with a preferred embodiment of the invention;

Figure 7 illustrates received groups of symbols at their respective channel subcarriers, and illustrates the computation of differential symbols as well as of the array v in accordance with a preferred embodiment of the invention;

Figure 8 illustrates FFT coefficients obtained using a method in accordance with a preferred embodiment of the invention;

Figure 9 illustrates received groups of symbols at their respective channel subcarriers, and illustrates the computation of differential symbols as well as of the array v in accordance with a preferred embodiment of the invention; Figure 10a illustrates the performance of methods in accordance with preferred embodiments of the invention, compared to prior art methods, in the presence of AWGN;

Figure 10b illustrates the performance of methods in accordance with preferred embodiments of the invention in the presence of AWGN;

Figure 1 la illustrates the performance of methods in accordance with preferred embodiments of the invention, compared to prior art methods, for an extended pedestrian A model channel with 1Hz Doppler;

Figure 1 lb illustrates the performance of methods in accordance with preferred embodiments of the invention for an extended pedestrian A model channel with 1Hz Doppler;

Figure 12a illustrates the performance of methods in accordance with preferred embodiments of the invention, compared to prior art methods, for an extended typical urban channel model with 1Hz Doppler;

Figure 12b illustrates the performance of methods in accordance with preferred embodiments of the invention for an extended typical urban channel model with 1Hz Doppler;

Figure 13a illustrates the performance of methods in accordance with preferred embodiments of the invention for 12 active UEs an extended pedestrian A model channel with 1Hz Doppler;

Figure 13b illustrates the performance of methods in accordance with preferred embodiments of the invention for 12 active UEs an extended typical urban channel model with 1Hz Doppler;

Detailed description

This section describes aspects of the invention in further detail based on preferred embodiments and on the figures, without being limited thereto.

Figure 1 outlines the main method steps in accordance with a preferred embodiment of the invention, while Figure 2 illustrates features of a system for implementing said method.

At a first step of the proposed method, a receiver 100 in a wireless communication network using orthogonal frequency -division multiplexing, OFDM, data communication channels, receives a signal 10. OFDM communication systems, the corresponding transmitters and receivers, as well as the implied signaling and modulation are well understood concepts in the art. They will not be explained in detail in the context of the present invention. The description focuses on the features that are most relevant for understanding the invention: the processing of a received signal, which may comprise a single-tone frequency hopping random access preamble, identifying its transmitter as being a User Equipment whish tries to establish data communication with the receiver, which is preferably a receiver 100 in a cellular data communication network.

Using known receiving means 110 comprising demodulating and decoding means such as a demodulator and a decoder, and at least one antenna, the signal 10 is received and demodulated. It comprises a sequence of groups of symbols SG, , 0 < i < m, m being an integer, wherein each group of symbols SG, has at least one symbol. The groups of symbols are sequentially received in time and on different subcarriers of the OFDM scheme, they may therefore be referenced using an index i that increases with time. Each group of symbols SG, is received on one of a plurality of available channel sub-carriers. Aside from a group prefix, each symbol within a given group may be identical. Typically the symbols are stored in a memory element of the receiver once they have been decoded. This corresponds to step a).

At step b) data processing means 120 are used to compute a differential symbol Zj i for each pair of groups of symbols (SG„ SG,_+;), by multiplying a representative symbol of the first group of symbols SG, with the conjugate of a representative symbol of the following group of symbols SG,_+;. The representative symbol may be any of the received symbols of the corresponding group. Alternatively the representative symbol may correspond to the sum of all symbols in the group, or to the average of all the symbols in the group. The data processing means 120 preferably comprise a data processor, which is programmed by appropriate software code for executing the required computations. Alternatively, the data processing means may comprise specific hardware such as an application specific integrated circuit, ASIC, designed for executing the required computations. While in Figure 2, the processing means are shown as being part of the signal receiving device 100, the invention is not limited to this example. The processing means may alternatively located at a distinct remote device having access to the received groups of symbols. The connection between the receiving means and the processing means may for example include a wired data connection bus, or a wired or wireless data communication channel, without departing from the scope of the present invention.

At a next step, c) using the data processing means 120, a frequency hop between the groups of symbols of each pair of groups of symbols (SG„ SG,_+;), having consecutive indexes in said sequence is determined. The returned frequency hop value may for example be a number of frequency subcarriers, which is then associated with the differential symbol Z, _x that corresponds to the groups of symbols (SG„ SG,_+;). A frequency hop or jump preferably corresponds to the difference between subcarrier indexes on which two consecutive groups of symbols are received. Preferably, a predetermined preamble pattern or sequence of expected frequency hops is pre-stored in a memory element to which the data processing means 120 have read access. In accordance with this pattern of expected frequency hops, the expected frequency hop values are associated with the corresponding differential symbols. Alternatively, the pattern may be computed using the data processing means.

An all-zero one-dimensional array v is initialized in a memory element 130 to which the data processing means 120 have read/write access. The number of positions of the array v, or equivalently, the length of the array, is such that is spans a range comprising all the determined expected frequency hops: there is at least one distinct position for each identified frequency hop. Ideally, the length of the array is such that it is capable of storing 2h+ 1 distinct values, where h is the largest identified frequency hop in absolute value. This allows all values from -h to +h to be stored at a distinct position of the array. This correspond to step d). At step e), each computed differential symbol Z^ is added to the (initially zero) value at the position in said array v that corresponds to the expected frequency hop, which is associated with the differential symbol Zj E.g., if a frequency hop of 3 subcarriers has been determined between the groups of symbols SG₂ and SG₃, then the corresponding differential symbol Z_2ji is added to position v[3]. If several frequency hops that correspond to a jump of 3 subcarriers are determined for different pairs of groups of symbols, the corresponding differential symbols will end up being summed up at position 3 of the array v, once step e) has been executed for each computed differential symbol.

A one-dimensional Fast Fourier Transform, FFT, of the resulting filled-in array v is performed at step f), and the coefficients are stored in a corresponding FFT array FFT(v) in a memory element to which the data processing means have read/write access.

The presence of a preamble is detected subject to the comparison of the maximum absolute value of said FFT(v) array with a predetermined threshold value. This corresponds to step g). The threshold value is preferably experimentally or empirically determined prior to the reception of the signal 10. It is preferably selected so that if the maximum absolute value of said FFT(v) array is larger than the threshold value, then the probability that the preamble pattern, which the method intends to detect, is present in the signal 10 is larger than 99,9%. As such the threshold value depends on the preamble pattern that is to be detected, and on the allowable probability of false detection. If the received symbols were transmitted using a frequency hopping pattern that matches the predetermined preamble pattern or sequence of frequency hops used at step c), then the corresponding transmitter may be identified by the receiver.

The method that in accordance with this preferred embodiment extends straightforwardly to the case in which the differential symbols are computed as well for pairs of groups of symbols that do not follow each other immediately in the received signal 10, but which are farther spaced in time. This case is also detailed here below.

In what follows, further preferred embodiments of the method in accordance with the invention are described with specific emphasis on the NB-IoT standard, in order to provide specific a specific use case and application scenario. It is understood that the invention, or the computational details explained in the context of these embodiments, are not limited to the use of this standard.

The narrowband internet of things, NB-IoT, standard is a new cellular wireless technology, which has been introduced by the 3^rd Generation Partnership Project, 3GPP, with the goal to connect massive low-cost, low-complexity and long-life loT devices with extended coverage. In order to improve power efficiency, 3GPP proposed a new Random Access, RA, waveform for NB-IoT based on a single-tone frequency hopping scheme. RA handles the first connection between user equipments, UEs, and the base station, BS. Through this, UEs can be identified and synchronized with the BS. In this context, receiver methods for the detection of the new waveform should satisfy the requirements on the successful user detection as well as the timing synchronization accuracy. This is not a trivial task, especially in the presence of radio impairments like carrier frequency offset, CFO, which constitutes one of the main radio impairments besides the noise. In order to tackle this problem, a new receiver method for the NB-IoT Physical Random Access Channel, NPRACH is proposed. The method in accordance with embodiments of the invention is designed to eliminate the CFO without any additional computational complexity and supports all NPRACH preamble formats. The associated performance has been evaluated under 3GPP conditions. A very high performance compared both to 3GPP requirements and to the existing state-of-the-art methods in terms of detection accuracy and complexity is observed. For the sake of clarity, the same notation and same variable definitions as provided in the 3GPP standard ([8], [15]) and previous works ( [13], [14]) are used throughout the remainder of the description.. The RA preamble in NB-IoT known as NPRACH preamble was originally proposed by [16]–[19] and then adopted by 3GPP and integrated in NB-IoT Release 13 [4]. It is based on single-tone, frequency-hopping scheme as illustrated in Figure 3. The preamble consists of four ’symbol groups’, SGs. Each SG is composed of five identical symbols with a cyclic prefix, CP, and occupies one tone of 3.75 kHz in frequency domain. The CP length is designed according to the targeted cell size. It can be either 66.67 us for preamble format 0 (i.e. corresponding to a cell radius of 10 km), or 266.67 us for preamble format 1 (i.e. corresponding to a cell radius of 40 km). Traditionally, the preamble is considered as a single-tone OFDM symbol with 3.75 kHz subcarrier spacing. This single tone OFDM symbol signal, however, hops between frequency tones from SG to SG following a predefined pattern to enable a satisfactory ToA estimation. In the 3GPP standard, four SGs are treated as the basic unit of the preamble. This basic unit can be repeated up to 2^j, j = {0,1,...,7} times for coverage extension. Accordingly, the length L of a preamble equals 4 × 2^j SGs [9]. The hopping pattern is fixed within the basic unit of four SGs. Between the SGs {0,1} and {2,3} the hopping distance equals one subcarrier spacing. Between the SGs {3,4} the distance equals six subcarrier spacings. However, when repetitions are configured, the hopping between the basic units is no longer fixed, but follows a pseudo-random selection procedure defined in [8]. In an NB-IoT system, each UE determines the time and frequency resources to transmit the NPRACH preamble based on the system information block broadcasted by the BS during the downlink. According to the 3GPP standard [8], [15], the possible resource configurations are as follows: ^• is the period of time within which NPRACH can be transmitted. Possible values are: 40, 8^{0, 160, 240, 320, 640, 1280, 2560 ms.} _{• denotes the number of NPRACH preamble repetitions per attempt. Possible values are: 1, 2,} 4, 8, 16, 32, 64, 128. • corresponds to the index of the first subcarrier allocated to NPRACH within 180 kHz bandwidth. Possible values are: 0, 12, 24, 36, 2, 18, 34. ^• corresponds to the number of subcarriers allocated to NPRACH. Possible values are: 12, 24, 36, 48. • corresponds to NPRACH transmission starting time. Possible values are: 8, 16, 32, 64,

128, 256, 512, 1024 ms. NPRACH transmission can start only a corresponding number of subframes after the first subframe in radio frames fulfilling where n_f is the system frame numbe

In practice, each UE selects randomly the starting subcarrier n_init from for the first SG. The next 3 subcarrier locations (corresponding to the next 3 SGs) are determined by a specific algorithm (based on modulo-sum) which depends only on the location of the first subcarrier. For the subcarrier selection of the first SG of the next repetition, a pseudo-random hopping, which utilizes a cell- ID as its initial seed, is applied. The subcarrier selection for the subsequent SGs depends only on the outcome of pseudo-random hopping [8]. Note that with a single-tone and subcarrier spacing of 3.75 kHz, a cell can configure 12, 24, 36, or 48 starting subcarriers for the NPRACH within the 180 kHz NB-IoT system bandwidth. This means that up to 48 orthogonal preambles are available to transmit an NPRACH. Each UE randomly selects one preamble among the 48 available and transmits it to the BS in the NPRACH resource. Figure 4 shows an example of 12 multiplexed Ues in an NPRACH resource. It is noted that if the same preamble is selected by two or more Ues, a collision is declared. At the receiver side, the BS tries to identify all 48 frequency hopping patterns (i.e. preamble signatures). The ones successfully identified represent the active Ues. In this configuration, the k-th UE is identified by its n_init in the range

that allows to construct the pattern as explained above. Based on [9] and [13], the transmitted baseband signal for the NPRACH preamble can be written as follows:

where s_m,i[n] is the n-th sample of the time domain waveform of i-th symbol in m-th SG and S_m,i[k] denotes the i-th symbol on the k-th subcarrier during the m-th SG. Furthermore, n = [N_m,i −N_CP,...,N_m,i +N −1], i = [0,...,4], where N_m,i = mN_g + iN, N_g = N_cp + 5N is the size of one SG, N_cp is the size of CP, N is the size of a symbol. Before providing the model for the received signal, it is worth noting that the NB-IoT channel varies extremely slowly in time. This comes from the fact that NB-IoT is not intended to support high mobility of the devices [20]. Accordingly, the channel is assumed to be invariant in time within at least 3 SGs and flat within 45 kHz frequency band (i.e. 12 subcarriers). This means that the channel response does not change at least during 3 SGs within 45 kHz bandwidth. Based on [9] and [13], the n-th sample of i-th symbol in m-th SG of the received signal y_m,i[n] can be written as:

where f_off is the CFO normalized by the sampling frequency, D is the RTD normalized by the symbol duration; h_m is the channel coefficient at m-th SG. In addition, w_m,i[n] is complex additive white Gaussian noise, AWGN, with zero mean and variance N₀. By removing the CP (i.e. N_cp samples) and performing FFT, one obtains

where W_m,i[l] denotes the frequency response of the noise signal. By exchanging the variables n’ = n – N_m,i, (3) can be expressed as

The equation (4) shows that the received signal consists of a signal term , inter-carrier interference (ICI) term and a noise term (W_m,i).

As specified in [8], the symbols are all identically equal to 1 for any m, i and the same (m-th)

SG. Here, is the subcarrier occupied by m-th SG.

Assuming that ICI is negligible, when holds, the received signal becomes:

By combining the signals within the same m-th SG, yields SG-Sum (SG-S):

where W_m is the noise term. This result will be used in the description of preferred embodiments for the design of the proposed method for preamble detection and ToA estimation. The following preferred embodiment of the method according to the invention, based on the NB-IoT standard, aims at detecting the NPRACH preamble and estimating the ToA in presence of CFO. Unlike known synchronization schemes that either estimate jointly the timing offset with CFO or estimate and compensate the CFO in the received signal before estimating the timing, the proposed method eliminates perfectly the CFO and estimates directly the timing offset (i.e. ToA). For the proposed method and its extended version, different sets of the combinations of SGs are used. Accordingly, the essence of the proposed method only uses a small number of such combinations. In what follows, the corresponding embodiment of the method is referred to as ”Differential processing with minimum combinations”. The extended version of the method is based on a more advanced processing, which includes additional combinations of SGs. Thus, more information can be extracted from the received signal, which helps to improve the estimation accuracy. In what follows, the corresponding embodiment of the method is referred to as ”Differential processing with extended combinations”. A. Differential processing with minimum combinations 1) Elimination of the CFO and signal preparation: After reception of a signal on an OFDM channel, which corresponds to method step a), the received signal is further processed. At first, a differential processing of the neighbouring SGs is performed by multiplying the m-th SG-S with the complex conjugated (m + 1)-th SG-S:

where is the hopping step between the m-th and (m + 1)-th SGs and

is the noise term of Z_m,1. This operation is performed for all SGs including the pseudo-random hopping between the repetitions (if configured). This corresponds to method steps b) and c). Secondly, a vector or array v[n] of length 13 is constructed in step d). The vector is filled in at step e) in such a way, that the (7 + ∆(m))-th element of v[n] is equal to Z_m,1. The numbers 13 and 7 are selected according to the maximum subcarrier spacing between two consecutive SGs, which is assumed to be 6. Apparently, in order to account for both positive and negative values of ∆(m) in the range between -6 and 6, vector v[n] needs to have 13 elements, where the 7^th element corresponds to ∆(m) = 0. Note, that there might be multiple Z_m,1 with equal value of ∆(m), i.e. ∆(m₁) = ∆(m₂) with m₁ ≠ m₂, their values are summed up before being inserted in v[n]. To clarify this, Figure 7 illustrates an example of NPRACH preamble with two repetitions (i.e. two basic preamble units). As an example, in the figure it is assumed that the hopping steps of the preamble are ∆(m) = [1,6,−1,−3,−1,6,1]. Accordingly, a vector v[n] is obtained with 13 elements at respective positions between −6 and 6, i.e. v[n] = [0,0,0,Z_3,1,0,(Z_2,1 +Z_4,1),0,(Z_0,1 +Z_6,1),0,0,0,0,(Z_1,1 + Z_5,1)]. Note that the CFO is still present in the vector v[n], since it affects the phase of the symbols Z_m,1 that constitute it. Rather than estimating the CFO and compensating it in the signal as performed in [13], it is made sure that the CFO factor is common for all Z_m,1 symbols. This is valid, if a differential processing is considered only for neighbouring SGs (see (7)). Accordingly, and since the phase rotation of noise does not affect its probability distribution (due to the circular symmetry of the noise), one can pull the common factor e^{−j2πfoffNg} out of vector v[n] to obtain

such that v^’[n] is independent from f_off. Obviously, v’[n] only depends on ToA (vector v’[n] also contains the noise terms according to the derivations of Zm,1.), which has a similar impact on v’[n] like the classical frequency offset on the received signals in traditional wireless communications. Hence, in order to estimate ToA, the well-known Rife&Boorstyn (R&B) method (cf. [21]) is performed, which resembles an approximation of the maximum-likelihood frequency offset estimation. Accordingly, the next step is to perform an 1D-FFT on v[n], and take the absolute maximum of the results. This can be written as:

where N_FFT is the number of FFT points. Since the FFT is a linear operation, using (11), one can express

where U’[k] is independent from f_off. Hence, by taking the absolute of U[k] the impact of CFO given by ^{e- j2πfoffNg} term is eliminated, since it affects only the phase of U[k], not its magnitude. Combining non-coherently over the 2 receive antennas, leads to

Figure 8 shows an example of the 256-FFT spectrum of the vector v at SNR = -5 dB under AWGN channel. The next step is to determine X_max = max_k{X[k]} and k_max ∈ [0,N_FFT], for which X_max = X[k_max]. Similarly to the frequency estimation using the R&B method, the resolution of the ToA estimation (i.e. ) depends on the N_FFT, since it can be expressed as where ∆f is the subcarrier spacing of NPRACH (i.e.

3.75kHz). Of course, by increasing the number of FFT points a much better resolution and estimation accuracy can be achieved. At this stage, first a decision on the presence of the preamble is made, then the ToA is deduced. This corresponds to method step f) 2) Preamble detection at method step g): To declare the presence of the preamble, the metric X_max is compared to a predefined threshold τ. This threshold is preferably set through simulations. In practice the threshold can alternatively be determined experimentally. In order to determine the threshold, the metric X_max is first calculated via multiple attempts to receive a known preamble in absence of the useful signal, i.e. only noise is present. Then the cumulative distribution function, CDF, of the X_max values is obtained. The threshold τ is set equal to the X_max value, which pertains to the probability of 99.9% (corresponding to the false alarm rate of 0.1%) as shown in Figure 5. Taking into account all possible preamble lengths, every preamble repetition has its own threshold τ calculated as above and stored in a look-up table. The detection of the preamble (P_detection) is decided online (both signal and noise are present):

If the noise level varies considerably during the system operation, the predefined threshold τ may need to be calculated taking into account the noise power. In this case, the metric X_max obtained in absence of the useful signal is normalized by the noise power. Then, the threshold is determined in a similar way by selecting the value, which pertains to the probability of 99.9%. In this configuration, the decision for the preamble detection is done with the help of an estimate of the noise variance, which can be obtained from the collected statistics across symbol groups, repetitions and antennas. For this, the metric X_max is first normalized with the estimated noise variance. The result is compared with the threshold τ. Note that the threshold becomes independent from the noise and preamble parameters due to the normalization. However, this strategy requires an accurate estimation of the noise variance during the NPRACH reception as described in [13], which can be challenging in practice. 3) ToA calculation at method step h): If the presence of the preamble is declared, the ToA is calculated as follows (k_max can obtain values between 0 and N_FFT – 1, where k_max = 0 implies D = 0):

In order to further increase the accuracy of the estimation, a well-known and frequently used quadratic interpolation around the maximum X_max [22] is performed, and the location of the maximum of the interpolation function is computed. Accordingly, the final ToA estimate is given by:

where and α,β, and γ are the indices corresponding to

1], respectively, as shown in Figure 6.

It is worth noting here, that for NPRACH format 0, where the RTD is known to not exceed the CP length of 66.67 us, the maximum is determined only within the CP-window length plus the maximum tolerated error, which equals ±3.646us for NPRACH according to [10]. This reduces the probability of spurious peaks outside of the coverage area that may outperform the correct peak in some cases. Correspondingly, the method can be made more robust by reducing the search range. B. Differential processing with extended combinations The method proposed above can be extended to another embodiment in order to further improve the accuracy of ToA estimation. For this, more SG combinations within the preamble basic unit (i.e. 4 SGs) and over repetition (if configured) are considered. In particular, the focus is on combinations of SGs with indices that differ by at most c_max, where c_max is a strictly positive integer. If c_max = 1 holds, only the neighbouring SGs are combined according to the previously described embodiment, implying the minimum number of SG combinations. If c_max ≥ 2 holds, there are more possibilities for the SG combinations and these combinations are referred to as extended combinations. In this case all combinations c ≤ c_max are considered. The main difference between the method outlined above and its extended version is the way of how these extended combinations are incorporated in the calculation. For the m-th combination with the difference c between the SG indices, one multiplies the m-th SG-S with the conjugate of (m + c)-th SG-S:

where

is the hopping step between the m-th and (m+c)-th SGs, and is

the noise term of Z_m,c. Next, the minimum common multiple M of all c ≤ c_max is computed. Then, the phase of each Z_m,c is multiplied by the factor

in order to obtain the multiple of the CFO as a common factor for all Z_m,c. Thus:

One my notice that e^{−j2π(Mfoff)Ng} (the term containing CFO) is independent from c and hence it is a common factor for all

symbols. At this stage, the vector or array v[n] is constructed with length of 2L_m,c + 1, and filled with

symbols for all c ≤ c_max at (L_m,c + α_m,c∆_c(m) + 1)-th positions, where

Figure 9 shows an example of extended combinations with c_max = 2, i.e. c = 1, c = 2 and M = 2. The original hopping pattern of the example is the same as the previous one (i.e. example depicted in Figure 7), which is ∆₁(m) = [1,6,−1,−3,−1,6,1]. For c = 1 (Z_m,1 symbols in Figure 9), the phase of Z_m,1 is multiplied by α_m,1 = M/1 = 2. The hopping of these symbols becomes α_m,1 × ∆(m) = [2,12,−2,−6,−2,12,2]. This is why the black symbols are placed at positions −6,−2,2 and 12 in vector v[n]. As a reminder, all symbols with the same position within v[n] are summed up. For c = 2 (i.e. highlighted Z_m,2 symbols in Figure 9), α_m,1 = M/2 = 1 and ∆₂(m) = [7,5,−4,5,7]. The Z_m,2 is placed in v[n] at the positions ∆₂(m), and no phase multiplication is required in this case. The next steps of the method are the same as with the minimum combinations, as described in the previous embodiment. The FFT is performed on v[n], then the [X_max,k_max] quantities are determined. If the preamble detection is declared, the ToA is deduced as described above. In this section numerical results for the performance evaluation of the proposed NPRACH reception method are provided. The described preferred embodiments with minimum combinations and with extended combinations are distinguished. When referring to extended version of the proposed method, extended combinations described by c_max = 2 are considered. The method has been implemented in MATLAB™ and simulated under the 3GPP test conditions. Table I summarizes the link-level simulation parameters.

Both preamble formats 0 and 1 are simulated. Accordingly, the timing offset is selected randomly in the interval [0,66.67] us for preamble format 0, and [0,259] us for preamble format 1. The number of repetitions is set to 8 or 32. A timing offset limit of 259us was chosen rather than 266.67 us for Format 1 in order to keep a safety interval of ±2 x 3.646 us that helps to avoid the phase ambiguity. AWGN, extended pedestrian A model with 1 Hz Doppler (EPAI) and extended typical urban model (ETU) with 1 Hz Doppler (ETUI) radio channel models are considered [23], It is worth noting that 3GPP considers only AWGN (without CFO) and EPA 1 (with 200 Hz CFO) channels for NPRACH test requirements, i.e. not ETU 1. Nevertheless the ETUI channel is added for completeness, since 3 GPP may add this channel to the NPRACH requirements in future releases. The number of FFT points used in the method is set to 256 points for a fair comparison with the work in [13],

A. 3GPP requirements and performance metrics

Regarding the performance metric, the 3 GPP requirement is expressed in [10] in terms of the minimum SNR, for which the probability of preamble detection is greater than or equal to 99% (i.e. missed detection rate below 1%), and false alarm probability being less than or equal to 0. 1%.

According to [10], the probability of detection is defined as the conditional probability of correct detection of the preamble when the signal is present. There are several error cases:

• detection of a wrong preamble (different than sent),

• no detection of any preamble,

• correct preamble detection but with the wrong timing, ToA, estimation.

This latter occurs, if the estimation error of the timing is larger than 3.646 us.

The false alarm probability is defined as the conditional total probability of erroneous detection of the preamble when input only contains the noise, i.e. in absence of the useful signal.

To summarize, the performance metric is the minimum required SNR, for which the preamble is correctly detected and the ToA error is below 3.646 us in 99% of cases while the false alarm probability is below 0. 1%.

B. Obtained results

The obtained results are depicted in Figures 10a, b, lla,b and 12a, b for AWGN, EPAI and ETUI radio channels, respectively.

For AWGN (see Figure 10) with 8 repetitions, the missed detection target of 10“² (which corresponds to detection probability > 99%) is reached at SNR of -7.68 dB and -9.41 dB for the minimum and extended combinations, respectively. A gain of 1.73 dB is observed with extended combinations compared to the minimum combinations. In case of 32 repetition, the missed detection target is reached at -12.7 dB for minimum combinations and at -13.7 dB for extended combinations, respectively, which leads to 1 dB gain between the two cases. Once observes only a slight deviation of these SNR values for preamble format 1 compared to format 0, such that the proposed method can be applied without change for both formats.

For EPAI (see Figure 11), the missed detection target is reached at SNR of -2.6 dB and -3.8 dB for minimum and extended combinations, respectively, in case of 8 repetitions. For 32 repetitions, the target performance is reached at -7.5 dB and -8.2 dB for minimum and extended combinations, respectively. Under ETUI (see Figure 12) channel, the observed SNR for the missed detection target is -1.4 dB and -3.8 dB for minimum and extended combinations in case of 8 repetitions. For 32 repetitions, the SNR at the missed detection target for minimum and extended combinations is about -6.33 dB and 8.10 respectively. Like the AWGN observation, these SNR levels are almost the same for both preamble formats 0 and 1 . In addition, it can be observed that the false alarm is less than 0.1% in all considered scenarios.

C. Comparison and discussion

To evaluate these results, a comparison of the proposed work with the 3GPP requirements [10] and with the most representative state-of-the-art works [13], [14] is provided in the following. It is worth noting here that the relevant performance analysis for the algorithm proposed in [ 11 ] has been provided in [ 14] .

The numerical results, which are relevant for the comparison, are provided in Figures 10-12, and summarized in Table II. Note that the results for the ETU 1 channel are provided only for the sake of completeness, since no requirements have been imposed by 3 GPP for this type of channel yet. First of all, the obtained performance meets the 3 GPP requirements [10] for both preamble formats and with both minimum and extended combinations. Under the AWGN channel and for all numbers of repetitions (i.e. ^a'«™^ac” = 8 or 32) a margin of ~ 5.5 dB (in case of minimum combinations) and ~ 7 dB (in case of extended combination) is observed compared to 3GPP requirements. Under EPAI channel, even larger margins are observed. Interestingly, ~ 8.6 dB and 10 dB margins are obtained in case of minimum and extended combinations, respectively. These large margins demonstrate a very high accuracy of our proposed method. Regarding the works in [13] and [14], the performance is compared only for preamble format 0 in AWGN and EPAI channels, since the method proposed in [13] does not support format 1 and the method in [14] provides only performance analysis for format 0. For ETUI, only preamble format 0 with 8 repetitions is compared, since [14] provides the results only for this configuration. The proposed method clearly outperforms the methods in [13] and [14] in all considered cases.

Under AWGN channel and for any number of repetitions, performance margins of at least 3.1 dB and 1.1 dB are observed (at missed detection target of 10^-2) compared to [13] and [14], respectively, with just the minimum combinations.

TABLE II: Performance summary and comparison

With extended combinations, these margins increase to at least 4.5 dB and 2.5 dB compared to [13] and [14], respectively. One can see (see Figure 10a) that the performance of [13] with 32 repetitions is equivalent to the performance of the proposed method with only 8 repetitions in case of extended combination, such that the preamble detection can be done four times faster.

Interestingly, under EPAI and ETU 1 channels, the margins are even larger. The proposed method can even outperform the other known methods with lower repetitions (see Figure 1 la). Regarding the work in [13], and in case of 8 repetitions, margins of 6.2 dB and 7.65 dB are observed (at missed detection target of 10“²) with minimum and extended combinations, respectively, while in case of 32 repetitions, these margins are ~ 5.77 dB and 6.43 dB. Compared to [14], the observed margins under EPAI channel are 3.26 dB and 4.7 dB with minimum and extended combinations, respectively, if the number of repetitions is 8. For 32 repetitions, the margin remains approximately the same with minimum combinations (i.e. 3.2 dB), whereas with extended combinations the margin decreases to 3.88 dB. Under ETUI channel, the observed margins are 2.6 dB and 5 dB with minimum and extended combinations, respectively.

In the following, a brief explanation for such a substantial performance improvement using the proposed method is provided by analyzing the potential weaknesses of the state-of-theart methods. The method in [14] is based on 2D-FFT [11], as mentioned earlier. In general, when the CFO is absent, the performance of this method is theoretically close to the proposed method with minimum combinations. This is why only 1 dB gain is observed in case of minimum combination under AWGN channel compared to [14], This remaining 1 dB gain can be explained by the fact that in the proposed method, the pseudo-random hopping is included in the pre-FFT vector v[n] in contrast to [9], By adding a pseudorandom hopping (which is not fixed) in v[n] allows to increase diversity within the vector leading to higher post-FFT peak and hence a better performance. For the extended combination, the additional gain is the result of adding more symbols to v[n] vector due to higher number of combinations compared to the minimum combinations. In a realistic scenario with a non-vanishing CFO (i.e. EPAI, ETUI), the method in [14] is sensitive to the CFO. A joint estimation of multiple parameters (CFO and ToA in case of [14]) is typically less accurate under the same conditions than the estimation of just one parameter (ToA in case of the proposed method), if all other parameters are either known or perfectly eliminated. This is why at least 2.6 dB gain is observed in ETU 1 channel using the proposed method.

A very high performance gain obtained with the proposed method compared to the method in [13] is explained by the sensitivity of the latter to the CFO. The estimation and compensation of the CFO not only leads to additional complexity, but also to a degradation of the ToA estimation performance, since imperfect CFO estimation and compensation leads to residual CFO, which dramatically affects the accuracy of To A estimation.

In the light of these results, one can notice that the performance of the proposed technique is substantially higher, especially in the realistic scenario with non-vanishing CFO. This high performance can be exploited to reduce the number of repetitions within the NPRACH preamble while satisfying the 3 GPP requirements. Correspondingly, a successful synchronization can be achieved faster, leading to overhead reduction, and thus to an increase of the energy and spectral efficiency desired in the context of loT system.

The proposed algorithm can work with any frequency hopping pattern under the assumption that this pattern is known to the receiver. However, the maximum delay offset (e.g. RTD) that can be estimated corresponds to the reciprocal minimum hopping distance. Furthermore, the hopping pattern impacts the spectrum of the vector v (after the FFT processing), such that the detection and the estimation performance depends on the pattern. Hence, the design of the optimal pattern should be addressed in future works by taking into account the peculiarities of signal detection associated with the proposed algorithm.

D. Performance in practical system

To evaluate the performance of the proposed method in a practical system, simulations have been conducted with 12 active Ues under realistic scenarios with non-vanishing CFO. Accordingly, the CFO is no longer fixed (e.g. 200 Hz) as before but randomly selected (with uniform distribution) in the interval ± 200 Hz. Furthermore, realistic signal propagation models are assumed, i.e. EPAI and ETUI. Note that the previous simulations with a single UE and with fixed CFO 200 Hz represent a pessimistic case, since in a real scenario the CFO is not fixed but uniformly distributed in the range between -200 Hz and 200 Hz. Since the results are very similar for format 0 and 1, only the results for format lare provided. Except for the parameters mentioned above, all other simulation parameters remain unchanged, see Table I. The obtained results are depicted in Figure 13a and Figure 13b. Similarly to the previous simulations, the performance of the extended combinations is better than with the minimum combinations. For EPAI channel 8 repetitions (see Figure 13a), the SNR corresponding to the missed detection rate below 1% is - 3.3 dB and -4.6 dB for minimum and extended combinations, respectively. With 32 repetitions, these values are -8.3 dB and -8.8 dB. For ETUI channel (see Figure 13b), the observed SNRs at the missed detection target are -1.9 dB and -4.4 dB with 8 repetitions for minimum and extended combination, respectively, and -6.9 dB and -8.7 dB with 32 repetitions, respectively. As expected, the results in EP Al channel outperform the results in ETUI channel, since the latter is associated with more severe propagation conditions compared to EPAI as outlined in [23], Interestingly, the obtained results constitute a new reference for NPRACH detection performance in practical system configurations, since none of the existing works provides the performance analysis of the respective method in practical scenarios, but solely the performance with respect to the 3GPP requirements, i.e. with fixed CFO and single UE.

E. Complexity analysis

In order to justify the use of the proposed method in practical scenarios, a complexity analysis and a comparison with the complexity of the mentioned state of-the-art works is herewith provided. The complexity comparison with [9] is not needed since it apparently has a much higher complexity than the proposed method due to the mentioned 2D-FFT calculation (the proposed method requires a single 1D- FFT calculation). Hence, the number of complex multiplications required by the proposed method and by the method from [13] is of prime focus. In [13], the frequency estimation block requires a number of complex multiplications of

On the other hand, the compensation block requires complex multiplications. For the ToA

estimation part, no multiplication is required since the calculated symbols during the frequency estimation and compensation stages can be reused. Only 1D-FFT is required in this part. However, ≈ 5 real multiplications (≈ 1 complex multiplication) are needed to: (1) calculate the square of absolute value of the metric, (2) deduce ToA, (3) obtain quadratic interpolation factor and (4) perform the correction of the estimated ToA using the interpolation factor. It is noted that all multiplications by a factor 2ⁿ are not considered since they can be implemented via shift registers. Taking into account the maximum Ues that can simultaneously send their NPRACH in NB-IoT (i.e.48 Ues), the overall complexity in term of complex multiplication is about in addition to a 1D-FFT with 256 points per receiver antenna. Regarding the proposed method, the complexity estimation is done first for the minimum combination and then for the extended combinations. For the minimum combinations, the ToA estimation part requires complex multiplications in addition to 1D-FFT with 256 points. The same real multiplications as [13] are required (i.e. ≈ 5 real multiplications). For 48 Ues, the overall complexity for the minimum combination is in addition to a 1D-FFT with 256 points per receiver antenna. Clearly, the proposed method with minimum combinations has 50% less complexity compared to [13]. With the extended combinations, the ToA estimation requires complex multiplications in addition to the same aforementioned real multiplications and one 1DFFT of 256 points. In total, the complexity of the maximum combinations is O(48 · 8N_rep ^NPRACH) in addition to a 1DFFT per receiver antenna. Obviously, even with the extended combination, the complexity of the proposed method is not higher than the complexity of the algorithm proposed in [13]. This analysis proves that the proposed method has the lowest complexity compared to the state-of-the-art works. Taking into account the mentioned performance improvements, our method is in fact a very promising solution for realistic scenarios of NB-IoT. Embodiments of the present invention proposed a novel reception method for NB-IoT random access. The proposed method is designed in a way that the CFO present in the received signal is perfectly eliminated. An extended version of the method is also proposed. The method has been simulated under the 3GPP conditions to test its conformity towards 3GPP requirements. Comparisons with relevant state-of-the-art work are also provided. The obtained results and complexity analysis illustrated the effectiveness of the proposed method in term of flexibility, low-complexity and high accuracy of ToA estimation. Here, the flexibility results from the fact that the proposed method: (i) eliminates perfectly the CFO, and performs equally well with any CFO, and (ii) supports both preamble formats 0 and 1. Moreover, the absence of the CFO estimation and compensation reduce considerably the computational complexity leading to ≈ 50% complexity savings compared to the previous work. Last but not least, 8.5 dB to 10 dB margins are obtained under a realistic scenario (EPAI channel) compared to 3GPP requirements. The capabilities of the proposed method can be exploited in order to reduce the length of the NPRACH preamble. Correspondingly, successful synchronization can be achieved much faster, which would allow to relax the hardware design, reduce the power consumption of the loT Ues and contribute to the overall throughput increase of the system saving thus the scarce system resources.

It should be noted that features described for a specific embodiment may be combined with the features of other embodiments, unless the contrary is explicitly mentioned. Based on the description and figures that have been provided, a person with ordinary skills in the art will be able to provide a computer program for implementing the described method steps without undue burden.

It should be understood that the detailed description of specific preferred embodiments is given by way of illustration only, since various changes and modifications within the scope of the invention will be apparent to the person skilled in the art. The scope of protection is defined by the following set of claims.

REFERENCES

[1] Ericsson, “Cellular iot evolution for industry digitalization,” Ericsson white paper, January 2019. [Online]. Available: https://www.ericsson.com/en/white-papers/cellular-iot-evolutionfor-industry- digitalization

[2] LoRa- Alliance, “LoRaWAN, what is it?” A technical overview of LoRa R and LoRaWAN R , November 2015. [Online]. Available: https://lora-alliance.org/resource-hub/what-lorawam

[3] Sigfox, http://www.sigfox.com, accessed: November 2015.

[4] 3^rd Generation Partnership Project, “LTE; Evolved Universal Terrestrial Radio Access (E-UTRA) and Evolved Universal Terrestrial Radio Access Network (E-UTRAN); Overall description,” 3GPP TS 36.300 version 13.2.0 Release 13, 2016-01.

[5] J. Schlienz and D. Raddino, “Narrowband internet of things whitepaper,” White Paper, Rohde&Schwarz , pp. 1-42, 2016.

[6] M. Elsaadany, A. Ali, and W. Hamouda, “Cellular LTE-A technologies for the future Intemet-of- Things: Physical layer features and challenges,” IEEE Communications Surveys & Tutorials, vol. 19, no. 4, pp. 2544- 2572, 2017.

[7] A. Rico-Alvarino, M. Vajapeyam, H. Xu, X. Wang, Y. Blankenship, J. Bergman, T. Tirronen, and E. Yavuz, “An overview of 3 GPP enhancements on machine to machine communications,” IEEE Communications Magazine , vol. 54, no. 6, pp. 14-21, 2016.

[8] 3^rd Generation Partnership Project, “LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation,” 3GPP TS 36.211 version 13. 7.1 Release 13, 2017-10.

[9] X. Lin, A. Adhikary, and Y.-P. Wang, “Random access preamble design and detection for 3GPP narrowband loT systems,” IEEE Wireless Communications Letters, vol. 5, no. 6, pp. 640-643, 2016.

[10] 3^rd Generation Partnership Project, “LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) radio transmission and reception,” 3GPP TS 36.104 version 14.3.0 Release 14, 2017-04.

[11] X. Lin, Y.-P. Wang, and A. Adhikary, “Preamble detection and timeof-arrival estimation for a single-tone frequency hopping random access preamble,” U.S. Patent US20170324587A1, Nov. 9,2017.

[12] J. Hwang, C. Li, and C. Ma, “Efficient Detection and Synchronization of Superimposed NB-IoT NPRACH Preambles,” IEEE Internet of Things Journal, vol. 6, no. 1, pp. 1173-1182, Feb 2019.

[13] A. Chakrapani, “NB-IoT Uplink Receiver Design and Performance Study,” IEEE Internet of Things Journal, pp. 1-1, 2019.

[14] Ericsson, “NPRACH demodulation requirements,” R4-168206, 3GPP TSG-RAN WG4 Meeting #80bis, October 2016.

[15] 3^rd Generation Partnership Project, “LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Radio Resource Control (RRC); Protocol specification,” 3GPP TS 36.331 version 13.8.1 Release 13, 2018-01.

[16] Ericsson, “Narrowband LTE - random access design,” Rl-156011, 3GPP TSG-RAN 1 #82his, October 2015.

[17] - , “NB-IoT - random access design,” Rl-157424, 3GPP TSG-RAN1 #83, November 2015. [18] - , “NB-IoT - design considerations for single tone frequency hopped NB-PRACH,” Rl-160093,

3GPP TSG-RAN1 AH-NB-IoT, January 2016.

[19] - , “NB-IoT - single tone frequency hopping NB-PRACH design,” Rl-160275, 3GPP TSG-

RAN1 #84, February 2016. [20] 3^rd Generation Partnership Project, “Technical Specification Group GSM/EDGE Radio Access

Network; Cellular System Support for Ultra Low Complexity and Low Throughput Internet of Things; (Release 13),” 3GPP TR 45.820 V2.1.0, 2015-08.

[21] D. Rife and R. Boorstyn, “Single tone parameter estimation from discrete-time observations,” IEEE Transactions on Information Theory, vol. 20, no. 5, pp. 591-598, Sep. 1974. [22] M. Abe and J. O. Smith, “Design criteria for simple sinusoidal parameter estimation based on quadratic interpolation of fft magnitude peaks,” Audio Engineering Society Convention, San Francisco, 2004, preprint 6256.

[23] 3^rd Generation Partnership Project, “3^rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception; (Release 8) ,” 3GPP TS 36.803 version 1.1.0

Release 8, 2008-04.

[24] B. Sklar, “Rayleigh fading channels in mobile digital communication systems .1. Characterization,” IEEE Communications Magazine, vol. 35, no. 7, pp. 90-100, 1997.

Claims

Claims

1. A method for detecting a single-tone frequency hopping random access preamble at a receiver, comprising the steps of a) receiving and demodulating , using receiving means (110), a signal (10) on an orthogonal frequency-division multiplexing, OFDM, data communication channel, the demodulated signal comprising a sequence of groups of symbols SG, , 0 < i < m, wherein each group of symbols SG, has at least one symbol, and wherein each group of symbols SG, is received on one of a plurality of available channel sub-carriers; b) using data processing means (120), generating a differential symbol Z_{i l} for each pair of groups of symbols (SG„ SG,+y), by multiplying a representative symbol of the first group of symbols SG, with the conjugate of a representative symbol of the following group of symbols SG,₊ ; c) using data processing means (120), determining an expected frequency hop between the groups of symbols of each pair of groups of symbols (SG„ SG,+y), having consecutive indexes in said sequence, and associating said expected frequency hop with the differential symbol Z, ₄ that corresponds to the groups of symbols (SG„ SG,+y); d) using data processing means (120), generating an all-zero one-dimensional array v in a memory element (130), the array v having a number of positions that spans a range comprising all the determined expected frequency hops; e) using data processing means (120), adding each differential symbol Z, , to the value at the position in said array v that corresponds to the expected frequency hop, which is associated with the differential symbol Zjj; f) using data processing means (120), performing a one-dimensional Fast Fourier Transform, FFT, of the resulting array v and storing the coefficients in a corresponding FFT array FFT(v); g) using data processing means (120), determining the presence of a preamble subject to the comparison of the maximum absolute value of said FFT(v) array with a predetermined threshold value.

2. The method according to claim 1, further comprising the step of: h) upon detection of a preamble, estimating, using data processing means, a transmission delay between the transmitter of said preamble and the receiver, based on the position of said maximum absolute value in said FFT(v) array.

3. The method according to any of claims 1 or 2, wherein step b) further comprises b1) generating at least one additional differential symbol Z_i,c for each pair of groups of symbols (SG_i, SG_i+c), having an index difference c (1<c≤cmax) in said sequence, by multiplying a representative symbol of the first group SG_i with the conjugate of a representative symbol of the group of symbols SG_i+c; wherein step c) further comprises c1) determining at least one additional expected frequency hop between the groups of symbols of each pair of group of symbols (SG_i, SG_i+c), (1<c≤cmax), multiplying the determined frequency hop by M/c, M being the Minimum Common Multiple of all c≤cmax, and associating the resulting frequency hop with the differential symbol Z_i,c to the groups of symbols (SG_i, SG_i+c); c2) updating the expected frequency hops determined at step c) by multiplying them with M; and wherein step e) further comprises the preliminary step of e1) multiplying the phases of the differential symbols Z_i,1 by M and multiplying the phases of the differential symbols Z_i,c by M/c, prior to adding the resulting differential symbols Z’_i,1, Z’_i,c to the respective values at the positions in said array v that correspond to the expected frequency hops that are associated with said differential symbols Z’_i,1, Z’_i,c.

4. The method according to any of claims 1 to 3, wherein said representative symbol of a group of symbols SG_i is determined by summing up all the symbols of said group of symbols.

5. The method according to any of claims 1 to 4, wherein an pattern of expected frequency hops is pre-provided in a memory element to which the data processing means have read access.

6. The method according to any of claims 1 to 5, wherein said sequence of groups of symbols comprises at least one repetition of a frequency hopping pattern.

7. The method according to any of claims 1 to 6, wherein said signal is received on a Narrowband Internet of Things, NB-IoT, Physical Random Access channel, NPRACH.

8. The method according to any of claims 1 to 7, wherein said array has a size of 2h+l positions, wherein h is the largest expected frequency hop that is determined, and wherein the central position of the array corresponds to a frequency hop equal to 0.

9. The method according to any of claims 3 to 8, wherein cmax = 2.

10. The method according to any of claims 1 to 9, wherein said predetermined threshold value corresponds to a probability of 90% and preferably of at least 99% of said singletone frequency hopping random access preamble being present in said received signal.

11. A system (100) comprising data receiving means (110) comprising at least one antenna, and a data processor (120) configured for implementing the steps in accordance with any of claims 1 to 10.

12. A base station in a Narrowband-Internet of Things system for receiving signal from User Equipment devices, wherein the NB-IoT system comprises the system according to claim 11.

13. A computer program comprising computer readable code means, which, when run on a computer, causes the computer to carry out the method according to any of claims 1 to 10.

14. A computer program product comprising a computer readable medium on which the computer program according to claim 13 is stored.