The research reported in this thesis is concerned with robust precoder and transceiver optimization in multiuser multi-antenna wireless communication systems in the presence of imperfect channel state information(CSI). Precoding at the transmit side, which utilizes the CSI, can improve the system performance and simplify the receiver design. Transmit precoding is essential for inter-user interference cancellation in multiuser downlink where users do not cooperate. Linear and non-linear precoding have been widely investigated as low-complexity alternatives to dirty paper coding-based transmission scheme for multiuser multiple-input multiple-output(MU-MIMO)downlink. Similarly, in relay-assisted networks, precoding at the relay nodes have been shown to improve performance. The precoder and joint precoder/receive filter (transceiver) designs usually assume perfect knowledge of the CSI. In practical systems, however, the CSI will be imperfect due to estimation errors, feedback errors and feedback delays. Such imperfections in CSI will lead to deterioration of performance of the precoders/transceivers designed assuming perfect CSI. In such situations, designs which are robust to CSI errors are crucial to realize the potential of multiuser multi-antenna systems in practice. This thesis focuses on the robust designs of precoders and transceivers for MU-MIMO downlink, and for non-regenerative relay networks in the presence of errors in the CSI. We consider a norm-bounded error(NBE) model, and a stochastic error(SE) model for the CSI errors. These models are suitable for commonly encountered errors, and they allow mathematically and computationally tractable formulations for the robust designs. We adopt a statistically robust design in the case of stochastic error, and a minimax or worst-case robust design in the case of norm-bounded error. We have considered the robust precoder and transceiver designs under different performance criteria based on transmit power and quality-of-service(QoS) constraints. The work reported in this thesis can be grouped into three parts, namely,i ) robust linear pre-coder and transceiver designs for multiuser downlink, ii)robust non-linear precoder and transceiver designs for multiuser downlink, and iii)robust precoder designs for non-regenerative relay networks. Linear precoding: In this part, first, a robust precoder for multiuser multiple-input single-output(MU-MISO)downlink that minimizes the total base station(BS)transmit power with constraints on signal-to-interference-plus-noise ratio(SINR) at the user terminals is considered. We show that this problem can be reformulated as a second order cone program(SOCP) with the same order of computational complexity as that of the non-robust precoder design. Next, a robust design of linear transceiver for MU-MIMO downlink is developed. This design is based on the minimization of sum mean square error(SMSE) with a constraint on the total BS transmit power, and assumes that the error in the CSI at the transmitter(CSIT) follows the stochastic error model. For this design, an iterative algorithm based on the associated Karush-Kuhn-Tucker(KKT) conditions is proposed. Our numerical results demonstrate the robust performance of the propose designs. Non-linear precoding: In this part, we consider robust designs of Tomlinson-Harashima precoders(THP) for MU-MISO and MU-MIMO downlinks with different performance criteria and CSI error models. For MU-MISO systems with imperfect CSIT, we investigate the problem of designing robust THPs under MSE and total BS transmit power constraints. The first design is based on the minimization of total BS transmit power under constraints on the MSE at the individual user receivers. We present an iterative procedure to solve this problem, where each iteration involves the solution of a pair of convex optimization problems. The second design is based on the minimization of a stochastic function of the SMSE under a constraint on the total BS transmit power. We solve this problem efficiently by the method of alternating optimization. For MU-MIMO downlink, we propose robust THP transceiver designs that jointly optimize the TH precoder and receiver filters. We consider these transceiver designs under stochastic and norm-bounded error models for CSIT. For the SE model, we propose a minimum SMSE transceiver design. For the NBE model, we propose three robust designs, namely, minimum SMSE design, MSE-constrained design, and MSE-balancing design. Our proposed solutions to these robust design problems are based on iteratively solving a pair of sub-problems, one of which can be solved analytically, and the other can be formulated as a convex optimization problem that can be solved efficiently. Robust precoder designs for non-regenerative relay networks: In this part, we consider robust designs for two scenarios in the case of relay-assisted networks. First, we consider a non-regenerative relay network with a source-destination node pair assisted by multiple relay nodes, where each node is equipped with a single antenna. The set of the cooperating relay nodes can be considered as a distributed antenna array. For this scenario, we present a robust distributed beam former design that minimizes the total relay transmit power with a constraint on the SNR at the destination node. We show that this robust design problem can be reformulated as a semi-definite program (SDP)that can be solved efficiently. Next, we consider a non-regenerative relay network, where a set of source-destination node pairs are assisted by a MIMO-relay node, which is equipped with multiple transmit and multiple receive antennas. For this case, we consider robust designs in the presence of stochastic and norm-bounded CSI errors. We show that these problems can be reformulated as convex optimization problems. In the case of norm-bounded error, we use an approximate expression for the MSE in order to obtain a tractable solution.

Wireless systems with multiple antennas at both the transmitter and receiver (MIMO systems) have been the focus of research in the recent past due to their ability to provide higher data rates and better reliability than their single antenna counterparts. Designing a communication system for MIMO frequency selective channels provides many signal processing challenges. Popular methods like MIMOOFDM and space-time precoding linearly process blocks of data at both the transmitter and the receiver. Independence between the blocks is ensured by introducing sufficient redundancy between successive blocks. This approach has many pitfalls, including the limit on achievable data rate due to redundancy requirements and the need for additional coding/processing. In this thesis, we provide a filterbank precoding framework (FBP) for communication over MIMO frequency selective channels. By viewing the channel as a polynomial matrix, we derive the minimum redundancy required for achieving FIR equalization of the precoded channel. It is shown that, for most practical channels, a nominal redundancy is enough. The results are general, and hold for channels of any dimension and order. We derive the zero-forcing and MMSE equalizers for the precoded channel. The role of equalizer delay in system performance is analyzed. We extend the minimum redundancy result to the case of space-time filterbank precoding (STFP). Introducing the time dimension allows the channel to be represented by a block pseudocirculant matrix. By using the Smith form of block pseudocirculant matrices, we show that very high data rates can be achieved with STFP. When channel information is available at the transmitter, we derive an iterative algorithm for obtaining the MMSE optimal precoder-equalizer pair. We then provide a comparison of FBP with the block processing methods. It is shown that FBP provides better BER performance than the block processing methods at a lower computational cost. The reasons for the better performance of FBP are discussed.

This dissertation designs linear transceivers for the multiuser downlink in multiple-input multiple-output (MIMO) systems. The designs rely on an uplink/downlink duality for the mean squared error (MSE) of each individual data stream. We first consider the design of transceivers assuming channel state information (CSI) at the transmitter. We consider minimization of the sum-MSE over all users subject to a sum power constraint on each transmission. Using MSE duality, we solve a computationally simpler convex problem in a virtual uplink. The transformation back to the downlink is simplified by our demonstrating the equality of the optimal power allocations in the uplink and downlink. Our second set of designs maximize the sum throughput for all users. We establish a series of relationships linking MSE to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. We show that minimizing the product of MSE matrix determinants is equivalent to sum-rate maximization, but we demonstrate that this problem does not admit a computationally efficient solution. We simplify the problem by minimizing the product of mean squared errors (PMSE) and propose an iterative algorithm based on alternating optimization with near-optimal performance. The remainder of the thesis considers the more practical case of imperfections in CSI. First, we consider the impact of delay and limited-rate feedback. We propose a system which employs Kalman prediction to mitigate delay; feedback rate is limited by employing adaptive delta modulation. Next, we consider the robust design of the sum-MSE and PMSE minimizing precoders with delay-free but imperfect estimates of the CSI. We extend the MSE duality to the case of imperfect CSI, and consider a new optimization problem which jointly optimizes the energy allocations for training and data stages along with the sum-MSE/PMSE minimizing transceivers. We prove the separability of these two problems when all users have equal estimation error variances, and propose several techniques to address the more challenging case of unequal estimation errors.

This dissertation designs linear transceivers for the multiuser downlink in multiple-input multiple-output (MIMO) systems. The designs rely on an uplink/downlink duality for the mean squared error (MSE) of each individual data stream. We first consider the design of transceivers assuming channel state information (CSI) at the transmitter. We consider minimization of the sum-MSE over all users subject to a sum power constraint on each transmission. Using MSE duality, we solve a computationally simpler convex problem in a virtual uplink. The transformation back to the downlink is simplified by our demonstrating the equality of the optimal power allocations in the uplink and downlink. Our second set of designs maximize the sum throughput for all users. We establish a series of relationships linking MSE to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. We show that minimizing the product of MSE matrix determinants is equivalent to sum-rate maximization, but we demonstrate that this problem does not admit a computationally efficient solution. We simplify the problem by minimizing the product of mean squared errors (PMSE) and propose an iterative algorithm based on alternating optimization with near-optimal performance. The remainder of the thesis considers the more practical case of imperfections in CSI. First, we consider the impact of delay and limited-rate feedback. We propose a system which employs Kalman prediction to mitigate delay; feedback rate is limited by employing adaptive delta modulation. Next, we consider the robust design of the sum-MSE and PMSE minimizing precoders with delay-free but imperfect estimates of the CSI. We extend the MSE duality to the case of imperfect CSI, and consider a new optimization problem which jointly optimizes the energy allocations for training and data stages along with the sum-MSE/PMSE minimizing transceivers. We prove the separability of these two problems when all users have equal estimation error variances, and propose several techniques to address the more challenging case of unequal estimation errors.

This work deals with the design of MT transmit, MR receive antenna MIMO (Multiple Input Multiple Output) communication system where the transmitter performs a linear operation on data. This linear precoding model includes systems which involve signal shaping for achieving higher data rates, uncoded MIMO Multicarrier and Single-Carrier systems and, the more recent, MIMO-OFDM (Orthogonal Frequency Division Multiplexing) systems employing full diversity Space-Frequency codes. The objective of this work is to design diversity centric and rate centric linear precoded MIMO systems whose performance is better than the existing designs. In particular, we consider MIMO-OFDM systems, Zero Padded MIMO systems and MIMO systems with limited rate feedback. Design of full diversity MIMO-OFDM systems of rate symbol per channel use (1 s/ pcu) : In literature, MIMO-OFDM systems exploiting full diversity at a rate of 1 s/ pcu are based on a few specific Space-Frequency (SF)/ Space-Time-Frequency (STF) codes. In this work, we devise a general parameterized framework for the design of MIMO-OFDM systems employing full diversity STF codes of rate 1 s/ pcu. This framework unifies all existing designs and provides tools for the design of new systems with interesting properties and superior performance. Apart from rate and diversity, the parameters of the framework are designed for a low complexity receiver. The parameters of the framework usually depend on the channel characteristics (number of multipath, Delay Profile (DP)). When channel characteristics are available at the transmitter, a procedure to optimize the performance of STF codes is provided. The resulting codes are termed as DP optimized codes. Designs obtained using the optimization are illustrated and their performance is shown to be better than the existing ones. To cater to the scenarios where channel characteristics are not available at the transmitter, a complete characterization of a class of full diversity DP Independent (DPI) STF codes is provided. These codes exploit full diversity on channels with a given number of multipath irrespective of their characteristics. Design of DP optimized STF codes and DPI codes from the same framework highlights the flexibility of the framework. Design of Zero Padded (ZP) MIMO systems : While the MIMO-OFDM transmitter needs to precode data for exploiting channel induced multipath diversity, ZP MIMO systems with ML receivers are shown to exploit multipath diversity without any precoding. However, the receiver complexity of such systems is enormous and hence a study ZP MIMO system with linear receivers is undertaken. Central to this study involves devising low complexity receivers and deriving the diversity gain of linear receivers. Reduced complexity receiver implementations are presented for two classes of precoding schemes. An upper bound on the diversity gain of linear receivers is evaluated for certain precoding schemes. For uncoded systems operating on a channel of length L, this bound is shown to be MRL_MT +1 for uncoded transmissions, i.e, such systems tend to exploit receiver and multipath diversities. On the other hand, MIMO-OFDM systems designed earlier have to trade diversity with receiver complexity. These observations motivate us to use ZP MIMO systems with linear receivers for channels with large delay spread when receiver complexity is at a premium. Design examples highlighting the attractiveness of ZP systems when employed on channels with large delay spread are also presented. Efficient design of MIMO systems with limited feedback : Literature presents a number of works that consider the design of MIMO systems with partial feedback. The works that consider feedback of complete CSI, however, do not provide for an efficient system design. In this work, we consider two schemes, Correlation matrix feedback and Channel information feedback that convey complete CSI to the transmitter. This CSI is perturbed due to various impairments. A perturbation analysis is carried out to study the variations in mutual information for each of the proposed schemes. For ergodic channels, this analysis is used to design a MIMO system with a limited rate feedback. Using a codebook based approach, vector quantizers are designed to minimize the loss in ergodic capacity for each of the proposed schemes. The efficiency of the design stems from the ability to obtain closed-form expression for centroids during the iterative vector quantizer design. The performance of designed vector quantizers compare favorably with the existing designs. The vector quantizer design for channel information feedback is robust in the sense that the same codebook can be used across all operating SNR. Use of vector quantizers for improving the outage performance is also presented.

Multi-antenna wireless communication systems that employ a large number of antennas have recently stirred a lot of research interest. This is mainly due to the possibility of achieving very high spectral efficiency, power efficiency, and link reliability in such large-scale multiple-input multiple-output (MIMO) systems. An emerging architecture for large-scale multiuser MIMO communications is one where each base station (BS) is equipped with a large number of antennas (tens to hundreds of antennas) and the user terminals are equipped with fewer antennas (one to four antennas) each. The backhaul communication between base stations is also carried out using large number of antennas. Because of the high dimensionality of large-scale MIMO signals, the computational complexity of various transceiver operations can be prohibitively large. Therefore, low complexity techniques that scale well for transceiver signal processing in such large-scale MIMO systems are crucial. The transceiver operations of interest include signal encoding at the transmitter, and channel estimation, detection and decoding at the receiver. This thesis focuses on the design and analysis of novel low-complexity transceiver signal processing schemes for large-scale MIMO systems. In this thesis, we consider two types of large-scale MIMO systems, namely, massive MIMO systems and generalized spatial modulation MIMO (GSM-MIMO) systems. In massive MIMO, the mapping of information bits to modulation symbols is done using conventional modulation alphabets (e.g., QAM, PSK). In GSM-MIMO, few of the avail-able transmit antennas are activated in a given channel use, and information bits are conveyed through the indices of these active antennas, in addition to the bits conveyed through conventional modulation symbols. We also propose a novel modulation scheme named as precoder index modulation, where information bits are conveyed through the index of the chosen precoder matrix as well as the modulation symbols transmitted. Massive MIMO: In this part of the thesis, we propose a novel MIMO receiver which exploits channel hardening that occurs in large-scale MIMO channels. Channel hardening refers to the phenomenon where the off-diagonal terms of HH H become much weaker compared to the diagonal terms as the size of the channel gain matrix H increases. We exploit this phenomenon to devise a low-complexity channel estimation scheme and a message passing algorithm for signal detection at the BS receiver in massive MIMO systems. We refer to the proposed receiver as the channel hardening-exploiting message passing (CHEMP) receiver. The key novelties in the proposed CHEMP receiver are: (i) operation on the matched filtered system model, (ii) Gaussian approximation on the off-diagonal terms of the HH H matrix, and (iii) direct estimation of HH H instead of H and use of this estimate of HH H for detection The performance and complexity results show that the proposed CHEMP receiver achieves near-optimal performance in large-scale MIMO systems at complexities less than those of linear receivers like minimum mean squared error (MMSE) receiver. We also present a log-likelihood ratio (LLR) analysis that provides an analytical reasoning for this better performance of the CHEMP receiver. Further, the proposed message passing based detection algorithm enables us to combine it with low density parity check (LDPC) decoder to formulate a joint message passing based detector-decoder. For this joint detector-decoder, we design optimized irregular binary LDPC codes specific to the massive MIMO channel and the proposed receiver through EXIT chart matching. The LDPC codes thus obtained are shown to achieve improved coded bit error rate (BER) performance compared to off-the-shelf irregular LDPC codes. The performance of the CHEMP receiver degrades when the system loading factor (ratio of the number of users to the number of BS antennas) and the modulation alpha-bet size are large. It is of interest to devise receiver algorithms that work well for high system loading factors and modulation alphabet sizes. For this purpose, we propose a low-complexity factor-graph based vector message passing algorithm for signal detection. This algorithm uses a scalar Gaussian approximation of interference on the basic sys-tem model. The performance results show that this algorithm performs well for large modulation alphabets and high loading factors. We combine this detection algorithm with a non-binary LDPC decoder to obtain a joint detector-decoder, where the field size of the non-binary LDPC code is same as the size of the modulation alphabet. For this joint message passing based detector-decoder, we design optimized non-binary irregular LDPC codes tailored to the massive MIMO channel and the proposed detector. GSM-MIMO: In this part of the thesis, we consider GSM-MIMO systems in point-to-point as well as multiuser communication settings. GSM-MIMO has the advantage of requiring only fewer transmit radio frequency (RF) chains than the number of transmit antennas. We analyze the capacity of point-to-point GSM-MIMO, and obtain lower and upper bounds on the GSM-MIMO system capacity. We also derive an upper bound on the BER performance of maximum likelihood detection in GSM-MIMO systems. This bound is shown to be tight at moderate to high signal-to-noise ratios. When the number of transmit and receive antennas are large, the complexity of en-coding and decoding of GSM-MIMO signals can be prohibitively high. To alleviate this problem, we propose a low complexity GSM-MIMO encoding technique that utilizes com-binatorial number system for bits-to-symbol mapping. We also propose a novel layered message passing (LaMP) algorithm for decoding GSM-MIMO signals. Low computational complexity is achieved in the LaMP algorithm by detecting the modulation bits and the antenna index bits in two deferent layers. We then consider large-scale multiuser GSM-MIMO systems, where multiple users employ GSM at their transmitters to communicate with a BS having a large number of receive antennas. For this system, we develop computationally efficient message passing algorithms for signal detection using vector Gaussian approximation of interference. The performance results of these algorithms show that the GSM-MIMO system outperforms the massive MIMO system by several dBs for the same spectral efficiency. Precoder index modulation: It is known that the performance of a communication link can be enhanced by exploiting time diversity without reducing the rate of transmission using pseudo random phase preceding (PRPP). In order to further improve the performance of GSM-MIMO, we apply PRPP technique to GSM-MIMO systems. PRPP provides additional diversity advantage at the receiver and further improves the performance of GSM-MIMO systems. For PRPP-GSM systems, we propose methods to simultaneously precode both the antenna index bits and the modulation symbols using rectangular precoder matrices. Finally, we extend the idea of index modulation to pre-coding and propose a new modulation scheme referred to as precoder index modulation (PIM). In PIM, information bits are conveyed through the index of a prehared PRPP matrix, in addition to the information bits conveyed through the modulation symbols. PIM is shown to increase the achieved spectral efficiency, in addition to providing diver-sity advantages.

Abstract Multiple-input multiple-output transmitted signal design for the partially coherent Rayleigh fading channels with discrete inputs under a given average transmit power constraint is consider in this thesis. The objective is to design the space-time constellations and linear precoders to adapt to the degradation caused by the imperfect channel estimation at the receiver and the transmit-receive antenna correlation. The system is partially coherent so that the multiple-input multiple-output channel coefficients are estimated at the receiver and its error covariance matrix is fed back to the transmitter. Two constellation design criteria, one for the single and another for the multiple transmit antennae are proposed. An upper bound on the average bit error probability for the single transmit antenna and cutoff rate, i.e., a lower bound on the mutual information, for multiple transmit antennae are derived. Both criteria are functions of channel estimation error covariance matrix. The designed constellations are called as partially coherent constellation. Additionally, to use the resulting constellations together with forward error control codes requires efficient bit mapping schemes. Because these constellations lack geometrical symmetry in general, the Gray mapping is not always possible in the majority of the constellations obtained. Moreover, different mapping schemes may lead to highly different bit error rate performances. Thus, an efficient bit mapping algorithm called the modified binary switching algorithm is proposed. It minimizes an upper bound on the average bit error probability. It is shown through computer simulations that the designed partially coherent constellation and their optimized bit mapping algorithm together with turbo codes outperform the conventional constellations. Linear precoder design was also considered as a simpler, suboptimal alternative. The cutoff rate expression is again used as a criterion to design the linear precoder. A linear precoder is obtained by numerically maximizing the cutoff rate with respect to the precoder matrix with a given average transmit power constraint. Furthermore, the precoder matrix is decomposed using singular-value-decomposition into the input shaping, power loading, and beamforming matrices. The beamforming matrix is found to coincide with the eigenvectors of the transmit correlation matrix. The power loading and input shaping matrices are solved numerically using the difference of convex functions programming algorithm and optimization under the unitary constraint, respectively. Computer simulations show that the performance gains of the designed precoders are significant compared to the cutoff rate optimized partially coherent constellations without precoding. / Tiivistelmä Väitöskirjassa tarkastellaan lähetyssignaalien suunnittelua osittain koherenteissa Rayleigh-häipyvissä kanavissa toimiviin monitulo-monilähtöjärjestelmiin (MIMO). Lähettimen keskimääräinen lähetysteho oletetaan rajoitetuksi ja lähetyssignaali diskreetiksi. Tavoitteena on suunnitella tila-aikakonstellaatioita ja lineaarisia esikoodereita jotka mukautuvat epätäydellisen kanavaestimoinnin aiheuttamaan suorituskyvyn heikkenemiseen sekä lähetin- ja vastaanotinantennien väliseen korrelaatioon. Tarkasteltavien järjestelmien osittainen koherenttisuus tarkoittaa sitä, että MIMO-kanavan kanavakertoimet estimoidaan vastaanottimessa, josta niiden virhekovarianssimatriisi lähetetään lähettimelle. Työssä esitetään kaksi konstellaatiosuunnittelukriteeriä, toinen yhdelle lähetinantennille ja toinen moniantennilähettimelle. Molemmat kriteerit ovat kanavan estimaatiovirheen kovarianssimatriisin funktioita. Työssä johdetaan yläraja keskimääräiselle bittivirhetodennäköisyydelle yhden lähetinantennin tapauksessa sekä rajanopeus (cutoff rate), joka on alaraja keskinäisinformaatiolle, usean lähetinantennin tapauksessa. Konstellaatioiden käyttö yhdessä virheenkorjauskoodien kanssa edellyttää tehokaita menetelmiä, joilla bitit kuvataan konstellaatiopisteisiin. Koska tarvittavat konstellaatiot eivät ole tyypillisesti geometrisesti symmetrisiä, Gray-kuvaus ei ole yleensä mahdollinen.Lisäksi erilaiset kuvausmenetelmät voivat johtaa täysin erilaisiin bittivirhesuhteisiin. Tästä johtuen työssä esitetään uusi kuvausalgoritmi (modified bit switching algorithm), joka minimoi keskimääräisen bittivirhetodennäköisyyden ylärajan. Simulointitulokset osoittavat, että työssä kehitetyt konstellaatiot antavat paremman suorituskyvyn turbokoodatuissa järjestelmissä kuin perinteiset konstellaatiot. Työssä tarkastellaan myös lineaarista esikoodausta yksinkertaisena, alioptimaalisena vaihtoehtona uusille konstellaatioille. Esikoodauksen suunnittelussa käytetään samaa kriteeriä kuin konstellaatioiden kehityksessä eli rajanopeutta. Lineaarinen esikooderi löydetään numeerisesti maksimoimalla rajanopeus kun rajoitusehtona on lähetysteho. Esikoodausmatriisi hajotetaan singulaariarvohajotelmaa käyttäen esisuodatus, tehoallokaatio ja keilanmuodostusmatriiseiksi, jonka havaitaan vastaavan lähetyskorrelaatiomatriisin ominaisvektoreita. Tehoallokaatiomatriisi ratkaistaan numeerisesti käyttäen difference of convex functions -optimointia ja esisuodatusmatriisi optimoinnilla unitaarista rajoitusehtoa käyttäen. Simulaatiotulokset osoittavat uusien esikoodereiden tarjoavan merkittävän suorituskykyedun sellaisiin rajanopeusoptimoituihin osittain koherentteihin konstellaatioihin nähden, jotka eivät käytä esikoodausta.

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