Efficient Non-linear Equalization for 1-bit Quantized Cyclic Prefix-Free Massive MIMO Systems

Abstract

This paper addresses the problem of data detection for a massive Multiple-Input-Multiple-Output (MIMO) base station which utilizes 1-bit Analog-to-Digital Converters (ADCs) for quantizing the uplink signal. The existing literature on quantized massive MIMO systems deals with Cyclic Prefix (CP) transmission over frequency-selective channels. In this paper, we propose a computationally efficient block processing equalizer based on the Expectation Maximization (EM) algorithm in CPfree transmission for 1-bit quantized systems. We investigate the optimal block length and overlapping factor in relation to the Channel Impulse Response (CIR) length based on the Bit Error-Rate (BER) performance metric.As EM is a non-linear algorithm, the optimal estimate is found iteratively depending on the initial starting point of the algorithm. Through numerical simulations we show that initializing the EMalgorithm with a Wiener-Filter (WF) estimate, which takes the underlying quantization into account, achieves superior BERperformance compared to initialization with other starting points.

Divide and Conquer: One-bit MIMO-OFDM Detection by Inexact Expectation Maximization

“…We can exploit the problem structure related to DFT (or FFT) to reduce the computational cost, but still the cost is not cheap. In [14], the authors consider an approximation of ( 6) that can be seen as unconstrained relaxation. There they apply expectation maximization (EM)-in which the M-step is allows us to use the decoupling trick in unquantized MIMO-OFDM.…”

“…Fact 1 is a consequence of Jensen's inequality. The proof can be found in [1,14] (the style of presentation there is different, but the result is the same), and it is omitted here. By applying the variational characterization (8) to fn,w(S) in (6), we can recast the problem (7) as…”

“…In the E-step (12a), calculating the r j+1 n 's requires 2W N times of the calculation of function Φ. In the M-step (12b), if we use PG to solve each problem (14), the per-iteration complexity is O(N K); note that this process can be parallelized. The conversions from E-step to M-step, and from M-step to E-step, require DFT and IDFT, respectively, which demands O(N W log 2 W ) if FFT (IFFT) algorithm is used.…”

“…The majority of the current one-bit MIMO studies focus on frequency-flat channels. In comparison, there is a paucity of studies on one-bit MIMO with orthogonal frequency division multiplexing (OFDM) and over frequency-selective channels [6,[12][13][14][15]. This paper studies MIMO-OFDM detection.…”

“…This prevents us from taking advantage of the subcarrier-wise orthogonal separation-at least not directly. The existing one-bit MIMO-OFDM detection studies can be taxonomized into two classes: i) applying a first-order method, such as the projected gradient (PG) method, to the large-scale detection problem [12,15]; and ii) using expectation-maximization (EM) [13,14]. In particular, the M-step of EM allows us to decouple the one-bit MIMO-OFDM detection problem into a number of subcarrier-wise independent problems-just like the unquantized MIMO-OFDM detection.…”