Data-Aided Regularization of Direct-Estimate Combiner in Distributed MIMO Systems

TL;DR

Addresses covariance mismatch in the uplink direct-estimate combiner for distributed MIMO under limited pilot symbols. Proposes data-aided regularization by shrinking the pilot covariance using $\mathbf{R}(\alpha)$ and solving $\mathbf{W}=\frac{1}{\tau^{\mathrm{p}}}\mathbf{R}(\alpha)^{-1}\mathbf{Y}^{\mathrm{p}}\mathbf{P}$, with an initial closed-form $\alpha$ from covariance matching and a subsequent iterative update based on the hard-decision MSE $\epsilon(\alpha)$. Demonstrates substantial SER gains (3–4 dB) for small $\tau^{\mathrm{p}}$ and robustness improvements in interference scenarios, bringing performance closer to the perfect CSI benchmark and reducing reliance on explicit CSI in uplink distributed MIMO.

Abstract

This paper explores the data-aided regularization of the direct-estimate combiner in the uplink of a distributed multiple-input multiple-output system. The network-wide combiner can be computed directly from the pilot signal received at each access point, eliminating the need for explicit channel estimation. However, the sample covariance matrix of the received pilot signal that is used in its computation may significantly deviate from the actual covariance matrix when the number of pilot symbols is limited. To address this, we apply a regularization to the sample covariance matrix using a shrinkage coefficient based on the received data signal. Initially, the shrinkage coefficient is determined by minimizing the difference between the sample covariance matrices obtained from the received pilot and data signals. Given the limitations of this approach in interference-limited scenarios, the shrinkage coefficient is iteratively optimized using the sample mean squared error of the hard-decision symbols, which is more closely related to the actual system's performance, e.g., the symbol error rate (SER). Numerical results demonstrate that the proposed regularization of the direct-estimate combiner significantly enhances the SER, particularly when the number of pilot symbols is limited.

Figures (5)

• Figure 1: Uplink transmission of the pilot and data signals within the coherence interval.
• Figure 2: SER of QPSK versus UE transmit power for $K = 6$, $\tau^{\textnormal{\tiny{p}}} = 8$, and $\tau^{\textnormal{\tiny{d}}} = 1000$, without interference.
• Figure 3: SER of QPSK versus UE transmit power for $K = 6$, $\tau^{\textnormal{\tiny{p}}} = 8$, and $\tau^{\textnormal{\tiny{d}}} = 1000$, with interference.
• Figure 4: SER of QPSK versus pilot length for $K = 6$, $\rho_k = 15$ dBm, and $\tau^{\textnormal{\tiny{d}}} = 1000$, with interference.
• Figure : Iterative update of the shrinkage coefficient