DNN ‐ based distributed sequential uplink processing in cell ‐ free massive MIMO based on radio stripes

Cell ‐ free massive MIMO (mMIMO) has two distinctive advantages: first is, macrodiversity from large numbers of distributed access points and second, interference cancellation from cellular mMIMO is envisioned to be next ‐ generation wireless technology for beyond 5G. However, its practical deployment is extremely challenging due to large numbers of long cables (economic perspective) and network synchronisation. Cell ‐ free mMIMO system based on radio stripe (CFMMRS) network is one such architecture of cell ‐ free mMIMO suitable for practical deployment. This study proposes DNN ‐ based distributed sequential uplink processing for detecting symbols in the uplink of CFMMRS network architecture. Simulation results show that the proposed algorithm outperforms the traditional iterative soft interference cancellation ‐ based detection method.


| INTRODUCTION
Owing to the need to satisfy the ever increasing demand for high per user data requirement, one of the principal ways is adoption of network densification, wherein base station (BS) uses large numbers of antennas and installs smaller cells [1]. Massive MIMO (mMIMO), which involves large numbers of antennas installed at the BS simultaneously serves multiple users and as a promising access technology in 5G and beyond that improves spectral efficiency by at least 10 times than legacy cellular network [2], with high reliability and simple signal processing [3,4]. Although, mMIMO provides higher spectral efficiency and energy efficiency, its performance is limited by intercell interference which has become major bottleneck for network densification and this cannot be removed until we implement network on cell-centric approach [5], since it is inherent to cellular network [6].
This gives rise to cell-free mMIMO [7], which is a usercentric implementation and is a combination of distributed MIMO and mMIMO. Here many distributed access points (APs) are connected to the central processing unit (CPU) via front-haul and jointly serve user equipment's (UE) presence in the network. The CPU operates cell-free mMIMO in network MIMO fashion such that there are no cell boundaries and thereby serves UEs by combined transmission and reception acting coherently [8]. Compared to traditional cellular mMIMO networks, cell-free provides strong macrodiversity, superior multiuser interference suppression capability, owing to large numbers of serving APs users may experience good channel condition [9]. Cell-free mMIMO has been studied for different configurations [8], each configuration requires some information to be exchanged between APs and CPU, through parallel front-haul cables. However, its practical acceptance remains doubtful due to two reasons, at first from the economic perspective, since it requires large numbers of long cables and second from the network synchronisation.
Authors in [5] give solution to this problem by introducing cell-free mMIMO system based on radio stripe (CFMMRS), here APs are connected sequentially one after the other such that all APs in the radio stripe use same cables for their front-haul requirements and power supply, therefore, requirement for cabling reduces substantially. Authors in [10] propose sequential up-link processing for CFMMRS. The APs compute channel estimate and make soft estimate of received signal and thereby forwards channel state information (CSI) estimate, soft estimate to next AP (in sequential order). Upon receiving CSI estimate and, the soft estimate from previous AP, the subsequent AP uses those values and its own estimated CSI for computing the symbol's soft estimate. This process continued up to the last AP. The last AP passes the final estimate of the received signal to CPU for decoding.
One of the major challenges in multiuser, multiple-input, multiple-output (MU-MIMO) technology is the recovery of multiple transmitted symbols at the receiver in the up-link [11]. Traditionally, the receiver estimates the channel based on pilotbased schemes or other, and thereby detects symbols. However, the detection poses a challenge in terms of computational complexity [12]. The special case of MU-MIMO is mMIMO where the number of used antennas at the BS is very high (at least twice) then the UE it is serving. In [13], the author introduces DeepSIC which is a data-driven MU-MIMO receiver implementation of iterative soft interference cancellation (SIC) detection technique. DNN is used in conjunction with SIC detection algorithm, removing channel model dependence by replacing CSI based computation with dedicated DNN. As described above [10], each AP estimates CSI and makes soft estimate, and this can be computationally expensive especially with large numbers of APs. Therefore, ML based detection can be used well wherein each AP is trained on large samples to detect the transmitted symbols in CFMMRS.
The above-mentioned iterative detection algorithm [13] motivates us to leverage it to detection in CFMMRS. Since in [10], the processing is done sequentially DeepSIC can be used well to achieve the same in CFMMRS.
Machine learning and deep learning are used for wireless communication effectively [14]. Since there is no reported studies on receiver design in cell-free mMIMO based on radio stripes leveraging machine learning. This study focused on applying deep learning with the following contribution.
Contribution: Motivated by the studies [13], the iterative SIC is used in data-driven fashion (DeepSIC) for detection of symbols in MU-MIMO. We propose DNN-based distributed sequential uplink processing (DBDSUP) for detecting symbols in CFMMRS.
Restof the articleis organisedasfollows:In Section2,network model of CFMMRS is presented. In Section 3, algorithms are discussed namely, iterative SIC and the proposed DNN based distributedsequential uplink processing (DBDSUP).In Section 4, simulation parameters and numerical results are provided. Finally, article is concluded in Section 5.

| CFMMRS NETWORK MODEL
CFMMRS network consists of L APs and each AP has N antennas as shown in Figure 1, CPU is connected to last AP in sequential order (L th AP) of the radio stripe. Front-haul connections given as AP 1 -> AP 2 -> AP 3 ->… AP L ->CPU as indicated in the Figures 1  and 2. The CFMMRS network model consists of K UE each equipped with one antenna and is distributed arbitrarily in the CFMMRS network. The received signal at the l th AP is given by: where H ∈ R N X K is the channel matrix, S = [s 1, s 2, s 3,.., s K ] T is symbol vector of K users transmitted simultaneously at any particular instant. N l ∈ R N X 1 is the noise at the receiver whose entries are distributed with zero mean and variance of σ 2 . Since there are L numbers of APs, therefore each AP receives y 1, y 2, y 3, … y L.

| ALGORITHM DISCUSSIONS
Here in this section we discuss the iterative SIC algorithm and the proposed DBDSUP algorithm.

| Iterative SIC
Iterative SIC algorithm [15] is multiuser detection technique and comprises of two operations executed parallelly for each user namely, interference cancellation and soft decoding.
Considering K th user and c th iteration, during the interference cancellation stage, the expected values and variances of } u ≠ k is the estimated conditional distribution of interfering symbols obtained in the previous iteration.
The expected value is computed as: where {r w } W w = 1 are the indexed elements of the constellation set S. Variance of interfering symbols is given by, The contribution of the interfering symbols from the received signal y is cancelled by replacing it with mean {e u (c-1) } and subtracting the resultant term.Using the u th column of H named as h u for user u , the Interference canceled output of the channel is given by: The second step carried out in parallel for each user is soft decoding. The bijective transformation of y is G ðcÞ k , such that each possible value of y there is one unique value in G ðcÞ k : Therefore, P s k |y ðr w | yÞ ¼ P s k |G ðcÞ k ðr w | G ðcÞ k Þ for each r w ∈ S. Therefore, conditional distribution of s k given the observation y is approximated using conditional distribution of G ðcÞ k by Bayes theorem. When each symbol is equiprobable, the Conditional distribution is computed as: Symbols are decoded after the final iteration such that symbol which maximises estimated conditional distribution is decoded as transmitted symbol for each user. The iterative SIC algorithm is given below: The received signal y is given in Equation 1. For the first iteration, the initial guess of conditional distribution, which is distribution of k th user symbol s k is made randomly. Under the interference cancellation stage, for the c th iteration, expected values and variance of interfering symbols {s u } u ≠ k are calculated based on {P u (c-1) } u ≠ k , and thereby interference is cancelled in step 4. Then, soft decoding is carried out for each user which is the estimation of conditional distribution P k (c) .
Detailed equations and analysis are given in [13].
One important point to note here is that the iterative SIC algorithm is applicable for multiuser MIMO or mMIMO but not for CFMMRS since it involves multiple AP responsible for decoding the transmitted symbols.

| DBDSUP
The main idea behind DBDSUP is iterative SIC. However, there are two major differences between the two, at first the complex mathematical computations are replaced by neural networks and next iterative SIC is implemented on a single receiver, whereas the proposed algorithm is executed on several receivers.
Each AP has K numbers of soft estimate network (SEN) which computes conditional distribution estimate. Unlike iterative SIC, in the proposed algorithm each AP executes single iteration. In [10], each AP forwards local channel estimate and soft estimate of transmitted signal. However, in the proposed algorithm each AP forwards soft estimate (which is conditional distribution of transmitted symbols) to next AP. The last AP (L th AP) computes soft estimate which is passed on to CPU. The final soft estimation by L th AP received by CPU is then processed to recover the symbol. For example, if binary phase shift keying (BPSK) is used then CPU applies hard decoding. Algorithm 2 DNN-based distributed sequential uplink processing (DBDSUP) 1. Iteration-1(carried out in AP 1 ): Channel output at AP 1 is y 1 . y 1 is concatenated with the initial guess of conditional distribution P k (0) , and fed to SEN 1,1 , SEN 1,2 , …, SEN 1,K and produces conditional distribution P 1 (1) , P 2 , … P K (1) . Here, SEN c,k is SEN where c is iteration number of k th user. 2. Iteration-2(carried out in AP 2 ): Channel output at AP 2 is y 2 . y 2 is concatenated with {P u (1) } u ≠ K. and fed to SEN 2,1 , SEN 2,2 , …, SEN 2,K to produce P 1 (2) , P 2 (2) , … P K (2) .

| SIMULATION RESULTS
SEN as shown in Figure 3 is a neural network with three layers: first layer (N+K-1) � 100, second layer 100 � 50 and third layer 50 � B. The activation function used in first layer and second layer is sigmoid and rectified linear unit, respectively. BPSK is used in simulation. The constellation of BPSK is given by S = {−1, 1}, B = | S | = 2. Number of APs is set to be 5. The channel matrix (H) between users and each AP is independent of each other and is modelled as spatial exponential decay whose entries are given by: where i = {1, 2, … N} and j = {1, 2, …, K}. SENs were trained for 4400 samples. Simulation is carried out for K = 6, L = 5, N = 8. The simulation is carried out only for uncertain CSI as it resembles a practical scenario. Error variance of 0.1 is considered.
Performance analysis is carried out in terms of symbol error rate (SER) for iterative SIC and DBDSUP. The proposed DBDSUP is compared with cell-Free mMIMO with identical K, N, where each AP uses iterative SIC.
As shown in Figure 4, for 0 dB SNR, SER achieved for iterative SIC detector is 0.52 while for proposed DBDSUP is 0.156. Moreover, SER achieved by configuration using iterative SIC is 0.451, while DBDSUP has SER of 0.098 for 6dB SNR, and for 10dB, the former has an SER of 0.342 but the latter has an SER of 0.086.
The proposed algorithm outperforms iterative SIC by considerable margin. Figure 5 shows the analysis carried out for a combination of different activation functions in the first and second layers of the SEN. In particular, here, simulation is carried out for three different combinations of the activation function. The first combination is also shown in Figure 4. The results obtained show that there are slight variations in achieved SER between different combinations; for example, for 2 dB SNR, the SER achieved by first, second and third combinations are 0.122, 0.113 and 0.131, respectively. For 6dB SNR, the SER achieved is 0.098, 0.093 and 0.103 for the first, second and third combination, respectively. The second combination of activation function gives the lowest SER for most SNR; however, the difference is insignificant; thus, it can be concluded that the effect of the activation function of SEN on performance is not significant.

| CONCLUSION AND FUTURE WORK
This study introduces DBDSUP frame work for detection of symbols in CFMMRS. The proposed algorithm not only outperforms iterative SIC in terms of SER but also replaces complex computations (as suggested in the literature) by trained DNNs which reduce computational complexity considerably. In the future, more analysis can be carried out to investigate the effect of APs, numbers of users and training of SENs on performance.