Coherent signalling and receiver diversity for fading channels

Demands for faster data rates on wireless and cellular channels have led to much current interest in the use of two-dimensional (2-D) M-ary signalling formats and in the use of diversity techniques. Moreover, coherent detection of digital signallings transmitted over wireless fading channels has better power efficiency than conventional differential detectors. However, accurate performance analyses of general coherent two-dimensional signal constellations in fading environments have not been reported, particularly for diversity systems. In this thesis, new analytical expressions for the exact symbol error rates (SER) in slow Ricean, Rayleigh and Nakagami fading with diversity combining are presented for any 2-D signalling format having polygonal decision boundaries. Three types of combining techniques are considered: maximal ratio combining (MRC), equal gain combining (EGC) and selection combining (SC). These numerically efficient SER formulas make it possible for the first time to optimise parameters of various constellations precisely and to determine which constellation has the lowest probability of error. Numerical results for the performances of seventeen coherent 8-ary and 16-ary modulations in additive white Gaussian noise (AWGN) and slowly fading channels with diversity reception are discussed.; Perfect coherent detection is difficult to implement in a wireless environment. In the case of imperfect coherent detection, there is constant or varying error in the channel amplitude estimation or phase estimation or both. The robustness of a 2-D constellation to channel amplitude and phase error is indicated by its amplitude and phase error tolerance, two parameters examined in this thesis. Furthermore, new simple SER expressions for general 2-D constellations with polygonal decision boundaries in the presence of a constant channel estimation error are derived. This study vividly demonstrates the effect of imperfect channel estimation on the error performance of a 2-D constellation and easily distinguishes some signal sets from others for their strong tolerance to channel estimation error although these signal sets all have similar performance in the perfect coherent detection scenario. Practical pilot symbol aided 2-D modulation systems are analysed and simulated to demonstrate the effects of dynamic channel estimation errors on 2-D signalling in fading. The performance studies for both ideal and practical coherent detections provide a good reference for engineers to select a constellation to meet their design requirements.; The probability of error of higher dimensional signallings are investigated for three classes of M-ary orthogonal signals in Rayleigh fading. In particular, new symbol error rates (and bit error rates) for coherent 3-ary and 4-ary orthogonal and transorthogonal signallings, and 6-ary and 8-ary biorthogonal signallings in slow Rayleigh fading are presented and these new expressions are found to be close approximations for the error rates of arbitrary M-ary orthogonal, transorthogonal or biorthgonal signalling.