Interferometer Fiber Optic Gyroscope (IFOG) has established as critical sensor for advance navigation systems. Sensor coil is known to be heart of IFOG. The bias drift and scale factor performance of IFOG depend on the sensor coil. The environmental perturbations like vibration, shock, temperature and magnetic field can affect the measured phase difference between the counter propagating beams, thereby introducing a bias error resulting in degradation of IFOG performance. In general these factors are both time varying and unevenly distributed throughout the coil producing a net undesirable phase shift due to variations in the optical light path, which is undistinguishable from the rotation induced signal. The development of sensor coil for high performance includes selection of optical fiber, spool material, coil winding technique and potting adhesive. In the thesis, the effects of various perturbations like temperature, vibration and magnetic field on the sensor coil are analysed, which degrades the gyro performance. The effect of temperature and vibration can be reduced by proper selection of spool material, winding method and by applying adhesive during the winding of sensor coil. The effect of magnetic field can be reduced by using the high birefringence polarization maintaining fiber with shorter beat length, shielding the sensor coil and reducing the number of twist during the winding. Design and fabrication of the sensor coil is done for control grade & navigation grade FOG with fiber length of 100 m and 1000 m respectively with the polarization maintaining fiber of two different manufacturer Fiber Core, UK and Nufern, USA selected based upon the beat length and Numerical Aperture so that sensor coil has minimum effect of magnetic field and the bending of fiber. Presently the spool material used is Aluminium alloy (HE15) for the ease of fabrication and easily availability of material. The Quadrupolar winding is done to reduce the thermal gradient effects. The indigenously developed special adhesive is applied layer by layer to reduce the environmental effects. In order to study the lifetime of sensor coil accelerated aging test (85°C, RH 85 %) for 30 days is also carried out.

The paradigm of network coding was introduced as a means to conserve bandwidth (or equivalently increase throughput) in information flow networks. Network coding makes use of the fact that unlike physical commodities, information can be replicated and coded together at the nodes of the network. As a result, routing can be strictly suboptimal in many classes of information flow networks compared to network coding. Network-error correction is the art of designing network codes such that the sinks of the network will be able to decode the required information in the presence of errors in the edges of the network, known as network-errors. The network coding problem on a network with given sink demands can be considered to have the following three major subproblems, which naturally also extend to the study of network-error correcting codes, as they can be viewed as a special class of network codes (a) Existence of a network code that satisfies the demands (b) Efficient construction of such a network code (c) Minimum alphabet size for the existence of such a network code. This thesis primarily considers linear network coding and error correction and in- vestigates solutions to these issues for certain classes of network coding and error correction problems in acyclic networks. Our contributions are broadly summarised as follows. (1) We propose the use of convolutional codes for multicast network-error correc- tion. Depending upon the number of network-errors required to be corrected in the network, convolutional codes are designed at the source of the multicast network so that these errors can be corrected at the sinks of the networks as long as they are separated by certain number of time instants (for which we give a bound). In con- trast to block codes for network-error correction which require large field sizes, using convolutional codes enables the field size of the network code to be small. We discuss the performance of such networks under the BSC edge error model. (2)Existing construction algorithms of block network-error correcting codes require a rather large field size, which grows with the size of the network and the number of sinks, and thereby can be prohibitive in large networks. In our work, we give an algorithm which, starting from a given network-error correcting code, can obtain an- other network code using a small field, with the same error correcting capability as the original code. The major step in our algorithm is to find a least degree irreducible poly- nomial which is coprime to another large degree polynomial. We utilize the algebraic properties of finite fields to implement this step so that it becomes much faster than the brute-force method. A recently proposed algorithm for network coding using small fields can be seen as a special case of our algorithm for the case of no network-errors. (3)Matroids are discrete mathematical objects which generalize the notion of linear independence of sets of vectors. It has been observed recently that matroids and network coding share a deep connection, and several important results of network coding has been obtained using these connections from matroid theory. In our work, we establish that matroids with certain special properties correspond to networks with error detecting and correcting properties. We call such networks as matroidal error detecting (or equivalently, correcting) networks. We show that networks have scalar linear network-error detecting (or correcting) codes if and only if there are associated with representable matroids with some special properties. We also use these ideas to construct matroidal error correcting networks along with their associated matroids. In the case of representable matroids, these algorithms give rise to scalar linear network- error correcting codes on such networks. Finally we also show that linear network coding is not sufficient for the general network-error detection (correction) problem with arbitrary demands. (4)Problems related to network coding for acyclic, instantaneous networks have been extensively dealt with in the past. In contrast, not much attention has been paid to networks with delays. In our work, we elaborate on the existence, construction and minimum field size issues of network codes for networks with integer delays. We show that the delays associated with the edges of the network cannot be ignored, and in fact turn out to be advantageous, disadvantageous or immaterial, depending on the topology of the network and the network coding problem considered. In the process, we also show multicast network codes which involve only delaying the symbols arriving at the nodes of the networks and coding the delayed symbols over a binary field, thereby making coding operations at the nodes less complex. (5) In the usual network coding framework, for a given set of network demands over an arbitrary acyclic network with integer delays assumed for the links, the out- put symbols at the sink nodes, at any given time instant, is a Fq-linear combination of the input symbols generated at different time instants where Fq denotes the field over which the network operates. Therefore the sinks have to use sufficient memory elements in order to decode simultaneously for the entire stream of demanded infor- mation symbols. We propose a scheme using an ν-point finite-field discrete fourier transform (DFT) which converts the output symbols at the sink nodes at any given time instant, into a Fq-linear combination of the input symbols generated during the same time instant without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into ν-instantaneous networks (ν is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach.

Every auditory event provides an information-rich signal to the brain. The signal constitutes perceptual attributes of pitch, loudness, timbre, and also, conceptual attributes like location, emotions, meaning, etc. In the present work we examine the timbre perception of time-varying signals in particular. While stationary signal timbre, by-itself is complex perceptually, the time-varying signal timbre introduces an evolving pattern, adding to its multi-dimensionality. To characterize timbre, we conduct psycho-acoustic perception tests with normal-hearing human subjects. We focus on time-varying synthetic speech signals(can be extended to music) because listeners are perceptually consistent with speech. Also, we can parametrically control the timbre and pitch glides using linear time-varying models. In order to quantify the timbre change in time-varying signals, we define the JND(Just noticeable difference) of timbre using diphthongs, synthesized using time-varying formant frequency model. The diphthong JND is defined as a two dimensional contour on the plane of percentage change of formant frequencies of terminal vowels. Thus, we simplify the perceptual probing to a lower dimensional space, i.e, 2-D even for a diphthong, which is multi-parametric. We also study the impact of pitch glide on the timbre JND of the diphthong. It is observed that timbre JND is influenced by the occurrence of pitch glide. Focusing on the magnitude of perceptual timbre change, we design a MUSHRA-like listening test using the vowel continuum in the formant-frequency space. We provide explicit anchors for reference: 0% and 100%, thus quantifying the perceptual timbre change on a 1-D scale. We also propose an objective measure of timbre change and observe that there is good correlation between the objective measure and subjective human responses of percentage timbre change. Using the above experimental methodology, we studied the influence of pitch shift on timbre perception and observed that the perceptual timbre change increases with change in pitch. We used vowels and diphthongs with 5 different types of pitch glides-(i) Constant pitch,(ii) 3-semitone linearly-up,(iii) 3 semitone linearly-down, (iv)V–like pitch glide and (v) hat-like pitch glide. The present study shows that timbre change can be measured on a 1-D scale if the perturbation is along one-dimension. We observe that for bright vowels(/a/and/i/), linearly decreasing pitch glide(dull pitch glide)causes more timbre change than linearly increasing pitch glide(bright pitch glide).For dull vowels(/u/),it is vice-versa. To summarize, in congruent pitch glides cause more perceptual timbre change than congruent pitch glides.(Congruent pitch glide implies bright pitch glide in bright vowel or dull pitch glide in dull vowel and in congruent pitch glide implies bright pitch glide in dull vowel or dull pitch glide in bright vowel.) Experiments with quadratic pitch glides show that the decay portion of pitch glide affects timbre perception more than the attack portion in short duration signals with less or no sustained part. In case of time-varying timbre, bright diphthongs show patterns similar to bright vowels. Also, for bright diphthongs(/ai/), perceived timbre change is most with decreasing pitch glide(dull pitch glide). We also observed that listeners perceive more timbre change in constant pitch than in pitch glides, congruent with the timbre or pitch glides with quadratic changes. The main conclusion of this study is that pitch and timbre do interact and in congruent pitch glides cause more timbre change than congruent pitch glides. In the case of quadratic pitch glides, listener perception of vowels is influenced by the decay than the attack in pitch glide in short duration signals. In the case of time-varying timbre also, in congruent pitch glides cause the most timbre change, followed by constant pitch glide. For congruent pitch glides and quadratic pitch glides in time-varying timbre, the listeners perceive lesser timbre change than otherwise.

With the rapid increase in available compute power and memory, and bolstered by the advent of efficient formulations and algorithms, the role of 3D full-wave computational methods for accurate modelling of complex electromagnetic (EM) structures has gained in significance. The range of problems includes Radar Cross Section (RCS) computation, analysis and design of antennas and passive microwave circuits, bio-medical non-invasive detection and therapeutics, energy harvesting etc. Further, with the rapid advances in technology trends like System-in-Package (SiP) and System-on-Chip (SoC), the fidelity of chip-to-chip communication and package-board electrical performance parameters like signal integrity (SI), power integrity (PI), electromagnetic interference (EMI) are becoming increasingly critical. Rising pin-counts to satisfy functionality requirements and decreasing layer-counts to maintain cost-effectiveness necessitates 3D full wave electromagnetic solution for accurate system modelling. Method of Moments (MoM) is one such widely used computational technique to solve a 3D electromagnetic problem with full-wave accuracy. Due to lesser number of mesh elements or discretization on the geometry, MoM has an advantage of a smaller matrix size. However, due to Green's Function interactions, the MoM matrix is dense and its solution presents a time and memory challenge. The thesis focuses on formulation and development of novel techniques that aid in fast MoM based electromagnetic solutions. With the recent paradigm shift in computer hardware architectures transitioning from single-core microprocessors to multi-core systems, it is of prime importance to parallelize the serial electromagnetic formulations in order to leverage maximum computational benefits. Therefore, the thesis explores the possibilities to expedite an electromagnetic simulation by scalable parallelization of near-linear complexity algorithms like Fast Multipole Method (FMM) on a multi-core platform. Secondly, with the best of parallelization strategies in place and near-linear complexity algorithms in use, the solution time of a complex EM problem can still be exceedingly large due to over-meshing of the geometry to achieve a desired level of accuracy. Hence, the thesis focuses on judicious placement of mesh elements on the geometry to capture the physics of the problem without compromising on accuracy- a technique called Adaptive Mesh Refinement. This facilitates a reduction in the number of solution variables or degrees of freedom in the system and hence the solution time. For multi-scale structures as encountered in chip-package-board systems, the MoM formulation breaks down for parts of the geometry having dimensions much smaller as compared to the operating wavelength. This phenomenon is popularly known as low-frequency breakdown or low-frequency instability. It results in an ill-conditioned MoM system matrix, and hence higher iteration count to converge when solved using an iterative solver framework. This consequently increases the solution time of simulation. The thesis thus proposes novel formulations to improve the spectral properties of the system matrix for real-world complex conductor and dielectric structures and hence form well-conditioned systems. This reduces the iteration count considerably for convergence and thus results in faster solution. Finally, minor changes in the geometrical design layouts can adversely affect the time-to-market of a commodity or a product. This is because the intermediate design variants, in spite of having similarities between them are treated as separate entities and therefore have to follow the conventional model-mesh-solve workflow for their analysis. This is a missed opportunity especially for design variant problems involving near-identical characteristics when the information from the previous design variant could have been used to expedite the simulation of the present design iteration. A similar problem occurs in the broadband simulation of an electromagnetic structure. The solution at a particular frequency can be expedited manifold if the matrix information from a frequency in its neighbourhood is used, provided the electrical characteristics remain nearly similar. The thesis introduces methods to re-use the subspace or Eigen-space information of a matrix from a previous design or frequency to solve the next incremental problem faster.

There is an ever increasing demand for higher spectral usage in wireless communication, radar and imaging systems. Higher spectral efficiency can be achieved using components that are aware of system environment and adapt suitably to the operating conditions. In this regard, radio frequency (RF) signal analysis is of paramount interest. Emergence of dispersive delay networks (DDN) has led to the significant development of microwave analogue-signal processing (ASP) and analysis. DDN causes displacement of spectral components in time domain, relative to the frequency dependant group delay response. The main challenge in the design of DDN in this context is in achieving broad bandwidth with high group delay dispersion (GDD). In this regard, all-pass networks (APN) have been explored as a potential wide-band DDN owing to the possibility of controlling the magnitude of loss characteristics without affecting the dispersion in group delay response. The synthesis procedure of lumped element APN using approximation methods is well known at audio frequencies. Most of these use operational amplifier and cannot be extended directly to RF. There is no generalised closed form analytical procedure at RF for the synthesis of APN with the required GDD. In this regard, this dissertation presents the design and implementation of all-pass networks as wide-band dispersive delay networks at radio frequencies. In this work, we begin by analysing the signal propagation through a DDN with a linear group delay response over a broad bandwidth. It is found that the signal experiences expansion of pulse width, reduction of its peak amplitude and a temporal displacement of the spectral components. Analytical expressions derived help initial synthesis of group delay response required for various ASP applications. As the first step towards implementation at RF, a single stage APN is designed using surface mount devices (SMD). This design approach takes into account practical issues such as parasitic due to mounting pads, available component values, physical dimensions, self-resonance frequency (SRF) and finite Q factor of the components used. Full wave simulation of the design with transmission line pads and components is carried out. This implementation is useful for frequencies up to the component SRF, generally about 5 GHz. This design approach makes the circuit footprint independent of frequency and the performance is limited only by the Q factor of the adopted technology. The Q factor affects the loss characteristics with a negligible effect on group delay response in the frequency band of interest. In order to extend the APN design for high group delay, a novel board level implementation is developed consisting of both lumped SMD components and distributed elements. The implementation results in a lower sensitivity of group delay performance to the commercially specified component value tolerances than the approach using all SMD components. It has been experimentally verified that the measured group delay is 2.4 ns at 1.85 GHz, which is thrice that reported in other approaches. The implementation has a reduced circuit footprint and is attractive in practical applications as it is a single layer micro strip realisation with less complex fabrication procedure and fewer components to assemble. As an extension of this towards wideband cascaded APN, an iterative design procedure is developed to achieve a monotonous group delay response over a broad bandwidth. The approach facilitates cascading of multiple stages of lumped APN with different resonance frequency and peak group delay to obtain linear and non-linear group delay responses with both positive and negative GDD. Circuits with both positive and negative GDD are required for various ASP applications such as compressive receivers and the present approach is unique in obtaining both the responses, not possible with many other RF dispersion techniques. Circuit models have been simulated by cascading transfer function responses of the individual APNs. The design is further extended for SMD implementation. To validate the above approach, a two stage APN is designed in the frequency range [0.5 - 1] GHz for a linear GDD of ±6 ns/GHz. Two negative GDD APNs are further cascaded to obtain a four stage implementation with an overall GDD of -12 ns/GHz. The experimental results are compared with full wave simulations for validation. The design using lumped SMD components has greatly improved the performance in terms of GDD with a reduced circuit footprint and lower insertion loss than previously reported approaches. As practical examples, the ASP modules are experimentally demonstrated using the fabricated APN. Frequency discrimination of two input frequencies with a frequency resolution of 500 MHz is demonstrated. Higher GDD results in higher separation of frequency components in time domain. Pulse compression and magnification is also demonstrated for different wideband LFM input signals. The dispersion effects of amplitude reduction, pulse width expansion and frequency chirping are thereby validated experimentally. In summary, the approaches presented in this dissertation enable the design of wideband all-pass networks to introduce dispersion delays over wide bandwidths, opening up the possibility for their use in analogue signal processing at radio frequencies. Some of these applications have been experimentally demonstrated and validated using time frequency analysis.

Wireless networks have potential applications in wireless Internet connectivity, battlefields, disaster relief, and cyber-physical systems. While the nodes in these networks communicate with each other over the air, the challenges faced by and the subsequent design criteria of these networks are diverse. In this thesis, we study and discuss a few design requirements of these networks, such as efficient utilization of the network bandwidth in IEEE 802.11 infrastructure networks, evaluating utility of sensor node deployments, and security from eavesdroppers. The presence of infrastructure IEEE 802.11 based Wireless Local Area Networks (WLANs) allows mobile users to seamlessly transfer huge volumes of data. While these networks accommodate mobility, and are a cost-effective alternative to cellular networks, they are well known to display several performance anomalies. We study a few such anomalies, and provide a performance management solution for IEEE 802.11 based WLANs. On the other hand, in sensor networks, the absence of infrastructure mandates the use of adhoc network architectures. In these architectures, nodes are required to route data to gateway nodes over a multi-hop network. These gateway nodes are larger in size, and costlier in comparison with the regular nodes. In this context, we propose a unified framework that can be used to compare different deployment scenarios, and provide a means to design efficient large-scale adhoc networks. In modern times, security has become an additional design criterion in wireless networks. Traditionally, secure transmissions were enabled using cryptographic schemes. However, in recent years, researchers have explored physical layer security as an alternative to these traditional cryptographic schemes. Physical layer security enables secure transmissions at non-zero data rate between two communicating nodes, by exploiting the degraded nature of the eavesdropper channel and the inherent randomness of the wireless medium. Also, in many practical scenarios, several nodes cooperate to improve their individual secrecy rates. Therefore, in this thesis, we also study scenarios, where cooperative schemes can improve secure end-to-end data transmission rates, while adhering to an overall power budget. In spite of the presence of voluminous reservoirs of information such as digital libraries and the Internet, asking around still remains a popular means of seeking information. In scenarios where the person is interested in communal, or location-specific information, such kind of retrieval may yield better results than a global search. Hence, wireless networks should be designed, analyzed and controlled by taking into account the evolution of the underlying social networks. This alliance between social network analysis and adhoc network architectures can greatly advance the design of network protocols, especially in environments with opportunistic communications. Therefore, in addition to the above mentioned problem, in this thesis, we have also presented and studied a model that captures the temporal evolution of information in social networks with memory.

Cognitive radios require spectral occupancy information in a given location, to avoid any interference with the existing licensed users. This is achieved by spectrum sensing. Existing narrowband, serial spectrum sensors are spectrally inefficient and power hungry. Wideband spectrum sensing increases the number of probable fre-quency candidates for cognitive radio. Wideband RF systems cannot use analog to digital converters (ADCs) for spectrum sensing without increasing the sampling rate and power consumption. The use of ADCs is limited because of the dynamic range of the signals that need to be sampled and the frequency of operation. In this work, we have presented a CMOS based area efficient, dedicated and scalable wideband parallel/serial spectrum sensor for cognitive radio. The key contributions of the thesis are: 1. An injection locked oscillator cascade (ILOC) for parallel LO synthesis. An area-efficient, wideband RF frequency synthesizer, which simultaneously gen-erates multiple local oscillator (LO) signals, is designed. It is suitable for parallel wideband RF spectrum sensing in cognitive radios. The frequency synthesizer consists of an injection locked oscillator cascade where all the LO signals are derived from a single reference oscillator. The ILOC is implemented in a 130-nm technology with an active area of 0.017 mm2. It generates 4 uni-formly spaced LO carrier frequencies from 500 MHz to 2 GHz. 2. A wideband, parallel RF spectrum sensor for cognitive radios has been de-signed. This spectrum sensor is designed to detect RF occupancy from 250 MHz to 5.25 GHz by using an array of CMOS receivers with envelope detec-tors. A parallel LO synthesizer is implemented as an ILOC. The simulated sensitivity is around -25 dBm for 250 MHz wide bandwidth. 3. A mitigation technique for harmonic downconversion in wideband spectrum sensors. The downconversion of radio frequency (RF) components around the harmonics of the local oscillator (LO), and its impact on the accuracy of white space detection using integrated spectrum sensors, is (are) studied. We propose an algorithm to mitigate the impact of harmonic Down conversion by utilizing multiple parallel downconverters in the system architecture. The proposed algorithm is validated on a test-board using commercially avail-able integrated circuits (IC) and a test-chip implemented in a 130-nm CMOS technology. The measured data shows that the impact of the harmonic down-conversion is closely related to the LO characteristics, and that much of it can be mitigated by the proposed technique. 4. A wideband spectrum sensor for narrowband energy detection. A wideband spectrum sensing system for cognitive radio is designed and implemented in a 130-nm RF mixed-mode CMOS technology. The system employs an I-Q downconverter, a pair of complex filters and a pair of envelope detectors for energy detection. The spectrum sensor works from 250 MHz to 3.25 GHz. The design makes use of the band pass nature of the complex filter to achieve two objectives : i) Separation of upper sideband (USB) and lower sideband (LSB) around the local oscillator (LO) signal and ii) Resolution of smaller bands within a large detection bandwidth. The measured sensitivity is close to -45 dBm for a single tone test over a bandwidth of 40 MHz. The measured Image reject ratio (IRR) is close to 30 dB. The overall sensing bandwidth is 3.5 GHz and the overall wideband detection bandwidth is 250 MHz which is partitioned into 40 MHz narrowband chunks with 8 such overlapping chunks.

Multiple users compete for a common resource like bandwidth to communicate data in interference networks. Existing approaches in dealing with interference limit the rate of communication due to paucity of shared resources. This limitation in the rate gets more glaring as the number of users in the network increases. For example, existing wireless systems either choose to orthogonalize the users (for example, Frequency Division Multiple Access (FDMA) systems or Code Division Multiple Access (CDMA) systems) or treat interference as Gaussian noise at the receivers. It is well known that these approaches are sub-optimal in general. Orthogonalization of users limit the number of available interference-free channels (known as degrees of freedom, abbreviated as DoF) and treating interference as noise means that the receiver cannot make use of the structure in the interfering signals. This motivates the need to analyze alternate transmit and decoding schemes in interference networks. This thesis mainly analyzes transmit schemes that use linear precoding for various configurations of interference networks with some practical constraints imposed by the use of finite input constellations, propagation delays, and channel state availability at the transmitters. The main contributions of this thesis are listed below. Achievable rates using precoding with finite constellation inputs in Gaussian Interference Channels (GIC) is analyzed. A metric for finding the approximate angle of rotation to maximally enlarge the Constellation Constrained (CC) capacity of two-user Gaussian Strong Interference Channel (GSIC) is proposed. Even as the Gaussian alphabet FDMA rate curve touches the capacity curve of the GSIC, with both the users using the same finite constellation, we show that the CC FDMA rate curve lies strictly inside the CC capacity curve at high powers. For a K-user MIMO GIC, a set of necessary and sufficient conditions on the precoders under which the mutual information between between relevant transmit-receive pairs saturate like in the single user case is derived. Gradient-ascent based algorithms to optimize the sum-rate achieved by precoding with finite constellation inputs and treating interference as noise are proposed. For a class of Gaussian interference networks with general message demands, identified as symmetrically connected interference networks, the expected sumspectral efficiency (in bits/sec/Hz) is shown to grow linearly with the number of transmitters at finite SNR, using a time-domain Interference Alignment (IA) scheme in the presence of line of sight (LOS) channels. For a 2×2 MIMO X-Network with M antennas at each node, we identify spacetime block codes that could be coupled with an appropriate precoding scheme to achieve the maximum possible sum-DoF of 4M 3 , for M = 3, 4. The proposed schemes are shown to achieve a diversity gain of M with SNR-independent finite constellation inputs. The proposed schemes have lower CSIT requirements compared to existing schemes. This thesis also makes an attempt to guarantee a minimum throughput when the zero-interference conditions cannot be satisfied in a wireline network with three unicast sessions with delays, using Precoding Based Network Alignment (PBNA). Three different PBNA schemes namely PBNA with time-varying local encoding coefficients (LECs), PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs are proposed and their feasibility conditions analyzed.

Relay-based cooperation promises significant gains in a wireless network as it provides an inde-pendent path between a source and a destination. Using simple single antenna nodes, it exploits the spatial diversity provided by the geographically separated nodes in a network to improve the robustness of the communication system against fading. Among the cooperative commu¬nication schemes, the amplify-and-forward (AF) relaying scheme is considered to be easy to implement since the relay does not need to decode its received signal. Instead, it just forwards to the destination the signal it receives from the source. We analyze the performance of fixed-gain AF relaying with imperfect channel knowledge that is acquired through an AF relay-specific training protocol. The analysis is challenging because the received signal at the destination contains the product (or cascade) of source-relay (SR) and relay-destination (RD) complex baseband channel gains, and additional products terms that arise due to imperfect estimation related errors. We focus on the time-efficient cascaded channel estimation (CCE) protocol to acquire the channel estimates at the destination. Using it, the destination can only estimate the product of SR and RD complex baseband channel gains, but not the two separately. Our analysis encompasses a single AF relay system and an opportunistic system with mul¬tiple AF relays, among which one is selected to forward its received signal to the destination, based on its SR and RD complex baseband channel gains. For a single relay system, we first de¬velop a novel SEP expression and a tight SEP upper bound. We then analyze the opportunistic multi-relay system, in which both selection and coherent demodulation use imperfect channel estimates. A distinctive aspect of our approach is the use of as few simplifying approximations as possible. It results in a new analysis that is accurate at signal-to-noise-ratios as low as 1 dB for single and multi-relay systems. Further, the training protocol is an integral part of the model and analysis. Using an insightful asymptotic analysis, we then present a simple, closed-form, nearly-optimal solution for allocation of energy between pilot and data symbols at the source and relay(s). Further, the optimal energy allocation between a source and a relay is characterized when both together operate under a sum energy constraint, as has often been assumed in the literature. In summary, the sum total of the results in this work provides a rigorous and accurate performance characterization and optimization of cascaded channel estimation for AF relaying.

Multi-antenna wireless systems have become very popular due to their theoretically predicted higher spectral efficiencies and improved performance compared to single-antenna systems. Large-scale multiple-input multiple-output (MIMO) systems refer to wireless systems where communication terminals employ tens to hundreds of antennas to achieve in-creased spectral efficiencies/sum rates, reliability, and power efficiency. Large-scale multi-antenna systems are attractive to meet the increasing wireless data rate requirements, without compromising on the bandwidth. This thesis addresses key signal processing issues in large-scale MIMO systems. Specifically, the thesis investigates efficient algorithms for signal detection and channel estimation in large-scale MIMO systems. It also investigates ‘spatial modulation,’ a multi-antenna modulation scheme that can reduce the number of transmit radio frequency (RF) chains, without compromising much on the spectral efficiency. The work reported in this thesis is comprised of the following two parts: 1 investigation of low-complexity receiver algorithms based on Markov chain Monte Carlo (MCMC) technique, tabu search, and belief propagation for large-scale uplink multiuser MIMO systems, and 2 investigation of achievable rates and signal detection in generalized spatial modulation. 1. Receiver algorithms for large-scale multiuser MIMO systems on the uplink In this part of the thesis, we propose low-complexity algorithms based on MCMC techniques, Gaussian sampling based lattice decoding (GSLD), reactive tabu search (RTS), and factor graph based belief propagation (BP) for signal detection on the uplink in large-scale multiuser MIMO systems. We also propose an efficient channel estimation scheme based on Gaussian sampling. Markov chain Monte Carlo (MCMC) sampling: We propose a novel MCMC based detection algorithm, which achieves near-optimal performance in large dimensions at low complexities by the joint use of a mixed Gibbs sampling (MGS) strategy and a multiple restart strategy with an efficient restart criterion. The proposed mixed Gibbs sampling distribution is a weighted mixture of the target distribution and uniform distribution. The presence of the uniform component in the sampling distribution allows the algorithm to exit from local traps quickly and alleviate the stalling problem encountered in conventional Gibbs sampling. We present an analysis for the optimum choice of the mixing ratio. The analysis approach is to define an absorbing Markov chain and use its property regarding the expected number of iterations needed to reach the global minima for the first time. We also propose an MCMC based algorithm which exploits the sparsity in uplink multiuser MIMO transmissions, where not all users are active simultaneously. Gaussian sampling based lattice decoding: Next, we investigate the problem of searching the closest lattice point in large dimensional lattices and its use in signal detection in large-scale MIMO systems. Specifically, we propose a Gaussian sampling based lattice decoding (GSLD) algorithm. The novelty of this algorithm is that, instead of sampling from a discrete distribution as in Gibbs sampling, the algorithm iteratively generates samples from a continuous Gaussian distribution, whose parameters are obtained analytically. This makes the complexity of the proposed algorithm to be independent of the size of the modulation alpha-bet. Also, the algorithm is able to achieve near-optimal performance for different antenna and modulation alphabet settings at low complexities. Random restart reactive tabu search (R3TS): Next, we study receiver algorithms based on reactive tabu search (RTS) technique in large-scale MIMO systems. We propose a multiple random restarts based reactive tabu search (R3TS) algorithm that achieves near-optimal performance in large-scale MIMO systems. A key feature of the proposed R3TS algorithm is its performance based restart criterion, which gives very good performance-complexity tradeoff in large-dimension systems. Lower bound on maximum likelihood (ML) bit error rate (BER) performance: We propose an approach to obtain lower bounds on the ML performance of large-scale MIMO systems using RTS simulation. In the proposed approach, we run the RTS algorithm using the transmitted vector as the initial vector, along with a suitable neighborhood definition, and find a lower bound on number of errors in ML solution. We demonstrate that the proposed bound is tight (within about 0.5 dB of the optimal performance in a 16×16MIMO system) at moderate to high SNRs. Factor graph using Gaussian approximation of interference (FG-GAI): Multiuser MIMO channels can be represented by graphical models that are fully/densely connected (loopy graphs), where conventional belief propagation yields suboptimal performance and requires high complexity. We propose a solution to this problem that uses a simple, yet effective, Gaussian approximation of interference (GAI) approach that carries out a linear per-symbol complexity message passing on a factor graph (FG) based graphical model. The proposed algorithm achieves near-optimal performance in large dimensions in frequency-flat as well as frequency-selective channels. Gaussian sampling based channel estimation: Next, we propose a Gaussian sampling based channel estimation technique for large-scale time-division duplex (TDD) MIMO systems. The proposed algorithm refines the initial estimate of the channel by iteratively detecting the data block and using that knowledge to improve the estimated channel knowledge using a Gaussian sampling based technique. We demonstrate that this algorithm achieves near-optimal performance both in terms of mean square error of the channel estimates and BER of detected data in both frequency-flat and frequency-selective channels. 2. Generalized spatial modulation In the second part of the thesis, we investigate generalized spatial modulation (GSM) in point-to point MIMO systems. GSM is attractive because of its ability to work with less number of transmit RF chains compared to traditional spatial multiplexing, without com-promising much on spectral efficiency. In this work, we show that, by using an optimum combination of number of transmit antennas and number of transmit RF chains, GSM can achieve better throughput and/or BER than spatial multiplexing. We compute tight bounds on the maximum achievable rate in a GSM system, and quantify the percentage savings in the number of transmit RF chains as well as the percentage increase in the rate achieved in GSM compared to spatial multiplexing. We also propose a Gibbs sampling based algorithm suited to detect GSM signals, which yields impressive BER performance and complexity results.