Noncoherent Reception with Polynomial Approximation of Fast Fading Channel States

In noncoherent reception under Rayleigh channel conditions, a receiver based on the generalized likelihood ratio test (GLRT) has good performance. However, to implement the “true” GLRT, it is necessary to know the correlation properties and noise power of the communication channel. In this paper, an approximation of channel states using a polynomial basis is proposed. In this case, no additional information about the channel is required. Moreover, the computational complexity of this reception method is lower, since the number of necessary correlators depends on the degree of the polynomial, instead of the length of the signal. In the considered scenarios, the results align with the “true” GLRT under slow fading conditions, while under fast fading, the performance degradation does not exceed 2.5 dB.