| Περίληψη: | Wireless communication systems require advanced techniques at the transmitter and at the receiver that improve the performance in hostile radio environments. The received signal is significantly distorted due to the dynamic nature of the wireless channel caused by multipath fading and Doppler spread. In order to mitigate the negative impact of the channel to the received signal quality, techniques as equalization and diversity are usually employed in the system design.
During the transmission, the phenomenon of inter-symbol interference (ISI) occurs at the receiver due to the time dispersion of the involved channels. Hence, several delayed replicas of previous symbols interfere with the current symbol. Equalization is usually employed in order to combat the effect of the ISI. Several implementations for equalization filters have been proposed, including linear and non-linear processing, providing complexity-performance trade-offs. It is known that the length of the equalization filter determines the complexity of the technique. Since the wireless channels are characterized by long and sparse impulse responses, the conventional equalizers require high computational complexity due to the large size of their filters.
In this dissertation, we have further investigated the long standing problem of equalization in light of the recently derived theory of compressed sampling (CS) for sparse and redundant representations. The developed heuristic algorithms for equalization, can exploit either the sparsity of the channel impulse response (CIR), or the sparsity of the equalizer filters, in order to derive efficient implementation designs. To this end, building on basis pursuit and matching pursuit techniques new equalization schemes have been proposed that exhibit considerable computational savings, increased performance properties and short training sequence requirements. Our main contribution for this part is the Stochastic Gradient Pursuit algorithm for sparse adaptive equalization.
An alternative approach to combat ISI is based on the orthogonal frequency division multiplexing (OFDM) system. In this system, the entire channel is divided into many narrow subchannels, so as the transmitted signals to be orthogonal to each other, despite their spectral overlap. However, in the case of doubly selective channels, the Doppler effect destroys the orthogonality between subcarriers. Thus, similarly to ISI, the effect of intercarrier interference (ICI) is introduced at the receiver, where symbols which belong to other subcarriers interfere with the current one. Considering this problem, we have developed iterative algorithms which recursively cancels the ICI at the receiver, providing performance-complexity trade-offs.
For low or medium Doppler spreads, the typical approach is to approximate the frequency-domain channel matrix with a banded one. On this premise, we derived reduced-rank preconditioned conjugate gradient (PCG) algorithms in order to estimate the equalization matrix with a reduced number of iterations. Also developed an improved PCG algorithm with the same complexity order, using the Galerkin projections theory. However, in rapidly changing environments, a severe ICI is introduced and the banded approximation results in significant performance degradation. In order to recover this performance loss, we developed regularized estimation framework for ICI equalization, with linear complexity with respect the the number of the subcarriers. Moreover, we proposed a new equalization technique which has the potential to completely cancel the ICI. This approach works in a successive manner through a number of stages, conveying from the fully-connected ordered successive interference cancellation architecture (OSIC) in order to fully suppress the residual interference at each stage of the equalizer.
On the other hand, diversity can improve the performance of the communication system by sending the information symbols through multiple signal paths, each of which fades independently. One approach to obtain diversity is through cooperative transmission, considering a group of nearby terminals (relays) as forming one virtual antenna array and applying a spatial beamforming technique so as to optimize the communication via them. Such beamforming techniques differ from their classical counterparts where the array elements are located in a common processing unit, due to the distribution of the relays in the space.
In this setting, we developed new distributed algorithms which enable the relay cooperation for the computation of the beamforming weights leveraging the computational abilities of the relays. Each relay can estimate only the corresponding entry of the principal eigenvector, combining data from its network neighbours. The proposed algorithms are applied to two distributed beamforming schemes for relay networks. In the first scheme, the beamforming vector is computed through minimization of a total transmit power subject to the receiver quality-of-service (QoS) constraint. In the second scheme, the beamforming weights are obtained through maximization of the receiver SNR subject to a total transmit power constraint. Moreover, the proposed algorithms operate blindly, implying that no training data are required to be transmitted to the relays, and adaptively, exhibiting a quite short convergence period.
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