BER Performance of Uplink Massive MIMO With Low-Resolution ADCs

Massive multiple-input multiple-output (MIMO) is a promising technology for next generation wireless communication systems (5G). In this technology, Base Station (BS) is equipped with a large number of antennas. Employing high resolution analog-to-digital converters (ADCs) for all antennas may cause high costs and high power consumption for the BS. By performing numerical results, we evaluate the use of low-resolution ADCs for uplink massive MIMO by analyzing Bit Error Rate (BER) performance for different detection techniques (MMSE, ZF) and different modulations (QPSK, 16-QAM) to find an optimal quantization resolution. Our results reveal that the BER performance of uplink massive MIMO systems with a few-bit resolution ADCs is comparable to the case of having full precision ADCs. We found that the optimum choice of quantization level (number of bits in ADCs) depends on the modulation technique and the number of antennas at the BS.Comment: 4 pages, 9 figures; accepted for publication in iccke 201

Spectral shaping with low resolution signals

We aim at investigating the impact of low resolution digital-to-analog converters (DACs) at the transmitter and low resolution analog-to-digital converters (ADCs) at the receiver on the required bandwidth and the required signalto- noise ratio (SNR). In particular, we consider the extreme case of only 1-bit resolution (with oversampling), where we propose a single carrier system architecture for minimizing the spectral occupation and the required SNR of 1-bit signals. In addition, the receiver is optimized to take into account the effects of quantization at both ends. Through simulations, we show that despite of the coarse quantization, sufficient spectral confinement is still achievable.Comment: Presented in Asilomar Conference on Signals, Systems, and Computers 2015, Pacific Grove, C

Low-Complexity Multiuser QAM Detection for Uplink 1-bit Massive MIMO

This work studies multiuser detection for one-bit massive multiple-input multiple-output (MIMO) systems in order to diminish the power consumption at the base station (BS). A low-complexity near-maximum-likelihood (nML) multiuser detection algorithm is designed, assuming that each BS antenna port is connected with a pair of single-bit resolution analog-to-digital converters (ADCs) and each user equipment (UE) transmits symbols from a quadrature amplitude modulation (QAM) constellation. First, a novel convex program is formulated as a convex surrogate of the ML detector and subsequently solved through an accelerated first-order method. Then, the solution of the convex optimization problem is harnessed to solve a refined combinatorial problem with reduced search space, requiring non-exponential complexity on the number of the UEs. Judicious simulation study corroborates the efficacy of the resulting two-phase detection algorithm. The proposed two-phase algorithm can achieve symbol error rate (SER) performance close to the ML detector, with significantly reduced computation cost compared to the nML detection schemes in prior art

BER Performance Analysis of Coarse Quantized Uplink Massive MIMO

Having lower quantization resolution, has been introduced in the literature, as a solution to reduce the power consumption of massive MIMO and millimeter wave MIMO systems. In this paper, we analyze bit error rate (BER) performance of quantized uplink massive MIMO employing a few-bit resolution ADCs. Considering Zero-Forcing (ZF) detection, we derive a closed-form quantized signal-to-interference-plus-noise ratio (SINR) to achieve an analytical BER approximation for coarse quantized M-QAM massive MIMO systems, by using a linear quantization model. The proposed expression is a function of quantization resolution in bits. We further numerically investigate the effects of different quantization levels, from 1-bit to 4-bits, on the BER of three modulation types of QPSK, 16-QAM, and 64-QAM. Uniform and non-uniform quantizers are employed in our simulation. Monte Carlo simulation results reveal that our approximate formula gives a tight upper bound for the BER performance of $b$-bit resolution quantized systems using non-uniform quantizers, whereas the use of uniform quantizers cause a lower performance for the same systems. We also found a small BER performance degradation in coarse quantized systems, for example 2-3 bits QPSK and 3-4 bits 16-QAM, compared to the full-precision (unquantized) case. However, this performance degradation can be compensated by increasing the number of antennas at the BS.Comment: 9 pages, 7 figures, submitted to the IEEE Journal

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

Adopting one-bit analog-to-digital convertors (ADCs) for massive multiple-input multiple-output (MIMO) implementations has great potential in reducing the hardware cost and power consumption. However, distortions caused by quantization raise great challenges. In MIMO orthogonal frequency-division modulation (OFDM) detection, coarse quantization renders the orthogonal separation among subcarriers inapplicable, forcing us to deal with a problem that has a very large problem size. In this paper we study the expectation-maximization (EM) approach for one-bit MIMO-OFDM detection. The idea is to iteratively decouple the MIMO-OFDM detection problem among subcarriers. Using the perspective of block coordinate descent, we describe inexact variants of the classical EM method for providing more flexible and computationally efficient designs. Simulation results are provided to illustrate the potential of the divide-and-conquer strategy enabled by EM

Near Maximum-Likelihood Detector and Channel Estimator for Uplink Multiuser Massive MIMO Systems with One-Bit ADCs

In massive multiple-input multiple-output (MIMO) systems, it may not be power efficient to have a high-resolution analog-to-digital converter (ADC) for each antenna element. In this paper, a near maximum likelihood (nML) detector for uplink multiuser massive MIMO systems is proposed where each antenna is connected to a pair of one-bit ADCs, i.e., one for each real and imaginary component of the baseband signal. The exhaustive search over all the possible transmitted vectors required in the original maximum likelihood (ML) detection problem is relaxed to formulate an ML estimation problem. Then, the ML estimation problem is converted into a convex optimization problem which can be efficiently solved. Using the solution, the base station can perform simple symbol-by-symbol detection for the transmitted signals from multiple users. To further improve detection performance, we also develop a two-stage nML detector that exploits the structures of both the original ML and the proposed (one-stage) nML detectors. Numerical results show that the proposed nML detectors are efficient enough to simultaneously support multiple uplink users adopting higher-order constellations, e.g., 16 quadrature amplitude modulation. Since our detectors exploit the channel state information as part of the detection, an ML channel estimation technique with one-bit ADCs that shares the same structure with our proposed nML detector is also developed. The proposed detectors and channel estimator provide a complete low power solution for the uplink of a massive MIMO system.Comment: 13 pages, 8 figures, 2 tables, submitted to IEEE Transactions on Communication

Reliable OFDM Receiver with Ultra-Low Resolution ADC

The use of low-resolution analog-to-digital converters (ADCs) can significantly reduce power consumption and hardware cost. However, their resulting severe nonlinear distortion makes reliable data transmission challenging. For orthogonal frequency division multiplexing (OFDM) transmission, the orthogonality among subcarriers is destroyed. This invalidates conventional OFDM receivers relying heavily on this orthogonality. In this study, we move on to quantized OFDM (Q-OFDM) prototyping implementation based on our previous achievement in optimal Q-OFDM detection. First, we propose a novel Q-OFDM channel estimator by extending the generalized Turbo (GTurbo) framework formerly applied for optimal detection. Specifically, we integrate a type of robust linear OFDM channel estimator into the original GTurbo framework and derive its corresponding extrinsic information to guarantee its convergence. We also propose feasible schemes for automatic gain control, noise power estimation, and synchronization. Combined with the proposed inference algorithms, we develop an efficient Q-OFDM receiver architecture. Furthermore, we construct a proof-of-concept prototyping system and conduct over-the-air (OTA) experiments to examine its feasibility and reliability. This is the first work that focuses on both algorithm design and system implementation in the field of low-resolution quantization communication. The results of the numerical simulation and OTA experiment demonstrate that reliable data transmission can be achieved.Comment: 14 pages, 17 figures; accepted by IEEE Transactions on Communication

Mixed-ADC Massive MIMO Uplink in Frequency-Selective Channels

The aim of this paper is to investigate the recently developed mixed-ADC architecture for frequency-selective channels. Multi-carrier techniques such as orthogonal frequency division multiplexing (OFDM) are employed to handle inter-symbol interference (ISI). A frequency-domain equalizer is designed for mitigating the inter-carrier interference (ICI) introduced by the nonlinearity of one-bit quantization. For static single-input-multiple-output (SIMO) channels, a closed-form expression of the generalized mutual information (GMI) is derived, and based on which the linear frequency-domain equalizer is optimized. The analysis is then extended to ergodic time-varying SIMO channels with estimated channel state information (CSI), where numerically tight lower and upper bounds of the GMI are derived. The analytical framework is naturally applicable to the multi-user scenario, for both static and time-varying channels. Extensive numerical studies reveal that the mixed-ADC architecture with a small proportion of high-resolution ADCs does achieve a dominant portion of the achievable rate of ideal conventional architecture, and that it remarkably improves the performance as compared with one-bit massive MIMO.Comment: 14 pages, 10 figures, to appear in IEEE Transactions on Communication

Joint Channel-Estimation/Decoding with Frequency-Selective Channels and Few-Bit ADCs

We propose a fast and near-optimal approach to joint channel-estimation, equalization, and decoding of coded single-carrier (SC) transmissions over frequency-selective channels with few-bit analog-to-digital converters (ADCs). Our approach leverages parametric bilinear generalized approximate message passing (PBiGAMP) to reduce the implementation complexity of joint channel estimation and (soft) symbol decoding to that of a few fast Fourier transforms (FFTs). Furthermore, it learns and exploits sparsity in the channel impulse response. Our work is motivated by millimeter-wave systems with bandwidths on the order of Gsamples/sec, where few-bit ADCs, SC transmissions, and fast processing all lead to significant reductions in power consumption and implementation cost. We numerically demonstrate our approach using signals and channels generated according to the IEEE 802.11ad wireless local area network (LAN) standard, in the case that the receiver uses analog beamforming and a single ADC

Low SNR Asymptotic Rates of Vector Channels with One-Bit Outputs

We analyze the performance of multiple-input multiple-output (MIMO) links with one-bit output quantization in terms of achievable rates and characterize their performance loss compared to unquantized systems for general channel statistical models and general channel state information (CSI) at the receiver. One-bit ADCs are particularly suitable for large-scale millimeter wave MIMO Communications (massive MIMO) to reduce the hardware complexity. In such applications, the signal-to-noise ratio per antenna is rather low due to the propagation loss. Thus, it is crucial to analyze the performance of MIMO systems in this regime by means of information theoretical methods. Since an exact and general information-theoretic analysis is not possible, we resort to the derivation of a general asymptotic expression for the mutual information in terms of a second order expansion around zero SNR. We show that up to second order in the SNR, the mutual information of a system with two-level (sign) output signals incorporates only a power penalty factor of pi/2 (1.96 dB) compared to system with infinite resolution for all channels of practical interest with perfect or statistical CSI. An essential aspect of the derivation is that we do not rely on the common pseudo-quantization noise model