Optimally-tuned nonparametric linear equalization for massive MU-MIMO systems

Abstract

Abstract-This paper deals with linear equalization in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. We first provide simple conditions on the antenna configuration for which the well-known linear minimum meansquare error (L-MMSE) equalizer provides near-optimal spectral efficiency, and we analyze its performance in the presence of parameter mismatches in the signal and/or noise powers. We then propose a novel, optimally-tuned NOnParametric Equalizer (NOPE) for massive MU-MIMO systems, which avoids knowledge of the transmit signal and noise powers altogether. We show that NOPE achieves the same performance as that of the L-MMSE equalizer in the large-antenna limit, and we demonstrate its efficacy in realistic, finite-dimensional systems. From a practical perspective, NOPE is computationally efficient and avoids dedicated training that is typically required for parameter estimation. I. INTRODUCTIONMassive (or large-scale) multi-user multiple-input multipleoutput (MU-MIMO) will be among the key technologies for fifth-generation (5G) wireless systems as it provides (often significantly) higher spectral efficiency than traditional, smallscale MIMO [1], [2]. Data detection at the infrastructure base-stations (BSs) in such massive MU-MIMO systems is among the most critical components from a spectral efficiency and computational complexity perspective. In particular, since optimal data detection is known to be an NP-hard problem [3], a naïve exhaustive search over all possible transmit signals would result in prohibitive computational complexity for such largedimensional systems. Hence, alternative algorithms that achieve high spectral efficiency at low complexity must be deployed in practice. In addition, practical massive MU-MIMO systems suffer-as do traditional MIMO systems-from real-world hardware impairments and model mismatches (for example amplifier nonlinearities, phase noise, quantization artifacts, channel-estimation errors, etc.). Such system nonidealities are known to substantially reduce the performance of optimal data-detection algorithms unless one explicitly models these impairments and estimates the associated parameters [4].

Low-Complexity Statistically Robust Precoder/Detector Computation for Massive MIMO Systems

“…5 It is also seen that the AMP MMSED [45] is able to converge to the original MMSED when the channel is uncorrelated (a ≈ 0), with an order of 24MK operations. 6 However, for a slightly correlated channel (a ≥ 0.6), neither the standard AMP [45] nor the nonparametric AMP [24] are able to suitably recover the users symbols even for a large number of iterations whereas our proposed algorithm becomes slower due to channel correlation but still converges by slightly increasing the number of iterations.…”

“…In the UL, we compare the performance of our algorithm with a very recent approximate message passing (AMP) technique proposed in [24,45], especially with [45] where the authors used AMP to build a nonparametric MMSE detector for massive MIMO that is able to obtain an estimate of the signal and noise power. Fig.…”

“…A similar approach for linear MMSE detection consists of using a reduced rank filter, as in [23]. In a recent line of work [24], the approximate message passing (AMP) algorithm, initially developed for sparse signal recovery in [25], has been used to reduce the computational complexity of massive MIMO precoding and detection.…”

Decentralized Equalization With Feedforward Architectures for Massive MU-MIMO

“…The post-equalization SINR performance of centralized linear equalization algorithms, such as MRC, ZF, and L-MMSE, has been analyzed in [25]- [28] in the large-system limit. We will investigate the SINR performance of these algorithms for the two proposed decentralized feedforward architectures, and also investigate the efficacy of nonlinear equalization for decentralized massive MU-MIMO architectures.…”

“…The PD architecture significantly outperforms the FD architecture for all equalizers, which implies that for high-rates the PD architecture is the preferred choice. Interestingly, the minimum BS-to-UE antenna ratio remains constant for ZF; this implies that as long as one operates below a certain antenna ratio β * , ZF is able to support all transmission rates; see [28] for additional details on this behavior. Finally, we see that the minimum BS-to-UE ratio β −1 decreases for LAMA-FD and LAMA-PD at high rates; this behavior is due to the fact that LAMA in overloaded systems is particularly robust at low and high values of SNR (see [22] for a detailed discussion).…”