Asymptotic Performance of Linear Receivers in MIMO Fading Channels (0810.0883v2)

Abstract: Linear receivers are an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-SNR regime in terms of the Diversity-Multiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear Zero-Forcing (ZF) and linear Minimum Mean-Square Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and non-asymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of a MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear receiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.

• The paper analyzes the diversity-multiplexing tradeoff (DMT) for ZF and MMSE linear receivers, showing they are suboptimal compared to maximum likelihood (ML) decoding but potentially viable with increased antennas.
• The study characterizes error probability, noting that while MMSE receivers perform comparably to ML at low rates, this advantage diminishes at higher rates.
• It shows that the mutual information output of MMSE and ZF linear receivers converges to a Gaussian distribution in large antenna scenarios, providing a framework for performance prediction at scale.

Analysis of Asymptotic Performance of Linear Receivers in MIMO Fading Channels

The paper explores the characterization of multi-input multi-output (MIMO) systems that employ linear receivers as an alternative to optimal decoding methods, which are notably complex. The authors present an extensive information-theoretic analysis to capture the performance dynamics of these linear receivers across two significant asymptotic regimes: fixed antenna count with high signal-to-noise ratio (SNR) and large but finite antenna arrays with fixed SNR.

Key Contributions and Findings

The primary contributions of this paper can be summarized as follows:

1. Diversity-Multiplexing Tradeoff (DMT) Analysis: The research provides a detailed examination of the DMT for MIMO channels when using zero-forcing (ZF) and minimum mean-square error (MMSE) linear receivers. It establishes that both receiver types achieve suboptimal DMT levels relative to maximum likelihood (ML) decoding, despite employing outer coding and decoding.
2. Error Probability Characterization: The paper differentiates between high-SNR regime measures based on the DMT and large-system limits where the antenna count is significant. It highlights that, while the performance of MMSE receivers at low rates is comparable to ML receivers, this advantage diminishes significantly at higher rates.
3. Asymptotic Gaussianity in Large Antenna Regimes: When considering large antenna scenarios, the paper demonstrates that the mutual information output of MMSE and ZF linear receivers converges to a Gaussian distribution. This result is pivotal for system design, providing a framework to predict system performance at scale.
4. Impact of Antenna Scaling on System Design: The researchers argue that increasing the number of antennas in conjunction with linear processing may be a viable strategy to achieve performance targets set for spectral efficiency and block-error rates without the complexities associated with optimal receivers.

Theoretical and Practical Implications

The results outlined offer both theoretical insights and practical implications for the design and analysis of future wireless systems:

• Theoretical Insight: By extending the DMT framework to linear receivers, the paper bridges a gap in understanding how simplified receiver architectures scale in challenging environments. The demonstrated asymptotic Gaussian behavior advocates for revisiting assumptions in the dominant channel models and assessing them under varying system scales.
• Practical Implications: The paper supports the design rationale of relying on low-complexity linear receivers to balance computational cost and performance. It offers a profound message that practitioners can leverage to optimize wireless system design by favoring more antennas over increased receiver complexity, particularly in scenarios where massive MIMO deployments are feasible.

Future Directions

The research opens avenues for future work, suggesting deviations from traditional optimal decoding might be strategically favorable when balanced by increasing spatial resources. Investigation could further extend to scenarios of imperfect channel state information (CSI) or non-ideal transmission models such as frequency-selective channels, which remain pertinent areas relevant to applying these findings in practical frameworks.

In conclusion, this paper shifts the conventional focus from complexity-heavy MIMO receiver designs to scalable and pragmatic solutions by harnessing the asymptotic properties of linear detectors in conjunction with increasing antenna resources. The insights provided have enduring value as the telecommunications field progresses towards more efficient and scalable multi-user, multi-antenna solutions.