Closed-Form Word Error Rate Analysis for Successive Interference Cancellation Decoders

Abstract

We consider the estimation of an integer vector $\hbx\in \mathbb{Z}^n$ from the linear observation $\y=\A\hbx+\v$, where $\A\in\mathbb{R}^{m\times n}$ is a random matrix with independent and identically distributed (i.i.d.) standard Gaussian $\mathcal{N}(0,1)$ entries, and $\check{\in }{\mathbb{R}}^m$ is a noise vector with i.i.d. $\mathcal{N}(0,{\sigma }^2)$ entries with given $\sigma$. In digital communications, $\hbx$ is typically uniformly distributed over an $n$-dimensional box $\mathcal{B}$. For this estimation problem, successive interference cancellation (SIC) decoders are popular due to their low complexity, and a detailed analysis of their word error rates (WERs) is highly useful. In this paper, we derive closed-form WER expressions for two cases: (1) $\hbx\in \mathbb{Z}^n$ is fixed and (2) $\hbx$ is uniformly distributed over $\mathcal{B}$. We also investigate some of their properties in detail and show that they agree closely with simulated word error probabilities.

arXiv commentTo appear in IEEE Transactions on Wireless Communications

References in corpus (1)

• LLL Reduction Achieves the Receive Diversity in MIMO Decoding