Design of optimal equalizers and precoders for MIMO channels

Channel equalization has been extensively studied as a method of combating ISI and ICI for high speed MIMO data communication systems. This dissertation focuses on optimal channel equalization in the presence of non-white observation noises with unknown PSD but bounded power-norm. A worst-case approach to optimal design of channel equalizers leads to an equivalent optimal H-infinity filtering problem for the MIMO communication systems. An explicit design algorithm is derived which not only achieves the zero-forcing (ZF) condition, but also minimizes the RMS error between the transmitted symbols and the received symbols. The second part of this dissertation investigates the design of optimal precoders which minimize the bit error rate (BER) subject to a fixed transmit-power constraint for the multiple antennas downlink communication channels under the perfect reconstruction (PR) condition. The closed form solutions are derived and an efficient design algorithm is proposed. The performance evaluations indicate that the optimal precoder design for multiple antennas communication systems proposed herein is an attractive/reasonable alternative to the existing precoder design techniques

Joint bit allocation and precoding for filterbank transceivers in NOFDM systems

Recently, the non orthogonal frequency division multiplexing (NOFDM) systems have attracted increased interest. They have several advantages over traditional OFDM systems: higher bandwidth efficiency; reduced sensitivity to carrier frequency offsets, oscillator phase noise and narrowband interference; and reduced intersymbol/intercarrier interference (ISI/ICI). In particular, low ISI/ICI will be important for future systems where Doppler frequencies will be larger (equivalently, channel variations will be faster) due to higher carrier frequencies and higher mobile velocities. In the first part of this thesis the duality of multicarrier systems and Gabor frames is discussed and applied to the design of a generalized multicarrier system based on a filterbank structure. The efficient polyphase implementation is also discussed. In this thesis the channel capacity of a GMC systems is evaluated through the diagonalization of an equivalent matrix model where intersymbol and intercarrier interferences have been included. Exploiting the majorization theory, the mutual information can be represented as a Schur-concave function and it is maximized through a joint transceiver design adding a linear precoder at the transmitter and a LMMSE equalizer at the receiver. The capacity is derived by the eigenvalue decomposition of the global system matrix including the noise colored by the receiver filtering and employing a power allocation of the transmitted power according to the well-known water-filling solution. This thesis investigates also the behaviour of the NOFDM systems when a power and bit allocation algorithm (like the Campello one) is employed in order to satisfy a certain QoS constrain. A comparison of the performances with OFDM systems is included. Finally a simple application of the cognitive radio paradigm employing filterbankbased multicarrier systems is developed and some interesting results are showed

A compressed sensing approach to block-iterative equalization: connections and applications to radar imaging reconstruction

The widespread of underdetermined systems has brought forth a variety of new algorithmic solutions, which capitalize on the Compressed Sensing (CS) of sparse data. While well known greedy or iterative threshold type of CS recursions take the form of an adaptive filter followed by a proximal operator, this is no different in spirit from the role of block iterative decision-feedback equalizers (BI-DFE), where structure is roughly exploited by the signal constellation slicer. By taking advantage of the intrinsic sparsity of signal modulations in a communications scenario, the concept of interblock interference (IBI) can be approached more cunningly in light of CS concepts, whereby the optimal feedback of detected symbols is devised adaptively. The new DFE takes the form of a more efficient re-estimation scheme, proposed under recursive-least-squares based adaptations. Whenever suitable, these recursions are derived under a reduced-complexity, widely-linear formulation, which further reduces the minimum-mean-square-error (MMSE) in comparison with traditional strictly-linear approaches. Besides maximizing system throughput, the new algorithms exhibit significantly higher performance when compared to existing methods. Our reasoning will also show that a properly formulated BI-DFE turns out to be a powerful CS algorithm itself. A new algorithm, referred to as CS-Block DFE (CS-BDFE) exhibits improved convergence and detection when compared to first order methods, thus outperforming the state-of-the-art Complex Approximate Message Passing (CAMP) recursions. The merits of the new recursions are illustrated under a novel 3D MIMO Radar formulation, where the CAMP algorithm is shown to fail with respect to important performance measures.A proliferação de sistemas sub-determinados trouxe a tona uma gama de novas soluções algorítmicas, baseadas no sensoriamento compressivo (CS) de dados esparsos. As recursões do tipo greedy e de limitação iterativa para CS se apresentam comumente como um filtro adaptativo seguido de um operador proximal, não muito diferente dos equalizadores de realimentação de decisão iterativos em blocos (BI-DFE), em que um decisor explora a estrutura do sinal de constelação. A partir da esparsidade intrínseca presente na modulação de sinais no contexto de comunicações, a interferência entre blocos (IBI) pode ser abordada utilizando-se o conceito de CS, onde a realimentação ótima de símbolos detectados é realizada de forma adaptativa. O novo DFE se apresenta como um esquema mais eficiente de reestimação, baseado na atualização por mínimos quadrados recursivos (RLS). Sempre que possível estas recursões são propostas via formulação linear no sentido amplo, o que reduz ainda mais o erro médio quadrático mínimo (MMSE) em comparação com abordagens tradicionais. Além de maximizar a taxa de transferência de informação, o novo algoritmo exibe um desempenho significativamente superior quando comparado aos métodos existentes. Também mostraremos que um equalizador BI-DFE formulado adequadamente se torna um poderoso algoritmo de CS. O novo algoritmo CS-BDFE apresenta convergência e detecção aprimoradas, quando comparado a métodos de primeira ordem, superando as recursões de Passagem de Mensagem Aproximada para Complexos (CAMP). Os méritos das novas recursões são ilustrados através de um modelo tridimensional para radares MIMO recentemente proposto, onde o algoritmo CAMP falha em aspectos importantes de medidas de desempenho

Doctor of Philosophy

dissertationThe demand for high speed communication has been increasing in the past two decades. Multicarrier communication technology has been suggested to address this demand. Orthogonal frequency-division multiplexing (OFDM) is the most widely used multicarrier technique. However, OFDM has a number of disadvantages in time-varying channels, multiple access, and cognitive radios. On the other hand, filterbank multicarrier (FBMC) communication has been suggested as an alternative to OFDM that can overcome the disadvantages of OFDM. In this dissertation, we investigate the application of filtered multitone (FMT), a subset of FBMC modulation methods, to slow fading and fast fading channels. We investigate the FMT transmitter and receiver in continuous and discrete time domains. An efficient implementation of FMT systems is derived and the conditions for perfect reconstruction in an FBMC communication system are presented. We derive equations for FMT in slow fading channels that allow evaluation of FMT when applied to mobile wireless communication systems. We consider using fractionally spaced per tone channel equalizers with different number of taps. The numerical results are presented to investigate the performance of these equalizers. The numerical results show that single-tap equalizers suffice for typical wireless channels. The equalizer design study is advanced by introducing adaptive equalizers which use channel estimation. We derive equations for a minimum mean square error (MMSE) channel estimator and improve the channel estimation by considering the finite duration of channel impulse response. The results of optimum equalizers (when channel is known perfectly) are compared with those of the adaptive equalizers, and it is found that a loss of 1 dB or less incurs. We also introduce a new form of FMT which is specially designed to handle doubly dispersive channels. This method is called FMT-dd (FMT for doubly dispersive channels). The proposed FMT-dd is applied to two common methods of data symbol orientation in the time-frequency space grid; namely, rectangular and hexagonal lattices. The performance of these methods along with OFDM and the conventional FMT are compared and a significant improvement in performance is observed. The FMT-dd design is applied to real-world underwater acoustic (UWA) communication channels. The experimental results from an at-sea experiment (ACOMM10) show that this new design provides a significant gain over OFDM. The feasibility of implementing a MIMO system for multicarrier UWA communication channels is studied through computer simulations. Our study emphasizes the bandwidth efficiency of multicarrier MIMO communications .We show that the value of MIMO to UWA communication is very limited

Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part I: Nash Equilibria

In this two-parts paper we propose a decentralized strategy, based on a game-theoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipoint-to-multipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and bandwidth. We assume, as optimality criterion, the achievement of a Nash equilibrium and consider two alternative optimization problems: 1) the competitive maximization of mutual information on each link, given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies; and 2) the competitive maximization of the transmission rate, using finite order constellations, under the same constraints as above, plus a constraint on the average error probability. In Part I of the paper, we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies. Then, we prove that the optimal precoding/multiplexing scheme for both games leads to a channel diagonalizing structure, so that both matrix-valued problems can be recast in a simpler unified vector power control game, with no performance penalty. Thus, we study this simpler game and derive sufficient conditions ensuring the uniqueness of the Nash equilibrium. Interestingly, although derived under stronger constraints, incorporating for example spectral mask constraints, our uniqueness conditions have broader validity than previously known conditions. Finally, we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a Pareto-optimal centralized scheme. To reach the Nash equilibria of the game, in Part II, we propose alternative distributed algorithms, along with their convergence conditions.Comment: Paper submitted to IEEE Transactions on Signal Processing, September 22, 2005. Revised March 14, 2007. Accepted June 5, 2007. To be published on IEEE Transactions on Signal Processing, 2007. To appear on IEEE Transactions on Signal Processing, 200

Doctor of Philosophy

dissertationThe use of multicarrier techniques has allowed the rapid expansion of broadband wireless communications. Orthogonal frequency division multiplexing (OFDM) has been the most dominant technology in the past decade. It has been deployed in both indoor Wi-Fi and cellular environments, and has been researched for use in underwater acoustic channels. Recent works in wireless communications include the extension of OFDM to multiple access applications. Multiple access OFDM, or orthogonal frequency division multiple access (OFDMA), has been implemented in the third generation partnership project (3GPP) long- term evolution (LTE) downlink. In order to reduce the intercarrier interference (ICI) when user's synchronization is relaxed, filterbank multicarrier communication (FBMC) systems have been proposed. The first contribution made in this dissertation is a novel study of the classical FBMC systems that were presented in 1960s. We note that two distinct methods were presented then. We show that these methods are closely related through a modulation and a time/frequency scaling step. For cellular channels, OFDM also has the weakness of relatively large peak-to-average power ratios (PAPR). A special form of OFDM for the uplink of multiple access networks, called single carrier frequency division multiple access (SC-FDMA), has been developed to mitigate this issue. In this regard, this dissertation makes two contributions. First, we develop an optimization method for designing an effective precoding method for SC-FDMA systems. Second, we show how an equivalent to SC-FDMA can be developed for systems that are based on FBMC. In underwater acoustic communications applications, researchers are investigating the use of multicarrier communication systems like OFDM in underwater channels. The movement of the communicating vehicles scales the received signal along the time axis, which is often referred to as Doppler scaling. To undo the signal degradation, researchers have investigated methods to estimate the Doppler scaling factor and restore the original signal using resampling. We investigate a method called nonuniform fast Fourier transform (NUFFT) and apply that to increase the precision in the detection and correction of the Doppler scaling factor. NUFFT is applied to both OFDM and FBMC and its performance over the experimental data obtained from at sea experiments is investigated