| Nowadays in the digital age it has become a very important task to transform natural analogsignals into digital ones that can then be further processed by computational devices. This is doneby sampling the analog signals through Nyquist rate to capture the essence of the signal.Unfortunately, in many important and emerging applications, the Nyquist rate is so high that it stillis too costly, or even physically impossible, to make devices capable of acquiring samples at thisrate. In some other applications, it may not be possible to store the data so sampled because ofeither the huge amount of data or the limited storage of the devices. Although a signal that is sparsein a certain basis could be well compressed by just storing the significant coefficients and theirlocations, the fundamental weakness of this approach is that most of the data that is acquired at avery high rate in the beginning would be discarded later for compression. As such, the sparse natureof this class of signals is exploited to reduce the amount of data to a reasonably approximation levelthat is required to represent the signal. In order to improve sensing efficiency for signals that have asparse representation, a new signal acquisition paradigm named as compressed sensing (CS) hasrecently been proposed. CS acquires a signal of interest indirectly by collecting a relatively smallnumber of its projections rather than evenly sampling it at the Nyquist rate. This data acquisitionmechanism measures the signal in an compressed manner, which marks a fundamental departurefrom the conventional data acquisition-compression-transmission-decompressed manner. CSenables a potentially large reduction in the sampling cost for sensing sparse signals, which hasattracted extensive attention from academic researchers and become a hot research topic in thesignal processing field. Although there now exist a wide variety of approaches in CS to recover asparse signal from a small number of linear measurements, this dissertation focuses on real-worldsystems in which the measurements are likely to be contaminated by some form of noise, andinvestigates algorithm for the reconstruction of sparse signals from noisy measurements.MIMO-OFDM (Multiple-In Multiple-Out Orthogonal Frequency Division Multiplexing) hasbeen considered as a key technology of4G wireless communication systems. It is well known thatthe equalization, coherent detection and the advantage promised by MIMO-OFDM systems rely onthe precise knowledge of the channel state information (CSI). In real wireless environments,however, the CSI is unknown. Therefore, channel estimation is of crucial importance in MIMO-OFDM systems. In conventional pilot signal assisted channel estimation approaches, inorder to keep track of the frequency-selective channel characteristics, the pilot symbols must beplaced frequently as coherent bandwidth is. In various wireless propagation environments, only afew dominant propagation paths are considered significant in the channel impulse response. Thesedominant paths make the channel impulse response have a sparse nature. However, conventionalchannel estimation methods ignore the inherent sparse prior knowledge of multipath channels, andmost of the existing sparse channel estimation methods ignore the effect of pulse-shaping filter andmatched filter. This dissertation focuses on the above-mentioned problem and investigatescompressed channel sensing method for pulse-shaping MIMO-OFDM systems through jointlyconsidring both the compressed sensing and channel estimation. The main work and contributionsof this dissertation are summarized as follows.First, a novel reconstruction algorithm named l2-Sl0(smoothed l0-norm regularized least-square)is proposed, which uses a regularization parameter to balance the influence of the data-fitting termand the sparsity-inducing term on its objective function. Four methods are proposed to solve theunconstrained optimization problem, namely, the quasi-Newton method BFGS, conjugate-gradientmethod, iterative optimization in the null and complement spaces of the measurement matrix, andan approximate gradient method. In addition, an improved-Sl0algorithm is proposed, which uses avariable factor rather than a constant factor to control the decrease step of the parameter in objectivefunction. The simulation results show that the improved-Sl0algorithm can obtain a betterreconstruction accuracy as compared with the Sl0algorithm, and the l2-Sl0algorithm has morerobust capability againt noise than the Sl0algorithm.Then, a compressed channel sensing approach for pulse-shaping MIMO-OFDM systems isproposed. In the case of sampling duration-based channels in which the path delay can be exactlymeasured by a multiple of the sampling duration, by applying the prior information of thepulse-shaping filter in the transmitter and the matched filter in the receiver, an expression for thecomposite channel including the two filters and the pure wireless channel is obtained, which can beviewed as a sparse representation of the composite channel. Based on the sparse representation, theproblem of pure wireless channel estimation in pulse-shaping MIMO-OFDM systems can bemodeled as a signal reconstruction problem in compressed sensing framework. In addition, adeterministic selection of pilot tones to be used for compressed channel sensing is proposed, which uses a polynomial with variable order and coefficients to obtain several candidate sets and thenselects the one that can minimize the coherence of the measurement matrix as the pilot tones.Simulation results show that the l2-Sl0compressed channel sensing method for pulse-shapingMIMO-OFDM systems can save many pilot signals to maintain the same estimation performance asgiven by the conventional LS (least square) method.Finally, a compressed channel sensing method for slow time-varying doubly-selective channelsis proposed. The two dimensional time-frequency bounded region, which is composed of time delayof multi-path channel and Doppler frequency shift, is quantized. Since the number of multi-path ismuch smaller than that of quantization points, the representation coefficient has obvious sparsecharacter when the channel impulse response is linear represented by all the quantization points,and every parameter in the actual model is approximated by a closest quantization point in the grid.Based on the sparse representation of channel impulse response, the estimation of slowtime-varying doubly-selective channel in OFDM, MIMO, and MIMO-OFDM systems is modeledas the problem of sparse signal reconstruction in compressed sensing. Simulation results show thatthe l2-Sl0compressed channel sensing method gives a better estimation performance in terms ofMSE (mean square error) than the OMP (orthogonal matching pursuit) method. |
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