Performance Analysis Of Multi-Dimensional Signal In Wireless Transmissions

Information theoretic results show that the increase of signal dimension is able to offer extra degree of freedom in the field of signal design. It makes the optimization more tractable in high-dimensional spaces than that in low-dimensional ones, which means better performance. This dissertation is based on the National 863 project and National 973 project, and focuses on the performance analysis of multi-dimensional signal in wireless transmissions. Power offset analysis of two transmit multiple receive MIMO systems with antenna arrays of fixed length, phase noise sensitivity analysis of lattice constellation and performance and applications of signal space diversity over Generalized-K fading channels and MIMO Rayleigh fading channels are studied deeply.In the first chapter, the characteristic and progress of the mobile communications are reviewed. The research background and current progress of MIMO capacity, lattice and signal space diversity are introduced.In high signal-to-noise ratio (SNR) region of wireless transmissions, power offset is the zero-order term in SNR axis of SNR-capacity curve and its optimization is helpful to improve capacity. In the second chapter, based on fitting determinant curve of tri-diagonal toeplitz matrix, expression of extreme points is derived to analyze power offset of two transmit multiple receive single-user MIMO systems with uniform linear antenna array of fixed length. These proposed extreme points are determined by correlation of receive antenna elements and maximum of number of antenna elements between transmit and receive arrays. According to the obtained expression, the simulation results show that optimal power offset can be achieved by selecting suitable number of receive antenna.In the third chapter, on the assumption of large number of constellation points and high signal-to-noise ratio, phase noise sensitivity of lattice constellation is analyzed. Upper bound of symbol error rate (SER) in additive white Gaussian noise (AWGN) channel is derived from pairwise error probability. For small phase noise, phase noise channel is transformed to AWGN channel. With the aid of Wiener model, the obtained upper bound can be extended to phase noise channel. The proposed upper bound can be used as performance criterion to analyze the sensitivity of phase noise in multi-dimension lattice constellation. Simulation results show that with the same normalized spectral efficiency, higher dimension lattice constellations are more sensitive than lower ones in phase noise channel; and with the same dimension of constellation, larger normalized spectral efficiency means more performance loss in phase noise channel.In the forth chapter, Generalized-K distribution is used to model the wireless channels with composite fading. Application of signal space diversity over Generalized-K fading channel is analyzed. The expression of pairwise error probability is derived over Generalized-K fading channel. Depending on the obtained expression, it is then demonstrated that error performance in Generalized-K fading channel can approach that over AWGN channel when diversity order tends to sufficiently large. When it comes to numerical results, Generalized-K distribution is approximated by the Gamma distribution. Based on the approximation, numerical results, which are tractable, coincide with the theoretical analysis.In the fifth chapter, signal space diversity is extended to MIMO systems. Error performance of signal space diversity over MIMO Rayleigh fading channels is analyzed. Based on the small argument approximation, the probability density function of the sum of independently and identically distributed Rayleigh random variables has the form of the Nakagami density. With the aid of the approximation, expression of pairwise error probability with signal space diversity over MIMO Rayleigh channels is derived. Depending on the obtained expression, it is then demonstrated that error performance over MIMO Rayleigh fading channels can approach that over AWGN channel when diversity order tends to sufficiently large. Numerical results are provided to agree with the theoretical analysis.At last, conclusions are remarked and the possible research issues are shown.