SNR Estimation for Multi-dimensional Cognitive Receiver under Correlated Channel/Noise

In addition to Spectrum Sensing (SS) capability required by a Cognitive Radio (CR), Signal to Noise Ratio (SNR) estimation of the primary signals at the CR receiver is crucial in order to adapt its coverage area dynamically using underlay techniques. In practical scenarios, channel and noise may be correlated due to various reasons and SNR estimation techniques with the assumption of white noise and uncorrelated channel may not be suitable for estimating the primary SNR. In this paper, firstly, we study the performance of different eigenvalue-based SS techniques in the presence of channel or/and noise correlation. Secondly, we carry out detailed theoretical analysis of the signal plus noise hypothesis to derive the asymptotic eigenvalue probability distribution function (a.e.p.d.f.) of the received signal´s covariance matrix under the following two cases: (i) correlated channel and white noise, and (ii) correlated channel and correlated noise, which is the main contribution of this paper. Finally, an SNR estimation technique based on the derived a.e.p.d.f is proposed in the presence of channel/noise correlation and its performance is evaluated in terms of normalized Mean Square Error (MSE). It is shown that the PU SNR can be reliably estimated when the CR sensing module is aware of the channel/noise correlation.