Abstract-Multiple-input multiple-output (MIMO) detection algorithms providing soft information for a subsequent channel decoder pose significant implementation challenges due to their high computational complexity. In this paper, we show how sphere decoding can be used as an efficient tool to implement softoutput MIMO detection with flexible trade-offs between computational complexity and (error rate) performance. In particular, we provide VLSI implementation results which demonstrate that single tree-search, sorted QR-decomposition, channel matrix regularization, log-likelihood ratio clipping, and imposing runtime constraints are the key ingredients for realizing soft-output MIMO detectors with near max-log performance at a chip area that is only 58% higher than that of the best-known hard-output sphere decoder VLSI implementation.Index Terms-Multiple-input multiple-output (MIMO) communication systems, soft-output sphere decoding, VLSI implementation, MIMO detection.

Abstract-We investigate the uplink throughput achievable by a multiple-user (MU) massive multiple-input multiple-output (MIMO) system in which the base station is equipped with a large number of low-resolution analog-to-digital converters (ADCs). Our focus is on the case where neither the transmitter nor the receiver have any a priori channel state information. This implies that the fading realizations have to be learned through pilot transmission followed by channel estimation at the receiver, based on coarsely quantized observations. We propose a novel channel estimator, based on Bussgang's decomposition, and a novel approximation to the rate achievable with finite-resolution ADCs, both for the case of finite-cardinality constellations and of Gaussian inputs, that is accurate for a broad range of system parameters. Through numerical results, we illustrate that, for the 1-bit quantized case, pilot-based channel estimation together with maximal-ratio combing or zero-forcing detection enables reliable multi-user communication with high-order constellations in spite of the severe nonlinearity introduced by the ADCs. Furthermore, we show that the rate achievable in the infinite-resolution (no quantization) case can be approached using ADCs with only a few bits of resolution. We finally investigate the robustness of low-ADC-resolution MU-MIMO uplink against receive power imbalances between the different users, caused for example by imperfect power control.Index Terms-Analog-to-digital converter (ADC), channel capacity, linear minimum mean square error (LMMSE) channel estimation, low-resolution quantization, multi-user massive multiple-input multiple-output (MIMO).

Abstract-Large-scale (or massive) multiple-input multipleoutput (MIMO) is expected to be one of the key technologies in next-generation multi-user cellular systems based on the upcoming 3GPP LTE Release 12 standard, for example. In this work, we propose-to the best of our knowledge-the first VLSI design enabling high-throughput data detection in single-carrier frequency-division multiple access (SC-FDMA)-based large-scale MIMO systems. We propose a new approximate matrix inversion algorithm relying on a Neumann series expansion, which substantially reduces the complexity of linear data detection. We analyze the associated error, and we compare its performance and complexity to those of an exact linear detector. We present corresponding VLSI architectures, which perform exact and approximate soft-output detection for large-scale MIMO systems with various antenna/user configurations. Reference implementation results for a Xilinx Virtex-7 XC7VX980T FPGA show that our designs are able to achieve more than 600 Mb/s for a 128 antenna, 8 user 3GPP LTE-based large-scale MIMO system. We finally provide a performance/complexity trade-off comparison using the presented FPGA designs, which reveals that the detector circuit of choice is determined by the ratio between BS antennas and users, as well as the desired error-rate performance.Index Terms-Approximate matrix inversion, FPGA design, large-scale (or massive) MIMO, linear soft-output detection, minimum mean square error (MMSE), Neumann series, VLSI.

Abstract-Massive multiuser (MU) multiple-input multipleoutput (MIMO) is foreseen to be one of the key technologies in fifth-generation wireless communication systems. In this paper, we investigate the problem of downlink precoding for a narrowband massive MU-MIMO system with low-resolution digital-toanalog converters (DACs) at the base station (BS). We analyze the performance of linear precoders, such as maximal-ratio transmission and zero-forcing, subject to coarse quantization. Using Bussgang's theorem, we derive a closed-form approximation on the rate achievable under such coarse quantization. Our results reveal that the performance attainable with infinite-resolution DACs can be approached using DACs having only 3 to 4 bits of resolution, depending on the number of BS antennas and the number of user equipments (UEs). For the case of 1-bit DACs, we also propose novel nonlinear precoding algorithms that significantly outperform linear precoders at the cost of an increased computational complexity. Specifically, we show that nonlinear precoding incurs only a 3 dB penalty compared to the infinite-resolution case for an uncoded bit error rate of 10 −3 , in a system with 128 BS antennas that uses 1-bit DACs and serves 16 single-antenna UEs. In contrast, the penalty for linear precoders is about 8 dB.Index Terms-Massive multi-user multiple-input multipleoutput, digital-to-analog converter, Bussgang's theorem, minimum mean-square error precoding, convex optimization, semidefinite relaxation, Douglas-Rachford splitting, sphere precoding.

Physical transceiver implementations for multipleinput multiple-output (MIMO) wireless communication systems suffer from transmit-RF (Tx-RF) impairments. In this paper, we study the effect on channel capacity and error-rate performance of residual Tx-RF impairments that defy proper compensation. In particular, we demonstrate that such residual distortions severely degrade the performance of (near-)optimum MIMO detection algorithms. To mitigate this performance loss, we propose an efficient algorithm, which is based on an i.i.d. Gaussian model for the distortion caused by these impairments. In order to validate this model, we provide measurement results based on a 4-stream Tx-RF chain implementation for MIMO orthogonal frequencydivision multiplexing (OFDM).