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

Abstract

Abstract-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 compressedsensing problem and solve it using efficient approximate message passing (AMP) algorithms. In particular, we model the angledelay coefficients using a Bernoulli-Gaussian-mixture distribution with unknown parameters and use the expectation-maximization (EM) forms of the generalized AMP (GAMP) and vector AMP (VAMP) 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, FFT-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 one-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 via gradient pursuit for mmWave massive MIMO systems with one-bit ADCs

“…6 and 7, we compare the performance of Algorithms 2, 3, and other estimators when H is random. The Bernoulli Gaussian-GAMP (BG-GAMP) algorithm [15] is an iterative approximate MMSE estimator of x * , which was derived based on the assumption that x * i is distributed as CN (0, 1) with probability L/B but zero otherwise, namely the BG distribution. The fast iterative shrinkage-thresholding algorithm (FISTA) [38] is an iterative MAP estimator of x * , which was derived based on the assumption that the logarithm of the PDF of x * is g FISTA (x) = −γ x 1 ignoring the constant factor, namely the Laplace distribution.…”

“…The achievable rate lower bound shown in Fig. 7 is presented in [15], which was derived based on the Bussgang decomposition [13] in conjunction with the fact that the worst-case noise is Gaussian. According to Fig.…”

“…In practice, the complexity of Algorithms 2 and 3 is demanding because h(x) and ∇h(x) are required at each iteration, which are high-dimensional functions defined on C B where B ≫ M N . In recent works on channel estimation and data detection in the mmWave band [14], [15], [28], the FFT-based implementation is widely used because H can be approximated by (7) using overcomplete DFT matrices. In this paper, an FFT-based fast implementation of h(x) and ∇h(x) is proposed, which is motivated by [14], [15], [28].…”

“…Achievable rate lower bound[15] vs. SNR where M = N = 64, T = 80, and L = 4 with varying B RX and B TX from algorithm to algorithm.…”

Dynamic Metasurface Antennas for Bit-Constrained MIMO-OFDM Receivers

“…To guarantee that the elements are configured with a feasible quality factor, we fix the ratio Ω R i,l χ i,l to be in the discrete set [0. 1,5,30], and carry out the non-linear least-squared curve fitting in Algorithm 3, implemented using the Levenberg-Marquardt method [43], with respect to the resonance frequency Ω R i,l for each…”