Finding the Optimal Demodulator Under Implementation Constraints

TL;DR

This paper develops practical approximation methods for demodulation and quantization in Gaussian channels, optimizing mutual information and capacity under implementation constraints, with applications to 8PSK BICM systems.

Contribution

It introduces simple, asymptotic solutions for quantization thresholds, mismatched decoding metrics, and demodulation strategies that enhance system performance within implementation limits.

Findings

Quantization thresholds linearly depend on noise standard deviation.

Mismatched capacity metric outperforms traditional metrics in simulations.

Proposed algorithms are efficient for firmware implementation and improve commercial chip performance.

Abstract

The common approach of designing a communication device is to maximize a well-defined objective function, e.g., the channel capacity and the cut-off rate. We propose easy-to-implement solutions for Gaussian channels that approximate the optimal results for these maximization problems. Three topics are addressed. First, we consider the case where the channel output is quantized, and we find the quantization thresholds that maximize the mutual information. The approximation derived from the asymptotic solution has a negligible loss on the entire range of SNR when 2-PAM modulation is used, and its quantization thresholds linearly depend on the standard deviation of noise. We also derive a simple estimator of the relative capacity loss due to quantization, based on the high-rate limit. Then we consider the integer constraint on the decoding metric, and maximize the mismatched channel capacity. We study the asymptotic solution of the optimal metric assignment and show that the same approximation we derived in the matched decoding case still holds for the mismatched decoder. Finally, we consider the demodulation problem for 8PSK bit-interleaved coded modulation(BICM). We derive the approximated optimal demodulation metrics that maximize the general cut-off rate or the mismatched capacity using max-log approximation . The error rate performances of the two metrics' assignments are compared, based on Reed-Solomon-Viterbi(RSV) code, and the mismatched capacity metric turns out to be better. The proposed approximation can be computed using an efficient firmware algorithm, and improves the system performance of commercial chips.