Robust Spectrum Sensing for Noncircular Signal in Multiantenna Cognitive Receivers

Although noncircular (NC) signals are frequently encountered in wireless communications, their statistical property has not yet been utilized in state-of-the-art methods for spectrum sensing. In this paper, a variant of Hadamard (HDM) ratio test is devised to exploit the NC property of the primary signals for spectrum sensing, which is named the NC-HDM algorithm. As the NC-HDM approach is able to exploit full statistical property of the NC signals and handle deviations from independent and identically distributed (IID) noise, it is superior to the state-of-the-art algorithms in detection accuracy and/or robustness. Moreover, performance analysis is conducted for the NC-HDM approach, including the invariant property, false-alarm probability and detection probability. That is, employing the moment-matching Box's Chi-square approximation, the false-alarm probability can be determined. Since the exact moments of the NC-HDM test statistic under the signal-absence hypothesis can be determined and all moments have been matched, the derived false-alarm probability is very accurate, leading to simple and precise computation of the theoretical decision threshold. On the other hand, as the first two exact moments of the NC-HDM test statistic under the signal-presence hypothesis can be precisely calculated, the detection probability based on moment-matching Beta approximation is quite accurate. Numerical results are included to demonstrate the superiority of the NC-HDM approach and validate our theoretical calculations.