Communication over a wireless channel is a challenging task because of the inherent fading effects. Any wireless communication system employs some form of diversity improving techniques in order to improve the reliability of the channel. This thesis deals with efficient code design for two different spatial diversity techniques, viz, diversity by employing multiple antennas at the transmitter and/or the receiver, and diversity through cooperative commu- nication between users. In other words, this thesis deals with efficient code design for (1) multiple-input multiple-output (MIMO) channels, and (2) wireless relay channels. Codes for the MIMO channel are termed space-time (ST) codes and those for the relay channels are called distributed ST codes. The first part of the thesis focuses on ST code construction for MIMO fading channel with perfect channel state information (CSI) at the receiver, and no CSI at the transmitter. As a measure of performance we use the rate-diversity tradeoff and the Diversity-Multiplexing Gain (D-MG) Tradeoff, which are two different tradeoffs characterizing the tradeoff between the rate and the reliability achievable by any ST code. We provide two types of code constructions that are optimal with respect to the rate-diversity tradeoff; one is based on the rank-distance codes which are traditionally applied as codes for storage devices, and the second construction is based on a matrix representation of a cayley algebra. The second contribution in ST code constructions is related to codes with a certain nonvanishing determinant (NVD) property. Motivation for these constructions is a recent result on the necessary and sufficient conditions for an ST code to achieve the D-MG tradeoff. Explicit code constructions satisfying these conditions are provided for certain number of transmit antennas. The second part of the thesis focuses on distributed ST code construction for wireless relay channel. The transmission protocol follows a two-hop model wherein the source broadcasts a vector in the first hop and in the second hop the relays transmit a vector that is a transformation of the received vector by a relay-specific unitary transformation. While the source and relays do not have CSI, at the destination we assume two different scenarios (a) destina- tion with complete CSI (b) destination with only the relay-destination CSI. For both these scenarios, we derive a Chernoff bound on the pair-wise error probability and propose code design criteria. For the first case, we provide explicit construction of distributed ST codes with lower decoding complexity compared to codes based on some earlier system models. For the latter case, we propose a novel differential encoding and differential decoding technique and also provide explicit code constructions. At the heart of all these constructions is the cyclic division algebra (CDA) and its matrix representations. We translate the problem of code construction in each of the above scenarios to the problem of constructing CDAs satisfying certain properties. Explicit examples are provided to illustrate each of these constructions.

It is well known that communication using multiple antennas provides high data rate and reliability. Coding across space and time is necessary to fully exploit the gains offered by multiple input multiple output (MIMO) systems. One such popular method of coding for MIMO systems is space-time block coding. In applications where the terminals do not have enough physical space to mount multiple antennas, relaying or cooperation between multiple single antenna terminals can help achieve spatial diversity in such scenarios as well. Relaying techniques can also help improve the range and reliability of communication. Recently it has been shown that certain space-time block codes (STBCs) can be employed in a distributed fashion in single antenna relay networks to extract the same benefits as in point to point MIMO systems. Such STBCs are called distributed STBCs. However an important practical issue with STBCs and DSTBCs is its associated high maximum likelihood (ML) decoding complexity. The central theme of this thesis is to systematically construct STBCs and DSTBCs applicable for various scenarios such that are amenable for low decoding complexity. The first part of this thesis provides constructions of high rate STBCs from crossed product algebras that are minimum mean squared error (MMSE) optimal, i.e., achieves the least symbol error rate under MMSE reception. Moreover several previous constructions of MMSE optimal STBCs are found to be special cases of the constructions in this thesis. It is well known that STBCs from orthogonal designs offer single symbol ML decoding along with full diversity but the rate of orthogonal designs fall exponentially with the number of transmit antennas. Thus it is evident that there exists a tradeoff between rate and ML decoding complexity of full diversity STBCs. In the second part of the thesis, a definition of rate of a STBC is proposed and the problem of optimal tradeoff between rate and ML decoding complexity is posed. An algebraic framework based on extended Clifford algebras is introduced to study the optimal tradeoff for a class of multi-symbol ML decodable STBCs called ‘Clifford unitary weight (CUW) STBCs’ which include orthogonal designs as a special case. Code constructions optimally meeting this tradeoff are also obtained using extended Clifford algebras. All CUW-STBCs achieve full diversity as well. The third part of this thesis focusses on constructing DSTBCs with low ML decoding complexity for two hop, amplify and forward based relay networks under various scenarios. The symbol synchronous, coherent case is first considered and conditions for a DSTBC to be multi-group ML decodable are first obtained. Then three new classes of four-group ML decodable full diversity DSTBCs are systematically constructed for arbitrary number of relays. Next the symbol synchronous non-coherent case is considered and full diversity, four group decodable distributed differential STBCs (DDSTBCs) are constructed for power of two number of relays. These DDSTBCs have the best error performance compared to all previous works along with low ML decoding complexity. For the symbol asynchronous, coherent case, a transmission scheme based on orthogonal frequency division multiplexing (OFDM) is proposed to mitigate the effects of timing errors at the relay nodes and sufficient conditions for a DSTBC to be applicable in this new transmission scheme are given. Many of the existing DSTBCs including the ones in this thesis are found to satisfy these sufficient conditions. As a further extension, differential encoding is combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full diversity in symbol asynchronous, non-coherent relay networks with no knowledge of the timing errors at the relay nodes. The DDSTBCs in this thesis are proposed for application in the proposed transmission scheme for symbol asynchronous, non-coherent relay networks. As a parallel to the non-coherent schemes based on differential encoding, we also propose non-coherent schemes for symbol synchronous and symbol asynchronous relay networks that are based on training. This training based transmission scheme leverages existing coherent DSTBCs for non-coherent communication in relay networks. Simulations show that this training scheme when used along with the coherent DSTBCs in this thesis outperform the best known DDSTBCs in the literature. Finally, in the last part of the thesis, connections between multi-group ML decodable unitary weight (UW) STBCs and groups with real elements are established for the first time. Using this connection, we translate the necessary and sufficient conditions for multi-group ML decoding of UW-STBCs entirely in group theoretic terms. We discuss various examples of multi-group decodable UW-STBCs together with their associated groups and list the real elements involved. These examples include orthogonal designs, quasi-orthogonal designs among many others.

Parameter estimation and signal detection are the two key components of a wireless communication system. They directly impact the bit-error-ratio (BER) performance of the system. Several criteria have been successfully applied for parameter estimation and signal detection. They include maximum likelihood (ML), maximum a-posteriori probability (MAP), least square (LS) and minimum mean square error (MMSE) etc. In the linear detection framework, linear MMSE (LMMSE) and LS are the most popular ones. Nevertheless, these criteria do not necessarily minimize the BER, which is one of the key aspect of any communication receiver design. Thus, minimization of BER is tantamount to an important design criterion for a wireless receiver, the minimum bit/symbol error ratio (MBER/MSER). We term this design criterion as the minimum-error-probability (MEP). In this thesis, parameter estimation and signal detection have been extensively studied based on the MEP framework for various unexplored scenar-ios of a wireless communication system. Thus, this thesis has two broad categories of explorations, first parameter estimation and then signal detection. Traditionally, the MEP criterion has been well studied in the context of the discrete signal detection in the last one decade, albeit we explore this framework for the continuous parameter es-timation. We first use this framework for channel estimation in a frequency flat fading single-input single-output (SISO) system and then extend this framework to the carrier frequency offset (CFO) estimation of multi-user MIMO OFDM system. We observe a reasonably good SNR improvement to the tune of 1 to 2.5 dB at a fixed BER (tentatively at 10−3). In this context, it is extended to the scenario of multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) or MIMO-OFDM with pa-rameter estimation error statistics obtained from LMMSE only and checked its effect at the equalizer design using MEP and LMMSE criteria. In the second exploration of the MEP criterion, it is explored for signal detection in the context of MIMO-relay and MIMO systems. Various low complexity solutions are proposed to alleviate the effect of high computational complexity for the MIMO-relay. We also consider various configurations of relay like cognitive, parallel and multi-hop relaying. We also propose a data trans-mission scheme with a rate of 1/Ns (Ns is the number of antennas at the transmitter) with the help of the MEP criterion to design various components. In all these cases, we obtain considerable BER improvement compared to the existing solutions.

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.

Bayesian approaches for sparse signal recovery have enjoyed a long-standing history in signal processing and machine learning literature. Among the Bayesian techniques, the expectation maximization based Sparse Bayesian Learning(SBL) approach is an iterative procedure with global convergence guarantee to a local optimum, which uses a parameterized prior that encourages sparsity under an evidence maximization frame¬work. SBL has been successfully employed in a wide range of applications ranging from image processing to communications. In this thesis, we propose novel, efficient and low-complexity SBL-based algorithms that exploit structured sparsity in the presence of fully/partially known measurement matrices. We apply the proposed algorithms to the problem of channel estimation and data detection in Orthogonal Frequency Division Multiplexing(OFDM) systems. Further, we derive Cram´er Rao type lower Bounds(CRB) for the single and multiple measurement vector SBL problem of estimating compressible vectors and their prior distribution parameters. The main contributions of the thesis are as follows: We derive Hybrid, Bayesian and Marginalized Cram´er Rao lower bounds for the problem of estimating compressible vectors drawn from a Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error(MSE) in the estimates. Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector. OFDM is a well-known multi-carrier modulation technique that provides high spectral efficiency and resilience to multi-path distortion of the wireless channel It is well-known that the impulse response of a wideband wireless channel is approximately sparse, in the sense that it has a small number of significant components relative to the channel delay spread. In this thesis, we consider the estimation of the unknown channel coefficients and its support in SISO-OFDM systems using a SBL framework. We propose novel pilot-only and joint channel estimation and data detection algorithms in block-fading and time-varying scenarios. In the latter case, we use a first order auto-regressive model for the time-variations, and propose recursive, low-complexity Kalman filtering based algorithms for channel estimation. Monte Carlo simulations illustrate the efficacy of the proposed techniques in terms of the MSE and coded bit error rate performance. • Multiple Input Multiple Output(MIMO) combined with OFDM harnesses the inherent advantages of OFDM along with the diversity and multiplexing advantages of a MIMO system. The impulse response of wireless channels between the Nt transmit and Nr receive antennas of a MIMO-OFDM system are group approximately sparse(ga-sparse),i.e. ,the Nt Nr channels have a small number of significant paths relative to the channel delay spread, and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wire¬less channels are also group approximately-cluster sparse(ga-csparse),i.e.,every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this thesis, we cast the problem of estimating the ga-sparse and ga-csparse block-fading and time-varying channels using a multiple measurement SBL framework. We propose a bouquet of novel algorithms for MIMO-OFDM systems that generalize the algorithms proposed in the context of SISO-OFDM systems. The efficacy of the proposed techniques are demonstrated in terms of MSE and coded bit error rate performance.

Photonics and Optical techniques have advanced recently by a great extend to play an important role in Microwave and Radar applications. Antenna array of modern active phased array radars consist of multiple low power transmit and receive mod- ules. This demands distribution of the various Local Oscillator(LO) signals for up conversion of transmit signals and down conversion of receive signals during various modes of operation of a radar system. Additionally, these receivers require control and clock signals which are digital and low frequency analog, for the synchronization between receive modules. This is normally achieved through RF cables with complex distribution networks which add significantly higher additional weight to the arrays. During radar operations, radio frequency (RF) transmit signal needs to be distributed through the same modules which will in turn get distributed to all antenna elements of the array using RF cables. This makes the system bulky and these large number of cables are prone to Electromagnetic Interference (EMI) and need additional shielding. Therefore it is very desirable to distribute a combination of these RF, analog and digital signals using a distribution network that is less complex, light in weight and immune to EMI. Advancements in Optical and Microwave photonics area have enabled carrying of higher datarate signals on a single fiber due to its higher bandwidth capability including RF signals. This is achieved by employing Wavelength Division Multi- plexing (WDM) that combine high speed channels at different wavelengths. This work proposes, characterizes and evaluates an optical Wavelength Division Multiplexed(WDM) distribution network that will overcome the above mentioned problems in a phased array radar application. The work carries out a feasibility analysis supported with experimental measurements of various physical parameters like am- plitude, delay, frequency and phase variation for various radar waveforms over WDM links. Different configurations of optical distribution network are analyzed for multipoint distribution of both digital and RF signals. These network configurations are modeled and evaluated against various parameters that include power level, loss, cost and component count. A configuration which optimizes these parameters based on the application requirements is investigated. Considerable attention is paid to choose a configuration which does not provide excess loss, which is economically viable, compact and can be realized with minimum component count. After analysing the link configuration, multiplexing density of the WDM link is considered. In this work, since the number of signals to be distributed in radar systems are small, a coarse WDM(CWDM) scheme is considered for evaluation. A comparative study is also performed between coarse and dense WDM (DWDM) links for selection of a suitable multiplexing scheme. These configurations are modeled and evaluated with power budgeting. Even though CWDM scheme does not permit the utilisation of the available bandwidth to the fullest extent, these links have the advantage of having less hardware complexity and easiness of implementation. As the application requires signal distribution to thousands of transmit-receive modules, amplifiers are necessary to compensate for the reduction of signal level due to the high splitting ratio. Introduction of commonly available optical amplifiers like Erbium Doped Fiber Amplifier (EDFA), affect the CWDM channel output powers adversely due to their non-flat gain spectrum. Unlike DWDM systems, the channel separation of CWDM systems are much larger causing significantly high channel gain differences at the EDFA output. So an analysis is carried out for the selection of a suitable wavelength for CWDM channels to minimize the EDFA output power variation. If the gain difference is still significant, separate techniques needs to be implemented to flatten the output power at the antenna end. A CWDM configuration using C-band and L-band EDFAs is proposed and is supported with a feasibility analysis. As a part of evaluation of these links for radar applications, a mathematical model of the WDM link is developed by considering both the RF and digital sig- nals. A generic CWDM system consisting of transmitters, receivers, amplifiers, multiplexers/ demultiplexers and detectors are considered for the modeling. For RF signal transmission, the transmitters with external modulators are considered. Mod- eling is done based on a bottom-top approach where individual component models are initially modeled as a function of input current/power and later cascaded to obtain the link model. These models are then extended to obtain the wavelength dependent model ( spectral response) of the hybrid signal distribution link Further mathematical analysis of the developed link model revealed its variable separable nature in terms of the input power and wavelength. This led to significant reduction in the link equation complexity and development of some approximation techniques to easily represent the link behavior. The reduced form of the link spectral model was very essential as the initially developed wavelength model had a lot of parametric dependency on the component models. This mathematical reduction process led to simplification of the spectral model into a product of two independent functions, the input current and wavelength. It is also noticed that the total link power within specific wavelength range can be obtained by the integrating these functions over a specific link input power. After the mathematical modelling, an experimental prototype physical link is set up and characterized using various radar signals like continuous wave (CW) RF, pulsed RF, non linear frequency modulated signal (NLFM) etc. Additionally a proof of concept Radio-Over-Fiber (RoF) link is established to prove the superior transmission of microwave signal through an optical link. The analysis is supported with measurements on amplitude, delay, frequency and phase variations. The NLFM waveforms transmissions are further analysed using a matched _ltering process to confirm the side lobe requirement. Further a prototype WDM link is built to study the performance when digitally modulated channels are also multiplexed into the link. The link is again validated for signal levels, delay, frequency and phase parameters. Since amplitude and delay are deterministic, it is proposed that these parameter variations can be compensated by using suitable components either in the electrical or the optical domain. Radar systems use low frequency digital signals of different duty-cycles for synchronization and control across various transmit-receive modules. In the proposed link, these digital signals also modulate a WDM channel and hence the link is called a hybrid system. As the proposed link has EDFA to compensate for the splitting losses, there are chances of transient effects at the EDFA output for these low bitrate channels. Owing to the long carrier lifetime, low bitrate digital channels are prone to EDFA transient effects under specific signal and pump power conditions. Additionally, the synchronization signals used in radar application vary the duty-cycle over time, which is found to introduce variations in transient output. This practical challenge is further studied and the thesis for the first time, includes an analysis of EDFA transient e_ects for variable duty-cycle pulsed signals. The analysis is carried out for various parameters like bitrate, input power, pump power and duty-cycle. Investigations on EDFA transients on variable duty-cycle signals help in proposing a viable method to predict the lower duty-cycle transients from higher duty-cycle transients. The predicted transients were again validated against simulated transients and experimental results. As these transient effects are not desirable for radar signals, we propose a novel transient suppression techniques in optical and electrical domain which are validated with simulation and experimental measures. One suppression technique tries to avoid transient effect by keeping the optical input to EDFA always constant by feeding an inverted version of the original pulse into the EDFA along with the actual pulse. It is observed that as the wavelength of the inverted pulse is closer to the original input pulse, the transient effect settles faster. These EDFA transients are evaluated with WDM link configurations, where both high and low bitrate signals are co-propagated. Another challenging aspect of the link operation is the non-at gain spectrum of EDFA. i.e., EDFA provides unequal power level for various signals at WDM link output. This is especially true in the case of local oscillator signals, where it is preferable to have the same amplitude signals before feeding it to the mixer stages. But in the radar applications, this will require additional hardware circuits to equalize the signal level within a phased array antenna. This work also proposes some of the power equalization methods that can be used along with the WDM links. This part of the work is also supported with simulation model and experimental results. The analytical and experimental study of this thesis aids the evaluation process of a suitable optical Wavelength Division Multiplexed(WDM) distribution network that can be used for the distribution of both RF and digital signals. The optical WDM links being superior with its light weight, less loss and EMI/ EMC immunity provides a better solution to future class of radars.

Compressed Sensing (CS) is a new paradigm in signal processing which exploits the sparse or compressible nature of the signal to significantly reduce the number of measurements, without compromising on the signal reconstruction quality. Recently, many algorithms have been reported in the literature for efficient sparse signal reconstruction. Nevertheless, it is well known that the performance of any sparse reconstruction algorithm depends on many parameters like number of measurements, dimension of the sparse signal, the level of sparsity, the measurement noise power, and the underlying statistical distribution of the non-zero elements of the signal. It has been observed that a satisfactory performance of the sparse reconstruction algorithm mandates certain requirement on these parameters, which is different for different algorithms. Many applications are unlikely to fulfil this requirement. For example, imaging speed is crucial in many Magnetic Resonance Imaging (MRI) applications. This restricts the number of measurements, which in turn affects the medical diagnosis using MRI. Hence, any strategy to improve the signal reconstruction in such adverse scenario is of substantial interest in CS. Interestingly, it can be observed that the performance degradation of the sparse recovery algorithms in the aforementioned cases does not always imply a complete failure. That is, even in such adverse situations, a sparse reconstruction algorithm may provide partially correct information about the signal. In this thesis, we study this scenario and propose a novel fusion framework and an iterative framework which exploit the partial information available in the sparse signal estimate(s) to improve sparse signal reconstruction. The proposed fusion framework employs multiple sparse reconstruction algorithms, independently, for signal reconstruction. We first propose a fusion algorithm viz. FACS which fuses the estimates of multiple participating algorithms in order to improve the sparse signal reconstruction. To alleviate the inherent drawbacks of FACS and further improve the sparse signal reconstruction, we propose another fusion algorithm called CoMACS and variants of CoMACS. For low latency applications, we propose a latency friendly fusion algorithm called pFACS. We also extend the fusion framework to the MMV problem and propose the extension of FACS called MMV-FACS. We theoretically analyse the proposed fusion algorithms and derive guarantees for performance improvement. We also show that the proposed fusion algorithms are robust against both signal and measurement perturbations. Further, we demonstrate the efficacy of the proposed algorithms via numerical experiments: (i) using sparse signals with different statistical distributions in noise-free and noisy scenarios, and (ii) using real-world ECG signals. The extensive numerical experiments show that, for a judicious choice of the participating algorithms, the proposed fusion algorithms result in a sparse signal estimate which is often better than the sparse signal estimate of the best participating algorithm. The proposed fusion framework requires toemploy multiple sparse reconstruction algorithms for sparse signal reconstruction. We also propose an iterative framework and algorithm called {IFSRA to improve the performance of a given arbitrary sparse reconstruction algorithm. We theoretically analyse IFSRA and derive convergence guarantees under signal and measurement perturbations. Numerical experiments on synthetic and real-world data confirm the efficacy of IFSRA. The proposed fusion algorithms and IFSRA are general in nature and does not require any modification in the participating algorithm(s).

The radio frequency (RF) spectrum as a natural resource is severely under-utilized over time and space due to an inefficient licensing framework. As a result, in-creasing cellular and wireless network usage is placing significant demands on the licensed spectrum. This has led to the development of cognitive radios, software defined radios and mm-wave radios. Cognitive radios (CRs) enable more efficient spectrum usage over a wide range of frequencies and hence have emerged as an effective solution to handle huge network demands. They promise versatility, flex-ability and cognition which can revolutionize communications systems. However, they present greater challenges to the design of radio frequency (RF) front-ends. Instead of a narrow-band front-end optimized and tuned to the carrier frequency of interest, cognitive radios demand front-ends which are versatile, configurable, tun-able and capable of transmitting and receiving signals with different bandwidths and modulation schemes. The primary purpose of this thesis is to design a re-configurable, wide-band and low phase-noise fast settling frequency synthesizer for cognitive radio applications. Along with frequency generation, an area efficient multi-band low noise amplifier (LNA) with integrated built-in-self-test (BIST) and a strong immunity to interferers has also been proposed and implemented for these radios. This designed LNA relaxes the specification of harmonic content in the synthesizer output. Finally some preliminary work has also been done for mm-wave (V-band) frequency synthesis. The Key Contributions of this thesis are: A frequency synthesizer, based on a type-2, third-order Phase Locked Loop (PLL), covering a frequency range of 0.1-5.4 GHz, is implemented using a 0.13 µm CMOS technology. The PLL uses three voltage controlled oscillators (VCOs) to cover the whole range. It is capable of switching between any two frequencies in less than 3 µs and has phase noise values, compatible with most communication standards. The settling of the PLL in the desired state is achieved in dynamic multiple steps rather than traditional single step settling. This along with other circuit techniques like a DAC-based discriminator aided charge pump, fast acquisition pulse-clocked based PFD and timing synchro-negation is used to obtain a significantly reduced settling time A single voltage controlled LC-oscillator (LC-VCO) has been designed to cover a wide range of frequencies (2.0-4.1 GHz) using an area efficient and switch-able multi-tap inductor and a capacitor bank. The switching of the multi-tap inductor is done in the most optimal manner so as to get good phase-noise at the output. The multi-tap inductor provides a significant area advantage, and in spite of a degraded Q, provides an acceptable phase noise of -123 dBc/Hz and -113 dBc/Hz at an offset of 1 MHz at carrier frequencies of 2 and 4 GHz, respectively. Implemented in a 0.13 µm CMOS technology, the oscillator with ≈ 69 % tuning range, occupies an active area of only 0.095 mm2. An active inductor based noise-filter has been proposed to improve the phase-noise performance of the oscillator without much increase in the area. A variable gain multi-band low noise amplifier (LNA) is designed to operate over a wide range of frequencies (0.8 GHz to 2.4 GHz) using an area efficient switchable-π network. The LNA can be tuned to different gain and linearity combinations for different band settings. Depending upon the location of the interferers, a specific band can be selected to provide optimum gain and the best signal-to-intermodulation ratio. This is accomplished by the use of an on-chip Built-in-Self-Test (BIST) circuit. The maximum power gain of the amplifier is 19 dB with a return loss better than 10 dB for 7 mW of power consumption. The noise figure is 3.2 dB at 1 GHz and its third-order intercept point (I I P3) ranges from -15 dBm to 0 dBm. Implemented in a 0.13 µm CMOS technology, the LNA occupies an active area of about 0.29 mm2. Three different types of VCOs (stand-alone LC VCO, push-push VCO and a ring oscillator based VCO) for generating mm-wave frequencies have been implemented using 65-nm CMOS technology and their measured results have been analyzed

Sensor interfaces are needed to communicate the measured real-world analog values to the base¬band digital processor. They are dominated by the presence of high accuracy, high resolution analog to digital converters (ADC) in the backend. On most occasions, sensing is limited to small range measurements and low-modulation sensors where the complete dynamic range of ADC is not utilized. Designing a subsystem that integrates the sensor and the interface circuit and that works with a low resolution ADC requiring a small die-area is a challenge. In this work, we present a CMOS based area efficient, integrated sensor interface for applications like capacitance, temperature and dielectric-constant measurement. In addition, potential applica-tions for this work are in Cognitive Radios, Software Defined Radios, Capacitance Sensors, and location monitoring. The key contributions in the thesis are: 1 High Sensitivity Frequency-domain CMOS Capacitance Interface: A frequency domain capacitance interface system is proposed for a femto-farad capacitance measurement. In this technique, a ring oscillator circuit is used to generate a change in time period, due to a change in the sensor capacitance. The time-period difference of two such oscillators is compared and is read-out using a phase frequency detector and a charge pump. The output voltage of the system, is proportional to the change in the input sensor capacitance. It exhibits a maximum sensitivity of 8.1 mV/fF across a 300 fF capacitance range. 2 Sensitivity Enhancement for capacitance sensor: The sensitivity of an oscillator-based differential capacitance sensor has been improved by proposing a novel frequency domain capacitance-to-voltage (FDC) measurement technique. The capacitance sensor interface system is fabricated in a 130-nm CMOS technology with an active area of 0.17mm2 . It exhibits a maximum sensitivity of 244.8 mV/fF and a measurement resolution of 13 aF in a 10-100 fF measurement range, with a 10 pF nominal sensor capacitance and an 8-bit ADC. 3 Frequency to Digital Converter for Time/Distance measurement: A new architecture for a Vernier-based frequency-to-digital converter (VFDC) for location monitoring is pre¬sented, in which, a time interval measurement is performed with a frequency domain approach. Location monitoring is a common problem for many mobile robotic applica¬tions covering various domains, such as industrial automation, manipulation in difficult areas, rescue operations, environment exploration and monitoring, smart environments and buildings, robotic home appliances, space exploration and probing. The proposed architecture employs a new injection-locked ring oscillator (ILR) as the clock source. The proposed ILR oscillator does not need complex calibration procedures, usually required by Phase Locked Loop (PLL) based oscillators in Vernier-based time-to-digital convert¬ers. It consumes 14.4 µW and 1.15 mW from 0.4 V and 1.2 V supplies, respectively. The proposed VFDC thus achieves a large detectable range, fine time resolution, small die size and low power consumption simultaneously. The measured time-difference error is less than 50 ps at 1.2 V, enabling a resolution of 3 mm/kHz frequency shift. 4 A bio-sensor array for dielectric constant measurement: A CMOS on-chip sensor is presented to measure the dielectric constant of organic chemicals. The dielectric constant of these chemicals is measured using the oscillation frequency shift of a current controlled os¬cillator (CCO) upon the change of the sensor capacitance when exposed to the liquid. The CCO is embedded in an open-loop frequency synthesizer to convert the frequency change into voltage, which can be digitized using an off-chip analog-to-digital converter. The dielectric constant is then estimated using a detection procedure including the calibration of the sensor. 5 Integrated Temperature Sensor for thermal management: An integrated analog temper¬ature sensor which operates with simple, low-cost one-point calibration is proposed. A frequency domain technique to measure the on-chip silicon surface temperature, was used to measure the effects of temperature on the stability of a frequency synthesizer. The temperature to voltage conversion is achieved in two steps i.e. temperature to frequency, followed by frequency to voltage conversion. The output voltage can be used to com¬pensate the temperature dependent errors in the high frequency circuits, thereby reduc¬ing the performance degradation due to thermal gradient. Furthermore, a temperature measurement-based on-chip self test technique to measure the 3 dB bandwidth and the central frequency of common radio frequency circuits, was developed. This technique shows promise in performing online monitoring and temperature compensation of RF circuits.

Network coding was introduced as a means to increase throughput in communication networks when compared to routing. Network coding can be used not only to communicate messages from some nodes in the network to other nodes but are also useful when some nodes in a network are interested in computing some functions of information generated at some other nodes. Such a situation arises in sensor networks. In this work, we study three problems in network coding. First, we consider the functional source coding with side information problem wherein there is one source that generates a set of messages and one receiver which knows some functions of source messages and demands some other functions of source messages. Cognizant of the receiver's side information, the source aims to satisfy the demands of the receiver by making minimum number of coded transmissions over a noiseless channel. We use row-Latin rectangles to obtain optimal codes for a given functional source coding with side information problem. Next, we consider the multiple receiver extension of this problem, called the functional index coding problem, in which there are multiple receivers, each knowing and demanding disjoint sets of functions of source messages. The source broadcasts coded messages, called a functional index code, over a noiseless channel. For a given functional index coding problem, the restrictions the demands of the receivers pose on the code are represented using the generalized exclusive laws and it is shown that a code can be obtained using the confusion graph constructed using these laws. We present bounds on the size of an optimal code based on the parameters of the confusion graph. For the case of noisy broadcast channel, we provide a necessary and sufficient condition that a code must satisfy for correct decoding of desired functions at each receiver and obtain a lower bound on the length of an error-correcting functional index code. In the second problem, we explore relation between network function computation problems and functional index coding and Metroid representation problems. In a network computation problem, the demands of the sink nodes in a directed acyclic multichip network include functions of the source messages. We show that any network computation problem can be converted into a functional index coding problem and vice versa. We prove that a network code that satisfies all the sink demands in a network computation problem exists if and only if its corresponding functional index coding problem admits a functional index code of a specific length. Next, we establish a relation between network computation problems and representable mastoids. We show that a network computation problem in which the sinks demand linear functions of source messages admits a scalar linear solution if and only if it is matricidal with respect to a representable Metroid whose representation fulfils certain constraints dictated by the network computation problem. Finally, we study the usage of the sum-product (SP) algorithm for decoding network codes. Though lot of methods to obtain network codes exist, the decoding procedure and complexity have not received much attention. We propose a SP algorithm based decoder for network codes which can be used to decode both linear and nonlinear network codes. We pose the decoding problem at a sink node as a marginalize a product function (MPF) problem over the Boolean smearing and use the SP algorithm on a suitably constructed factor graph to perform decoding. We propose and demonstrate the usage of trace back to reduce the number of operations required to perform SP decoding. The computational complexity of performing SP decoding with and without trace back is obtained. For nonlinear network codes, we define fast decidability of a network code at sinks that demand all the source messages and identify a sufficient condition for the same. Next, for network function computation problems, we present an MPF formulation for function computation at a sink node and use the SP algorithm to obtain the value of the demanded function.