This paper considers channel estimation and system performance for the uplink of a single-cell massive multiple-input multiple-output system. Each receiver antenna of the base station is assumed to be equipped with a pair of one-bit analog-to-digital converters to quantize the real and imaginary part of the received signal. We first propose an approach for channel estimation that is applicable for both flat and frequency-selective fading, based on the Bussgang decomposition that reformulates the nonlinear quantizer as a linear function with identical first- and second-order statistics. The resulting channel estimator outperforms previously proposed approaches across all SNRs. We then derive closed-form expressions for the achievable rate in flat fading channels assuming low SNR and a large number of users for the maximal ratio and zero forcing receivers that takes channel estimation error due to both noise and one-bit quantization into account. The closed-form expressions, in turn, allow us to obtain insight into important system design issues such as optimal resource allocation, maximal sum spectral efficiency, overall energy efficiency, and number of antennas. Numerical results are presented to verify our analytical results and demonstrate the benefit of optimizing system performance accordingly.

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Channel Estimation and Performance Analysis of One-Bit Massive MIMO Systems

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.

Throughput Analysis of Massive MIMO Uplink With Low-Resolution ADCs

Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas $M$ than scheduled users $K$ because the users’ channels are likely to be near-orthogonal when $M/K > 10$ . However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users $K^\star$ depends on $M$ and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of $K^\star$ in the large- $M$ regime is derived in closed form, while simulations are used to show what happens at finite $M$ , in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal $M/K$ is less than 10 in many cases of practical relevance. Interestingly, $K^\star$ depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same $K$ .

Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?

Random Matrix Methods for Wireless Communications: Estimation

We develop a broadband channel estimation algorithm for millimeter wave (mmWave) multiple input multiple output (MIMO) systems with few-bit analog-to-digital converters (ADCs). Our methodology exploits the joint sparsity of the mmWave MIMO channel in the angle and delay domains. We formulate the estimation problem as a noisy quantized compressed-sensing problem and solve it using efficient approximate message passing (AMP) algorithms. In particular, we model the angle-delay coefficients using a Bernoulli–Gaussian-mixture distribution with unknown parameters and use the expectation-maximization forms of the generalized AMP and vector AMP algorithms to simultaneously learn the distributional parameters and compute approximately minimum mean-squared error (MSE) estimates of the channel coefficients. We design a training sequence that allows fast, fast Fourier transform based implementation of these algorithms while minimizing peak-to-average power ratio at the transmitter, making our methods scale efficiently to large numbers of antenna elements and delays. We present the results of a detailed simulation study that compares our algorithms to several benchmarks. Our study investigates the effect of SNR, training length, training type, ADC resolution, and runtime on channel estimation MSE, mutual information, and achievable rate. It shows that, in a mmWave MIMO system, the methods we propose to exploit joint angle-delay sparsity allow 1-bit ADCs to perform comparably to infinite-bit ADCs at low SNR, and 4-bit ADCs to perform comparably to infinite-bit ADCs at medium SNR.

Channel Estimation in Broadband Millimeter Wave MIMO Systems With Few-Bit ADCs

In this letter, we investigate the downlink performance of massive multiple-input multiple-output (MIMO) systems where the base station is equipped with one-bit analog-to-digital/digital-to-analog converters (ADC/DACs) We assume that the base station employs the linear minimum mean-squared-error channel estimator and treats the channel estimate as the true channel to precode the data symbols We derive an expression for the downlink achievable rate for matched-filter precoding A detailed analysis of the resulting power efficiency is pursued using our expression of the achievable rate Numerical results are presented to verify our analysis In particular, it is shown that, compared with conventional massive MIMO systems, the performance loss in one-bit massive MIMO systems can be compensated for by deploying approximately 25 times more antennas at the BS

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Downlink Achievable Rate Analysis in Massive MIMO Systems With One-Bit DACs

In this letter, we investigate the downlink performance of massive multiple-input multiple-output (MIMO) systems where the base station is equipped with one-bit analogto-digital/digital-to-analog converters (ADC/DACs). Considering training-based transmission, we assume the base station (BS) employs the linear minimum mean-squared-error (LMMSE) channel estimator and treats the channel estimate as the true channel to precode the data symbols. We derive an expression for the downlink achievable rate for matched-filter (MF) precoding. A detailed analysis of the resulting power efficiency is pursued using our expression of the achievable rate. Numerical results are presented to verify our analysis. In particular it is shown that, compared with conventional massive MIMO systems, the performance loss in one-bit massive MIMO systems can be compensated for by deploying approximately 2.5 times more antennas at the BS.

Downlink Achievable Rate Analysis in Massive MIMO Systems with One-Bit DACs

This paper considers channel estimation and achievable rates for the uplink of a massive multiple-input multiple-output (MIMO) system where the base station is equipped with one-bit analog-to-digital converters (ADCs). By rewriting the nonlinear one-bit quantization using a linear expression, we first derive a simple and insightful expression for the linear minimum mean-square-error (LMMSE) channel estimator. Then employing this channel estimator, we derive a closed-form expression for the lower bound of the achievable rate for the maximum ratio combiner (MRC) receiver. Numerical results are presented to verify our analysis and show that our proposed LMMSE channel estimator outperforms the near maximum likelihood (nML) estimator proposed previously.

Channel Estimation and Uplink Achievable Rates in One-Bit Massive MIMO Systems

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Yongzhi Li

Papers

Channel Estimation and Performance Analysis of One-Bit Massive MIMO Systems

Downlink Achievable Rate Analysis in Massive MIMO Systems With One-Bit DACs

Downlink Achievable Rate Analysis in Massive MIMO Systems with One-Bit DACs

Channel Estimation and Uplink Achievable Rates in One-Bit Massive MIMO Systems

Channel estimation and uplink achievable rates in one-bit massive MIMO systems