Noncoherent MT-MFSK signals with diversity reception in arbitrarily correlated and unbalanced Nakagami-m fading channels

This paper studies the performance of diversity applied to an efficient modulation/coding scheme using M-ary frequency-shift keying (MFSK) signals, with postdetection noncoherent diversity reception and combining over slow nonselective arbitrarily correlated and unbalanced Nakagami-m fading channels, in which the diversity branches can have unequal signal-to-noise ratios (SNRs), as well as different severity parameter m. This modulation/coding scheme is referred to as multiple tone MFSK (MT-MFSK) and is implemented based on balanced incomplete block design (BIB-design) from combinatorial theory. In MT-MFSK modulation, the number of tones used to represent the signals set is reduced compared with the conventional MFSK modulation, and each MT-MFSK signal is represented by a number of distinct orthogonal tones selected according to BIB-design. This mechanism drastically increase the bandwidth efficiency of the modulated signal and allows the modulator to create implicit frequency diversity. In this paper, we show that by combining the implicit frequency diversity of MT-MFSK signals with the diversity reception introduced by employing multiple receiving antennas, substantial improvements in performance can be obtained. A noncoherent square-law combining (SLC) soft-decision receiver is introduced and a union bound expression for the average symbol error probability is obtained. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the unbalanced L diversity channels are considered. The system performance is compared with that of the conventional MFSK system. The results show that this modulation/coding scheme creates a multiplicative diversity and, therefore, performs better than the conventional MFSK system in terms of power and bandwidth efficiency.