Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance

Abstract

Abstract-We consider spectrum sensing of OFDM signals in an AWGN channel. For the case of completely known noise and signal powers, we set up a vector-matrix model for an OFDM signal with a cyclic prefix and derive the optimal NeymanPearson detector from first principles. The optimal detector exploits the inherent correlation of the OFDM signal incurred by the repetition of data in the cyclic prefix, using knowledge of the length of the cyclic prefix and the length of the OFDM symbol. We compare the optimal detector to the energy detector numerically. We show that the energy detector is near-optimal (within 1 dB SNR) when the noise variance is known. Thus, when the noise power is known, no substantial gain can be achieved by using any other detector than the energy detector.For the case of completely unknown noise and signal powers, we derive a generalized likelihood ratio test (GLRT) based on empirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise power or the signal power. The GLRT detector is compared to state-of-the-art OFDM signal detectors, and shown to improve the detection performance with 5 dB SNR in relevant cases.

Spectrum Sensing for Cognitive Radio : State-of-the-Art and Recent Advances

“…For example, it was shown in [7] that the performance of the energy detector is asymptotically equivalent, at low SNR, to that of the optimal detector when the signal is modulated with a zero-mean finite signal constellation, assuming that the symbols are independent of each other and that all probability distributions are perfectly known. A similar result was shown numerically in [12] for the detection of an orthogonal frequencydivision multiplexing (OFDM) signal. These results hold if all probability density functions, including that of the noise, are perfectly known.…”

“…Interestingly, here, the energy detector has the best performance when the noise variance is known, and the worst performance when the noise variance is uncertain with as little as 1 dB. When the noise power is not known, more sophisticated detectors such as those of [17] and [12] must be used.…”

“…It has been argued that for several models, and if the probability density functions under both hypotheses are perfectly known, energy detection performs close to the optimal detector [7], [12]. For example, it was shown in [7] that the performance of the energy detector is asymptotically equivalent, at low SNR, to that of the optimal detector when the signal is modulated with a zero-mean finite signal constellation, assuming that the symbols are independent of each other and that all probability distributions are perfectly known.…”

“…This comparison uses an AWGN channel, and parameters as follows: Axell [12] Huawei [18] Lei [19] Energy detection noise variance significantly improves the detector performance. Interestingly, here, the energy detector has the best performance when the noise variance is known, and the worst performance when the noise variance is uncertain with as little as 1 dB.…”

“…[10] (multiple-input/multiple-output -MIMO), when the signal is encoded with an orthogonal space-time block code (OSTBC) [28], or if the signal is an OFDM signal [12]. In these cases, the covariance matrix has a known eigenvalue structure, as shown in [29].…”