Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals

TL;DR

This paper develops advanced detection techniques for multiple-antenna cognitive radios to identify primary user signals, providing analytical expressions for detection probabilities and practical design guidelines, especially when primary signals outnumber antennas.

Contribution

It introduces new analytical methods for signal detection in multi-antenna cognitive radios, including large-sample approximations and threshold design rules, for scenarios with multiple primary users.

Findings

Derived exact moments of the GLRT statistic.

Established Gaussian convergence of the normalized GLRT statistic.

Provided detection probability expressions without channel knowledge.

Abstract

We consider multiple-antenna signal detection of primary user transmission signals by a secondary user receiver in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary user. We first derive exact expressions for the moments of the generalized likelihood ratio test (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate. Further, using results from large random matrix theory, we derive expressions to compute the detection probability without explicit knowledge of the channel, and then particularize these expressions for two scenarios of practical interest: 1) a single primary user sending spatially multiplexed signals, and 2) multiple spatially distributed primary users. Our analytical results are finally used to obtain simple design rules for the signal detection threshold.