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Adaptive Neural Signal Detection for Massive MIMO Mehrdad Khani, Mohammad Alizadeh, Jakob Hoydis, Senior Member, IEEE, Phil Fleming, Senior Member, IEEE

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Adaptive Neural Signal Detection for Massive MIMO Mehrdad Khani, Mohammad Alizadeh, Jakob Hoydis, Senior Member, IEEE, Phil Fleming, Senior Member, IEEE This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2020.2996144, IEEE Transactions on Wireless Communications 1 Adaptive Neural Signal Detection for Massive MIMO Mehrdad Khani, Mohammad Alizadeh, Jakob Hoydis, Senior Member, IEEE, Phil Fleming, Senior Member, IEEE Abstract—Traditional symbol detection algorithms either per- In recent work, researchers have proposed several learning form poorly or are impractical to implement for Massive approaches for MIMO signal detection. Samuel et al. [8, 9] Multiple-Input Multiple-Output (MIMO) systems. Recently, sev- achieved impressive results with a deep neural network ar- eral learning-based approaches have achieved promising results on simple channel models (e.g., i.i.d. Gaussian channel coeffi- chitecture called DetNet, e.g., matching the performance of cients), but as we show, their performance degrades on real-world a semidefinite relaxation (SDR) baseline for independent and channels with spatial correlation. We propose MMNet, a deep identically distributed (i.i.d.) Gaussian channel matrices while learning MIMO detection scheme that significantly outperforms running 30× faster. He et al. [10] introduced OAMPNet, existing approaches on realistic channels with the same or lower a model inspired by the Orthogonal AMP algorithm [11], computational complexity. MMNet’s design builds on the theory of iterative soft-thresholding algorithms, and uses a novel training and demonstrated strong performance on both i.i.d. Gaussian algorithm that leverages temporal and spectral correlation in and small-sized correlated channel matrices based on the real channels to accelerate training. These innovations make Kronecker model [12]. DetNet and OAMPNet are both trained it practical to train MMNet online for every realization of offline: they try to learn a single detector during training for the channel. On i.i.d. Gaussian channels, MMNet requires two a family of channel matrices (e.g., i.i.d. Gaussian channels). orders of magnitude fewer operations than existing deep learning schemes but achieves near-optimal performance. On spatially- In this paper we show that neither approach is effective in correlated channels, it achieves the same error rate as the next- practice. We conduct extensive experiments using a dataset of best learning scheme (OAMPNet) at 2.5dB lower signal-to-noise channel realizations from the 3GPP 3D MIMO channel [13], ratio (SNR), and with at least 10× less computational complexity. as implemented in the QuaDRiGa channel simulator [14]. Our MMNet is also 4–8dB better overall than a classic linear scheme results show that DetNet’s training is unstable for realistic like the minimum mean square error (MMSE) detector. Index Terms—Massive MIMO, signal detection, deep learning, channels, while OAMPNet suffers a large performance gap −3 online adaptation, spatial channel correlation (4–7dB at symbol error rate of 10 ) compared to the optimal Maximum-Likelihood detector on these channels. Both models (as well as several classical baselines) perform well in simpler I. INTRODUCTION settings used for evaluation in prior work (e.g., i.i.d. Gaus- The fifth generation of cellular communication systems sian channels, low-order modulation schemes). Our results (5G) promises an order of magnitude higher spectral effi- demonstrate the difficulty of learning a single detector that ciency (measured in bits/s/Hz) than legacy standards such as generalizes across a wide range of realistic channel matrices Long Term Evolution (LTE) [1]. One of the key enablers (esp. poorly-conditioned channels that are difficult to invert). of this better efficiency is Massive Multiple-Input Multiple- Motivated by these findings, we revisit MIMO detection Output (MIMO) [2], in which a base station (BS) equipped from an online learning perspective. We ask: Can a receiver with a very large number of antennas (around 64–256) si- optimize its detector for every realization of the channel multaneously serves multiple single-antenna user equipments matrix? Intuitively, such an approach could perform better (UEs) on the same time-frequency resource. than using a fixed detector for a wide variety of channel Legacy systems already use MIMO [3], but this is the matrices. However, conventional wisdom suggests that training first time it will be deployed on such a large scale, creating a MIMO detector online is impossible because of the stringent significant challenges for signal detection. The goal of signal performance requirements [8]. detection is to infer the transmitted signal vector x from the Our design, MMNet, overcomes this challenge with two key vector y = Hx + n received at the BS antennas, where H is ideas. First, it uses a neural network architecture that strikes the channel matrix and n is Gaussian noise. Traditional MIMO a balance between flexibility and complexity. Prior neural signal detection schemes with strong performance [4, 5, 6, 7] network architectures for MIMO detection are poorly suited are feasible only for small systems and have prohibitive to online training. DetNet is a large model with 1-10 million complexity for massive MIMO deployments. Thus, there is parameters depending on the system size and modulation a need for low-complexity signal detection schemes that can scheme, making it prohibitively expensive to train online. both perform well and scale to large system dimensions. OAMPNet, on the other hand, is very restrictive, adding only 2 trainable parameters per iteration to the OAMP algorithm. M. Khani and M. Alizadeh are with the Computer Science & Artificial Intelligence Laboratory, MIT, Cambridge, MA 02139, USA ([email protected], Since the OAMP algorithm requires strong assumptions about [email protected]). channel matrices (unitarily-invariant channels [11]), OAMP- J. Hoydis is with Nokia Bell Labs, Paris-Saclay, 91620 Nozay, France Net, even with online training, performs poorly on channels ([email protected]). P. Fleming is with Ann Arbor Analytics, LLC, Ann Arbor, MI, USA that deviate from the assumptions. (phil.fl[email protected]). MMNet’s neural network is based on iterative soft- 1536-1276 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Authorized licensed use limited to: MIT Libraries. Downloaded on July 07,2020 at 23:17:28 UTC from IEEE Xplore. Restrictions apply. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2020.2996144, IEEE Transactions on Wireless Communications 2 thresholding algorithms, a popular class of solutions to “linear- (At; bt; y − Hx^t) inverse” problems [15, 16, 17] like MIMO detection. These algorithms repeatedly refine an estimate of the signal by al- x^t zt x^t+1 ternating between a linear detector and a non-linear denoising linear denoiser step. By preserving the core components of these algorithms in MIMO detection, such as a simple denoiser that is optimal Fig. 1: A block of an iterative detector in our general framework. for uncorrelated Gaussian noise, MMNet avoids the pitfalls Each block contains a linear transformation followed by a denoising of overly general neural network architectures like DetNet. At stage. the same time, unlike OAMPNet, MMNet provides adequate B. The MIMO Signal Detection Problem flexibility in the architecture through trainable parameters that N can be optimized for each channel realization. We consider a communication channel from t single- antenna transmitters to a receiver equipped with N antennas. MMNet’s second key idea is an online training algorithm r The received vector y 2 Nr is given as that exploits the locality of channel matrices at a receiver in C both the frequency and time domains. By leveraging spectral y = Hx + n; (1) and temporal locality, MMNet accelerates training by more 2 Nr ×Nt ∼ CN (0; σ2 ) than two orders of magnitude compared to naively retraining where H C is the channel matrix, n INr N the neural network from scratch for each channel realization. is complex Gaussian noise, and x 2 X t is the vector of Taken together, these ideas enable MMNet to achieve per- transmitted symbols. X denotes the finite set of constellation formance within ∼2dB of the optimal Maximum-Likelihood points. We assume that each transmitter chooses a symbol detector with 10-15× less computational complexity than the from X uniformly at random, and all transmitters use the same second-best scheme, OAMPNet. On random i.i.d. Gaussian constellation set. Further, as is standard practice, we assume channels, an even simpler version of MMNet (MMNet-iid) that the constellation set X is given by a quadrature amplitude with 100× less complexity than OAMPNet and DetNet modulation (QAM) scheme [18]. All constellations are nor- achieves near-optimal performance without any retraining. malized to unit average power (e.g., the QAM4 constellation is {± p1 ± j p1 g). We empirically analyze the dynamics of errors across dif- 2 2 ferent layers of MMNet and OAMPNet to understand how The channel matrix H is assumed to be known at the MMNet achieves higher detection accuracy. Our analysis re- receiver. The goal of the receiver is to compute the maximum veals that MMNet “shapes” the distribution of noise at the likelihood (ML) estimate x^ of x: input of the denoisers to ensure they operate effectively. In x^ = arg min jjy − Hxjj2: (2) particular, as signals propagate through the MMNet neural x2X Nt network, the noise distribution at the input of the denoiser The optimization problem in (2) is NP-hard due to the stages approaches a Gaussian distribution, create precisely finite-alphabet constraint x 2 X Nt [19]. Therefore, over the the conditions in which the denoisers can attenuate noise last three decades, researchers have proposed a variety of maximally.
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