Error Performance of circular 16-DAPSK in Frequency- Selective Rayleigh Fading Channels with Diversity Reception

An expression for the error probability of raised cosine filtered circular 16-ary differential amplztude and phase shift keying (circular 16-DAPSK) in a frequency-selective Rayleigh fading channel with pos td t tection diversity reception i s o(5tained. T h e effect of delay spread, modulation ring ratio and ,jilter roll-off are also considered in the formula t ion . For a constant bit rate, the average irreducible bit error probability f o r circular 1 tiDAPSK is shown t o be superior t o th8at of 16-DPSK but slightly worse t h a n Q-DPSK. Introduction Future mobile networks are looking to integrate digital voice with high capacity data based services. Digitid modems are prone to the introduction of an irreducible error rate that arises as a result of user motion and/or time dispersion in the channel [l]. The resulting error floors are independent of signal strength and, unless corrected, can limit either the speed of the mobile (Doppler) or the maximum transmission rate (time dispersion). Hence, for a high data rate wireless modem, the effect of delay spread must be carefully considered. The effect of delay spread on bandwidth efficient modulations schemes has already been investigated by various authors. The error performance of quadrature coherent PSK with bandlimiting raised cosine (YLC)i pulse shaping was examined in [2],[3]. Both papers concluded that Q-PSIK outperform B-PSK under the same channel conditions. An indepth treatment of the error performance of RC filtered Q-DPSK with postdetection diversity combining is covered in [4]. The error performance of M-ary DPSK in frequency selective channels has already been analysed including the effects of Doppler shift [ 5 ] , where diversity combining was considered with time-limited pulse shapes. Recently, work in [6] has formulated the error performance of RC filtered M-DPSK in a frequency-selective Rayleigh fading channel with diversity reception. The irrducible bit error probability of B-DPSK is worse than higher level schemes such as 4, 8 and 16-DPSK. No improvement is observed when the modulation level is greater than four. This trend arises since the impact of a more complex, higher level, constellation pattern can override the advantages of a longer symbol period. The error performance of PSK and APSK (amplitude and phase shift keying) in a frequency-selective Rayleigh fading channel has also been reported in earlier works. In [7], 16-QAM was compared with M-PSK assumming coherent detection. In [8], circular 16-DAPSK was compared with M-DPSK. Both works used RC pulse shaping, however diversity reception was not considered in the comparison. Recently, in [9], the authors have calculated the error probability of circular 16-DAPSK in a frequency-selective Rayleigh fading channel with postdetection diversity reception and tirnelimited pulse shapes. The results have shown that circular 16-DAPSK performs better when compared with 16DPSK and the improvement increases when diversity is applied. However, in a pratical situation, a bandlimited signal is normally used to improve bandwidth efficiency in a mobile system. Therefore, to justify the advantage of circular 16-DAPSK over 16-DPSK, it is essential to analysis t,he error performance of circular 16-DAPSK with bandliniited filtering. The aim of this paper is to extend the work in [9], so that the error probability can be calculated when bandlimited pulse shapes are applied to circular 16-DAPSK in a frequency-selective Rayleigh channel. The expression takes into account factors such as root mean square (rms) delay spread, ring ratio, raised cosine roll-off factor and post-detection diversity combining. Using such equations, the irreducible error floor introduced by delay spread can be evaluated and the sensitivity to the filter roll-off value determined both with and without the use of diversity combining.