Fundamental Limits for Jammer-Resilient Communication in Finite-Resolution MIMO

TL;DR

This paper provides a fundamental bound on the mutual information between the quantized receive signal and the legitimate transmit signal and shows that, for any fixed ADC resolution, the mutual information tends to zero as the jammer power tends to infinity, regardless of the quantization strategy.

Abstract

Spatial filtering based on multiple-input multiple-output (MIMO) processing is a powerful method for jammer mitigation. In principle, a MIMO receiver can null the interference of a single-antenna jammer at the cost of only one degree of freedom - if the number of receive antennas is large, communication performance is barely affected. In this paper, we show that the potential for MIMO jammer mitigation based on the digital outputs of finite-resolution analog-to-digital converters (ADCs) is fundamentally worse: Strong jammers will either cause the ADCs to saturate (when the ADCs' quantization range is small) or drown legitimate communication signals in quantization noise (when the ADCs' quantization range is large). We provide a fundamental bound on the mutual information between the quantized receive signal and the legitimate transmit signal. Our bound shows that, for any fixed ADC resolution, the mutual information tends to zero as the jammer power tends to infinity, regardless of the quantization strategy. Our bound also confirms the intuition that for every 6.02 dB increase in jamming power, the ADC resolution must be increased by 1 bit in order to prevent the mutual information from vanishing.

Figures (4)

• Figure 1: The bound from thm:quant as a function of the reciprocal signal-to-interference-plus-noise ratio $\mathsf{SINR}_c^{-1}$. The number $M$ of ADC quantization levels is expressed by the number of equivalent bits $\log M$. Dashed curves are based on the weaker (but more intuitive) bound from rem:simplified.
• Figure 2: Cumulative distribution functions (CDFs) over channel realizations of the bound from thm:main, for two different channel models. The number $M$ of ADC quantization levels is expressed by the number of equivalent bits $\log M$. Dashed curves are based on the weaker bound from rem:simplified.
• Figure 3: Cumulative distribution functions (CDFs) over channel realizations of the lower bound from prop:unquant_mi and of the jammer-free mutual information from \ref{['eq:jf_mi']} for two different channel models. fig:unquantized_rayleigh also plots the CDF of a jammer-free $(B\!-\!I)\times U$ MIMO system as described in prop:unquant_small.
• Figure 4: Top: Illustration of the integral in \ref{['eq:rewrite_min_max']} for an arbitrary boundary set $\Gamma$. Middle: Illustration of the discretization $g_n\approx g$ (for finite $n$) used in \ref{['eq:insert_limit']}. The discretization $p_n\approx p_{d_c}$ is not shown to preserve figure legibility. Bottom: For any $n$ and $\Gamma$, the inner product of $p_{d_c}$ (or its discretized version $p_n$) with $\max_{\gamma\in\Gamma} g_n(x-2^{-n}\phi_n(\gamma))$ is upper bounded by rearranging the piece-wise constant segments of the $M\!-\!1$ translations of $g_n$ as shown in the bottom figure. The rearranged segments converge to $g(x/(M\!-\!1))$ as $n\to\infty$.

Theorems & Definitions (9)

• Theorem 1
• Theorem 2
• Remark 1
• Theorem 3
• Remark 2
• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4