Novel complex adaptive signal processing techniques employing optimally derived time-varying convergence factors with applications in digital signal processing and wireless communications (2008)

In digital signal processing in general, and wireless communications in particular, the increased usage of complex signal representations, and spectrally efficient complex modulation schemes such as QPSK and QAM has necessitated the need for efficient and fast-converging complex digital signal processing techniques. In this research, novel complex adaptive digital signal processing techniques are presented, which derive optimal convergence factors or step sizes for adjusting the adaptive system coefficients at each iteration. In addition, the real and imaginary components of the complex signal and complex adaptive filter coefficients are treated as separate entities, and are independently updated. As a result, the developed methods efficiently utilize the degrees of freedom of the adaptive system, thereby exhibiting improved convergence characteristics, even in dynamic environments.
In wireless communications, acceptable co-channel, adjacent channel, and image interference rejection is often one of the most critical requirements for a receiver. In this regard, the fixed-point complex Independent Component Analysis (ICA) algorithm, called Complex FastICA, has been previously applied to realize digital blind interference suppression in stationary or slow fading environments. However, under dynamic flat fading channel conditions frequently encountered in practice, the performance of the Complex FastICA is significantly degraded. In this dissertation, novel complex block adaptive ICA algorithms employing optimal convergence factors are presented, which exhibit superior convergence speed and accuracy in time-varying flat fading channels, as compared to the Complex FastICA algorithm. The proposed algorithms are called Complex IA-ICA, Complex OBA-ICA, and Complex CBC-ICA. 
For adaptive filtering applications, the Complex Least Mean Square algorithm (Complex LMS) has been widely used in both block and sequential form, due to its computational simplicity. However, the main drawback of the Complex LMS algorithm is its slow convergence and dependence on the choice of the convergence factor. In this research, novel block and sequential based algorithms for complex adaptive digital filtering are presented, which overcome the inherent limitations of the existing Complex LMS. The block adaptive algorithms are called Complex OBA-LMS and Complex OBAI-LMS, and their sequential versions are named Complex HA-LMS and Complex IA-LMS, respectively. The performance of the developed techniques is tested in various adaptive filtering applications, such as channel estimation, and adaptive beamforming.
The combination of Orthogonal Frequency Division Multiplexing (OFDM) and the Multiple-Input-Multiple-Output (MIMO) technique is being increasingly employed for broadband wireless systems operating in frequency selective channels. However, MIMO-OFDM systems are extremely sensitive to Intercarrier Interference (ICI), caused by Carrier Frequency Offset (CFO) between local oscillators in the transmitter and the receiver. This results in crosstalk between the various OFDM subcarriers resulting in severe deterioration in performance. In order to mitigate this problem, the previously proposed Complex OBA-ICA algorithm is employed to recover user signals in the presence of ICI and channel induced mixing. The effectiveness of the Complex OBA-ICA method in performing ICI mitigation and signal separation is tested for various values of CFO, rate of channel variation, and Signal to Noise Ratio (SNR).