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

Abstract

Abstract-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.

Eigenvalue based SNR estimation for cognitive radio in presence of channel correlation

“…The theoretical analysis for SNR estimation in the presence of both noise and channel correlation can be found in [25].…”

“…SinceR Z follows MP law, its R transform can be written as the R transform of MP law and is given by (25). Using the transformations included in the preliminaries, we get the Stieltjes transform ofR Y as described in the next subsection.…”

Maximum Eigenvalue detection for spectrum sensing under correlated noise

“…The causes of noise correlation for a multi-dimensional CR in practical scenarios have been discussed in [21]. In this study, we consider noise correlation across the receive dimensions and not across the temporal dimension as mentioned before.…”

“…Subsequently, a Signal to Noise Ratio (SNR) estimation technique has been proposed in order to estimate the PU SNR in the presence of correlated noise based on the analysis under signal plus noise hypothesis. Furthermore, the contribution in [21] studies an SNR estimation technique for a multidimensional CR receiver under correlated channel/noise based on the maximum eigenvalue of the received signal's sample covariance matrix.…”

“…However, in practice, the noise may be correlated due to imperfections in filtering interference or oversampling operations [6,21]. Since the value of decision statistics in the presence of noise correlation deviates from its value in uncorrelated scenarios, a sensing threshold proposed for the uncorrelated scenario may not be suitable for sensing in the presence of noise correlation [10].…”