Channel Estimation in Massive MIMO under Hardware Non-Linearities: Bayesian Methods versus Deep Learning

This paper considers the joint impact of non-linear hardware impairments at the base station (BS) and user equipments (UEs) on the uplink performance of single-cell massive MIMO (multiple-input multiple-output) in practical Rician fading environments. First, Bussgang decomposition-based effective channels and distortion characteristics are analytically derived and the spectral efficiency (SE) achieved by several receivers are explored for third-order non-linearities. Next, two deep feedforward neural networks are designed and trained to estimate the effective channels and the distortion variance at each BS antenna, which are used in signal detection. We compare the performance of the proposed methods with state-of-the-art distortion-aware and -unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The proposed deep learning approach improves the estimation quality by exploiting impairment characteristics, while LMMSE methods treat distortion as noise. Using the data generated by the derived effective channels for general order of non-linearities at both the BS and UEs, it is shown that the deep learning-based estimator provides better estimates of the effective channels also for non-linearities more than order three.Comment: 14 pages, 10 figures, to appear in IEEE Open Journal of the Communications Societ

Limited-Fronthaul Cell-Free Massive MIMO with Local MMSE Receiver under Rician Fading and Phase Shifts

A cell-free Massive multiple-input multiple-output (MIMO) system is considered, where the access points (APs) are linked to a central processing unit (CPU) via the limited-capacity fronthaul links. It is assumed that only the quantized version of the weighted signals are available at the CPU. The achievable rate of a limited fronthaul cell-free massive MIMO with local minimum mean square error (MMSE) detection is studied. We study the assumption of uncorrelated quantization distortion, which is commonly used in literature. We show that this assumption will not affect the validity of the insights obtained in our work. To investigate this, we compare the uplink per-user rate with different system parameters for two different scenarios; 1) the exact uplink per-user rate and 2) the uplink per-user rate while ignoring the correlation between the inputs of the quantizers. Finally, we present the conditions which imply that the quantization distortions across APs can be assumed to be uncorrelated

Hardware-Impaired Rician-Faded Cell-Free Massive MIMO Systems With Channel Aging

We study the impact of channel aging on the uplink of a cell-free (CF) massive multiple-input multiple-output (mMIMO) system by considering i) spatially-correlated Rician-faded channels; ii) hardware impairments at the access points and user equipments (UEs); and iii) two-layer large-scale fading decoding (LSFD). We first derive a closed-form spectral efficiency (SE) expression for this system, and later propose two novel optimization techniques to optimize the non-convex SE metric by exploiting the minorization-maximization (MM) method. The first one requires a numerical optimization solver, and has a high computation complexity. The second one with closed-form transmit power updates, has a trivial computation complexity. We numerically show that i) the two-layer LSFD scheme effectively mitigates the interference due to channel aging for both low- and high-velocity UEs; and ii) increasing the number of AP antennas does not mitigate the SE deterioration due to channel aging. We numerically characterize the optimal pilot length required to maximize the SE for various UE speeds. We also numerically show that the proposed closed-form MM optimization yields the same SE as that of the first technique, which requires numerical solver, and that too with a much reduced time-complexity.Comment: This work has been submitted to the IEEE Transactions on Communications for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible, 32 pages, 14 figure

Large System Analysis of Box-Relaxation in Correlated Massive MIMO Systems Under Imperfect CSI (Extended Version)

In this paper, we study the mean square error (MSE) and the bit error rate (BER) performance of the box-relaxation decoder in massive multiple-input-multiple-output (MIMO) systems under the assumptions of imperfect channel state information (CSI) and receive-side channel correlation. Our analysis assumes that the number of transmit and receive antennas ($n$,and $m$) grow simultaneously large while their ratio remains fixed. For simplicity of the analysis, we consider binary phase shift keying (BPSK) modulated signals. The asymptotic approximations of the MSE and BER enable us to derive the optimal power allocation scheme under MSE/BER minimization. Numerical simulations suggest that the asymptotic approximations are accurate even for small $n$ and $m$. They also show the important role of the box constraint in mitigating the so called double descent phenomenon