Accelerating Iteratively Linear Detectors in Multi-User (ELAA-)MIMO Systems with UW-SVD

TL;DR

It is proven that the e-channel matrix is better conditioned than the original MIMO channel for spatially correlated (ELAA-)MIMO channels, which implies that UW-SVD can accelerate current iterative algorithms, which is confirmed by the simulation results.

Abstract

Current iterative multiple-input multiple-output (MIMO) detectors suffer from slow convergence when the wireless channel is ill-conditioned. The ill-conditioning is mainly caused by spatial correlation between channel columns corresponding to the same user equipment, known as intra-user interference. In addition, in the emerging MIMO systems using an extremely large aperture array (ELAA), spatial non-stationarity can make the channel even more ill-conditioned. In this paper, user-wise singular value decomposition (UW-SVD) is proposed to accelerate the convergence of iterative MIMO detectors. Its basic principle is to perform SVD on each user's sub-channel matrix to eliminate intra-user interference. Then, the MIMO signal model is effectively transformed into an equivalent signal (e-signal) model, comprising an e-channel matrix and an e-signal vector. Existing iterative algorithms can be used to recover the e-signal vector, which undergoes post-processing to obtain the signal vector. It is proven that the e-channel matrix is better conditioned than the original MIMO channel for spatially correlated (ELAA-)MIMO channels. This implies that UW-SVD can accelerate current iterative algorithms, which is confirmed by our simulation results. Specifically, it can speed up convergence by up to 10 times in both uncoded and coded systems.

Figures (8)

• Figure 1: Illustration of the major differences between the current iterative algorithms and UW-SVD-assisted iterative algorithms.
• Figure 2: The comparison of $\mathrm{cond}(\mathbf{A})$ and $\mathrm{cond}(\mathbf{\Phi})$ in Model 1 and Model 2; $M = 256$; $K = 8$; $N_{\textsc{ue}} = 4$; $\rho = 10$$\mathrm{dB}$. $\mathrm{cond}(\mathbf{\Phi})$ is smaller than $\mathrm{cond}(\mathbf{A})$ for both ZF/LMMSE detectors, especially in correlated MIMO channels. The matrices in Model 1 and Model 2 have almost the same condition numbers.
• Figure 3: The comparison of $\mathrm{cond}(\mathbf{A})$ and $\mathrm{cond}(\mathbf{\Phi})$ in Model 3 and Model 4; $M = 256$; $K = 8$; $N_{\textsc{ue}} = 4$. $\mathrm{cond}(\mathbf{\Phi})$ is much smaller than $\mathrm{cond}(\mathbf{A})$ for both ZF/LMMSE detectors in the presence of LoS links. The condition number of $\mathbf{\Phi}$ is similar to that of i.i.d. Rayleigh channel at different correlation levels.
• Figure 4: Convergence comparison between different iterative algorithms in Model 1. $M = 256$; $K = 8$; $N_{\textsc{ue}} = 4$; $16$ QAM. UW-SVD-assisted algorithms can provide faster convergence compared to the corresponding existing algorithms, especially for correlated MIMO channels.
• Figure 5: Convergence comparison between UW-SVD-assisted SSOR (red lines) and SSOR (black lines) methods converging to LMMSE detection performance; $M = 256$; $K = 8$; $N_{\textsc{ue}} = 4$. It is shown that SSOR (UW-SVD) converges faster than SSOR at all different SNR levels.

Theorems & Definitions (7)

• Remark 1
• Theorem 1
• Lemma 1
• Theorem 2
• Theorem 3
• Remark 2
• Remark 3