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 eigenvaluebased
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.