Distribution dependent adaptive learning

The aim of this thesis is to develop algorithms and techniques for adaptive signal processing in non-Gaussian noise environment with applications to communications channel estimation and equalisation. Practical communication systems are affected by thermal noise, caused by the thermal (Brownian) motion of particles in components. Thermal noise is readily modelled as a stationary independent Gaussian stochastic process popularly known as additive white Gaussian noise (AWGN). The adaptive signal processing for communication systems has been predominated by this AWGN assumption. Channel estimation and equalisation forms an integral part of communications receivers which are usually designed using the Gaussian noise assumption. In some communication channels, the observation noise exhibits impulsive, as well as Gaussian characteristics. On the other hand, recent increase in the use of wireless devices results in many such wireless devices operating in the vicinity of another wireless device. This has caused an increase in interference from the other wireless devices operating in the same band, which effectively causes the noise in the presence of interference to deviate from Gaussianity. Thus in practice the Gaussian noise assumption does not hold for practical communication systems and scenarios. To improve the performance of adaptive algorithms, we develop algorithms adapted on the noise characteristics rather than adapting only on second order statistics. The developments in this thesis can be classified in two major works. First work is on developing a minimum bit-error rate (MB ER) decision feedback equaliser (DFE) for impulsive noise modelled as an a-stable distribution. The development exploits the stable nature of the a-distribution and the concepts build on earlier work in a Gaussian noise environment. Further, a Wiener-filter-with-limiter solution is also presented and used as a performance bench mark. An improvement in convergence and BER performance is achieved by using a minimum bit error rate (MIBER) cost function instead of a conventional least mean square (LMS) based design. The ability of least BER (LB ER) equalisers based on a Gaussian noise assumption to operate in an a-stable noise environment is also highlighted. In the second work, a block based maximum-likelihood algorithm using kernel density estimates to improve channel estimation in non-Gaussian noise environment is proposed. The likelihood pdf is assumed unknown and is estimated by using a kernel density estimator at the receiver. Thereby combining log-likelihood as a cost function with a kernel density estimator provides a robust channel estimator, which could be used for various non-Gaussian noise environments without any modification. The performance of the proposed estimator is compared with the theoretical lower bounds for associated noise distribution. The simulations for impulsive noise and co-channel interference (CCI) in the presence of Gaussian noise, confirms that a better estimate can be obtained by using the proposed technique as compared to the traditional algorithms. The proposed algorithm is then applied to orthogonal frequency division multiplexing (OFDM) communication systems. A considerable performance improvement is observed when using a non-parametric channel estimator in conjunction with a symbol-by-symbol nonparametric maximum a-posteriori probability (MAP) equaliser. Since, in practice, CCI is correlated in nature, a whitening filter based approach for channel estimation is proposed. In order to make the channel estimation technique robust to channel order mismatch, a novel technique to simultaneously adapt the channel order and channel coefficient is discussed.