Mixed-ADC Massive MIMO Detectors: Performance Analysis and Design Optimization

Using a very low-resolution analog-to-digital convertor (ADC) unit at each antenna can remarkably reduce the hardware cost and power consumption of a massive multiple-input multiple-output (MIMO) system. However, such a pure low-resolution ADC architecture also complicates parameter estimation problems such as time/frequency synchronization and channel estimation. A mixed-ADC architecture, where most of the antennas are equipped with low-precision ADCs while a few antennas have full-precision ADCs, can solve these issues and actualize the potential of the pure low-resolution ADC architecture. In this paper, we present a unified framework to develop a family of detectors over the massive MIMO uplink system with the mixed-ADC receiver architecture by exploiting probabilistic Bayesian inference. As a basic setup, an optimal detector is developed to provide a minimum mean-squared-error (MMSE) estimate on data symbols. Considering the highly nonlinear steps involved in the quantization process, we also investigate the potential for complexity reduction on the optimal detector by postulating the common \emph{pseudo-quantization noise} (PQN) model. In particular, we provide asymptotic performance expressions including the MSE and bit error rate for the optimal and suboptimal MIMO detectors. The asymptotic performance expressions can be evaluated quickly and efficiently; thus, they are useful in system design optimization. We show that in the low signal-to-noise ratio (SNR) regime, the distortion caused by the PQN model can be ignored, whereas in the high-SNR regime, such distortion may cause 1-bit detection performance loss. The performance gap resulting from the PQN model can be narrowed by a small fraction of high-precision ADCs in the mixed-ADC architecture.Comment: 14 pages, 8 figures, 3 tables, submitted to IEEE Transactions on Wireless Communication

Joint Channel-and-Data Estimation for Large-MIMO Systems with Low-Precision ADCs

The use of low precision (e.g., 1-3 bits) analog-to-digital convenors (ADCs) in very large multiple-input multiple-output (MIMO) systems is a technique to reduce cost and power consumption. In this context, nevertheless, it has been shown that the training duration is required to be {\em very large} just to obtain an acceptable channel state information (CSI) at the receiver. A possible solution to the quantized MIMO systems is joint channel-and-data (JCD) estimation. This paper first develops an analytical framework for studying the quantized MIMO system using JCD estimation. In particular, we use the Bayes-optimal inference for the JCD estimation and realize this estimator utilizing a recent technique based on approximate message passing. Large-system analysis based on the replica method is then adopted to derive the asymptotic performances of the JCD estimator. Results from simulations confirm our theoretical findings and reveal that the JCD estimator can provide a significant gain over conventional pilot-only schemes in the quantized MIMO system.Comment: 7 pages, 4 figure

Bayes-Optimal Joint Channel-and-Data Estimation for Massive MIMO with Low-Precision ADCs

This paper considers a multiple-input multiple-output (MIMO) receiver with very low-precision analog-to-digital convertors (ADCs) with the goal of developing massive MIMO antenna systems that require minimal cost and power. Previous studies demonstrated that the training duration should be {\em relatively long} to obtain acceptable channel state information. To address this requirement, we adopt a joint channel-and-data (JCD) estimation method based on Bayes-optimal inference. This method yields minimal mean square errors with respect to the channels and payload data. We develop a Bayes-optimal JCD estimator using a recent technique based on approximate message passing. We then present an analytical framework to study the theoretical performance of the estimator in the large-system limit. Simulation results confirm our analytical results, which allow the efficient evaluation of the performance of quantized massive MIMO systems and provide insights into effective system design.Comment: accepted in IEEE Transactions on Signal Processin

Super-Resolution Blind Channel-and-Signal Estimation for Massive MIMO with One-Dimensional Antenna Array

In this paper, we study blind channel-and-signal estimation by exploiting the burst-sparse structure of angular-domain propagation channels in massive MIMO systems. The state-of-the-art approach utilizes the structured channel sparsity by sampling the angular-domain channel representation with a uniform angle-sampling grid, a.k.a. virtual channel representation. However, this approach is only applicable to uniform linear arrays and may cause a substantial performance loss due to the mismatch between the virtual representation and the true angle information. To tackle these challenges, we propose a sparse channel representation with a super-resolution sampling grid and a hidden Markovian support. Based on this, we develop a novel approximate inference based blind estimation algorithm to estimate the channel and the user signals simultaneously, with emphasis on the adoption of the expectation-maximization method to learn the angle information. Furthermore, we demonstrate the low-complexity implementation of our algorithm, making use of factor graph and message passing principles to compute the marginal posteriors. Numerical results show that our proposed method significantly reduces the estimation error compared to the state-of-the-art approach under various settings, which verifies the efficiency and robustness of our method.Comment: 16 pages, 10 figure

Bayesian Optimal Data Detector for mmWave OFDM System with Low-Resolution ADC

Orthogonal frequency division multiplexing (OFDM) has been widely used in communication systems operating in the millimeter wave (mmWave) band to combat frequency-selective fading and achieve multi-Gbps transmissions, such as IEEE 802.15.3c and IEEE 802.11ad. For mmWave systems with ultra high sampling rate requirements, the use of low-resolution analog-to-digital converters (ADCs) (i.e., 1-3 bits) ensures an acceptable level of power consumption and system costs. However, orthogonality among sub-channels in the OFDM system cannot be maintained because of the severe non-linearity caused by low-resolution ADC, which renders the design of data detector challenging. In this study, we develop an efficient algorithm for optimal data detection in the mmWave OFDM system with low-resolution ADCs. The analytical performance of the proposed detector is derived and verified to achieve the fundamental limit of the Bayesian optimal design. On the basis of the derived analytical expression, we further propose a power allocation (PA) scheme that seeks to minimize the average symbol error rate. In addition to the optimal data detector, we also develop a feasible channel estimation method, which can provide high-quality channel state information without significant pilot overhead. Simulation results confirm the accuracy of our analysis and illustrate that the performance of the proposed detector in conjunction with the proposed PA scheme is close to the optimal performance of the OFDM system with infinite-resolution ADC.Comment: 32 pages, 12 figures; accepted by IEEE JSAC special issue on millimeter wave communications for future mobile network

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

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

Performance Analysis for Channel Estimation with 1-bit ADC and Unknown Quantization Threshold

In this work, the problem of signal parameter estimation from measurements acquired by a low-complexity analog-to-digital converter (ADC) with $1$-bit output resolution and an unknown quantization threshold is considered. Single-comparator ADCs are energy-efficient and can be operated at ultra-high sampling rates. For analysis of such systems, a fixed and known quantization threshold is usually assumed. In the symmetric case, i.e., zero hard-limiting offset, it is known that in the low signal-to-noise ratio (SNR) regime the signal processing performance degrades moderately by ${2}/{\pi}$ ($-1.96$ dB) when comparing to an ideal $\infty$-bit converter. Due to hardware imperfections, low-complexity $1$-bit ADCs will in practice exhibit an unknown threshold different from zero. Therefore, we study the accuracy which can be obtained with receive data processed by a hard-limiter with unknown quantization level by using asymptotically optimal channel estimation algorithms. To characterize the estimation performance of these nonlinear algorithms, we employ analytic error expressions for different setups while modeling the offset as a nuisance parameter. In the low SNR regime, we establish the necessary condition for a vanishing loss due to missing offset knowledge at the receiver. As an application, we consider the estimation of single-input single-output wireless channels with inter-symbol interference and validate our analysis by comparing the analytic and experimental performance of the studied estimation algorithms. Finally, we comment on the extension to multiple-input multiple-output channel models

Linear Precoding for the MIMO Multiple Access Channel with Finite Alphabet Inputs and Statistical CSI

In this paper, we investigate the design of linear precoders for the multiple-input multiple-output (MIMO) multiple access channel (MAC). We assume that statistical channel state information (CSI) is available at the transmitters and consider the problem under the practical finite alphabet input assumption. First, we derive an asymptotic (in the large system limit) expression for the weighted sum rate (WSR) of the MIMO MAC with finite alphabet inputs and Weichselberger's MIMO channel model. Subsequently, we obtain the optimal structures of the linear precoders of the users maximizing the asymptotic WSR and an iterative algorithm for determining the precoders. We show that the complexity of the proposed precoder design is significantly lower than that of MIMO MAC precoders designed for finite alphabet inputs and instantaneous CSI. Simulation results for finite alphabet signalling indicate that the proposed precoder achieves significant performance gains over existing precoder designs.Comment: Accepted by IEEE Transactions on Wireless Communications. arXiv admin note: substantial text overlap with arXiv:1401.540

Optimal Data Detection in Large MIMO

Large multiple-input multiple-output (MIMO) appears in massive multi-user MIMO and randomly-spread code-division multiple access (CDMA)-based wireless systems. In order to cope with the excessively high complexity of optimal data detection in such systems, a variety of efficient yet sub-optimal algorithms have been proposed in the past. In this paper, we propose a data detection algorithm that is computationally efficient and optimal in a sense that it is able to achieve the same error-rate performance as the individually optimal (IO) data detector under certain assumptions on the MIMO system matrix and constellation alphabet. Our algorithm, which we refer to as LAMA (short for large MIMO AMP), builds on complex-valued Bayesian approximate message passing (AMP), which enables an exact analytical characterization of the performance and complexity in the large-system limit via the state-evolution framework. We derive optimality conditions for LAMA and investigate performance/complexity trade-offs. As a byproduct of our analysis, we recover classical results of IO data detection for randomly-spread CDMA. We furthermore provide practical ways for LAMA to approach the theoretical performance limits in realistic, finite-dimensional systems at low computational complexity