This paper investigates optimal symbol set selection for the generalized spatial modulation (GSM) in visible light communication (VLC) systems. Realizing that the optimal search involves a highly complex combinatorial problem, a symbol set generation tree is proposed. The tree allows assessment of the system performance at each node and can be terminated early to obtain near-optimal solutions with reduced complexity. It is observed that the proposed optimal symbol search provides performance improvement of many dBs over results obtained with averaged random sets. The benefit of the optimized symbol set design is found to increase with increasing number of pulse amplitude modulation levels. Our contributions also include integration of possible rotations of the array in the mathematical model, and the demonstration of the results to be robust to channel changes due to rotations and shifting of the array in the image plane. Finally, the results are validated through hardware experimental results.

Estimation of the image location of a mobile LED array transmitter on the camera sensor plane of a digital camera is considered. A Bayesian framework is used to design an initial large measurement matrix over multiple image frames to exploit inter-frame temporal correlations. This large matrix is then factorized into two component matrices; one is used as the front-end measurement matrix with the potential for hardware implementation while the other is designed for software implementation. The factorization can be performed offline through fixed point iterations. The proposed measurement matrix design directly exploits possible transmitter mobility through a parametric framework. The findings are validated through analysis, computer simulation and hardware experiments. Sub-pixel localization accuracy with significant compression is achieved, and the proposed compressive parameter estimation outperforms results obtained using a Gaussian measurement matrix.

A relaying scheme that uses both radio frequency (RF) and free space optical (FSO) links is proposed. The RF signal sent by the mobile source is received by both the relay and the destination. In our proposed quantize and encode forwarding (QEF), the relay quantizes each received log-likelihood ratio (LLR) value and transmits the corresponding bits to the destination through a high speed FSO link. The bit error rate (BER) performance of the proposed system is analyzed and approximate expressions avoiding numerical integrations of several integrals are given. A 3-bit quantizer is found to provide BER performance close to a genie-aided maximal ratio combiner that directly combines information available at the relay and the destination. Stronger atmospheric turbulence in the FSO link is found to reduce the benefit of using a larger number of quantization levels at the relay.

A novel type-II hybrid automatic repeat request (HARQ) algorithm over hybrid channels, consisting of parallel free space optical (FSO) and radio frequency (RF) links, is presented. The algorithm uses different jointly optimized puncturing and RF bit selection patterns for different retransmissions. Analytical bit error rate and throughput performance expressions for the algorithm in case of both time invariant and random fading channels for recursive systematic, non-recursive non-systematic convolutional codes and turbo codes are given. Numerical results show a gain of several dBs of the proposed algorithm when compared to HARQ that uses random bit selection for transmission through the RF channel. The performance of the algorithm for different FSO and RF link conditions is demonstrated.

The problem of selecting anchor-cum-relay (ACR) nodes for the dual purpose of tracking a mobile source as well as serving as relays for the source signal is considered. The proposed approach uses particle filters (PFs) with node selection based on the received signal-to-noise ratio (SNR) along with a localization constraint derived through the Fisher information matrix (FIM). The detail steps of implementation are given. A posterior Cramer-Rao lower bound approach is also explored to exploit information from previous node selections. Numerical results demonstrate that the proposed FIM-SNR approach achieves more than 16 dB in average source localization mean-squared error (MSE) over nearest node (NN) selection, while performing very close to FIM-based optimal localization. At the same time, the proposed FIM-SNR provides a received SNR nearly identical to NN selection but outperforming FIM-based selection's SNR by more than 5.5 dB.

Dual-role nodes that can work both as relays and also as anchors for joint communication and source localization are proposed. Selection and power allocation of a few dual-role nodes in the presence of many nodes in the network are considered. A novel approach is proposed that relies on maximizing the signal-to-noise ratio (SNR) at the destination node under a source localization constraint. Bounds on the number of nodes needed to achieve a certain localization performance, a concave bound on SNR at the destination node and a practical algorithm to select the dual-role nodes are presented. To estimate the source location using non- line-of-sight range measurements, a new algorithm using semi- definite programing with relaxation followed by majorization- minimization is presented. The results demonstrate excellent promise for obtaining joint improved bit error rate and mean- squared error localization performance by selecting nodes based on combined SNR and localization constraint.

In this paper, we investigate designing of hybrid free space optical (FSO)/ radio frequency (RF) symbol mappers using bit-interleaved coded modulation with iterative decoding (BICM-ID) with asymmetric data rates between the FSO and the RF links. Data bits are first encoded with a channel code and the coded bits after an interleaver are mapped to hybrid FSO/RF symbols instead of separate conventional RF symbols and on-off keyed FSO transmissions. Iterative decoding is used at the receiver. An orthogonal evolutionary (OE) algorithm to obtain optimal symbol mappings is used. Two cost functions to be used in the OE algorithm are proposed. For high signal-to-noise ratio (SNR) regime, analytical error bound expressions are used and at the low SNR regime, extrinsic information transfer (EXIT) chart is used for the cost function. The proposed mappings achieve significant gains over conventional mappings. For a hybrid FSO/RF link with an FSO and RF channel use ratio of 10:1, the proposed mapping achieves an optical SNR gain of more than 7 dB over conventional mapping. A good agreement between simulation and analysis results is obtained for the proposed scheme at high SNR.

We investigate the behavior of spatially partially coherent beams (PCBs) in the presence of pointing errors in the space communication environment. Closed form expressions for the optimal coherence length for minimizing outage probability and maximizing average signal-to-noise ratio (SNR) are derived. In the case of outage probablity, we observe that the optimal coherence parameter does not depend on the pointing error statistics. For average SNR results, PCBs can improve performance when large fixed beam offsets are present. We also provide BER performance analysis results for a convolutionally coded system and demonstrate significant performance improvement using PCBs with optimized parameters.

Turbo coded data transmission over a hybrid channel, consisting of parallel free space optical (FSO) and radio frequency (RF) links, is considered, and analytical bit error performance results are derived. The FSO link is modeled using the gamma-gamma distribution function, and both random and block fading channels are used. Random and specific codeword bit selections for transmission through the RF link are considered. Conditions to guarantee bit error rate (BER) performance improvement in hybrid channels over FSO only links are derived. In the case of block fading channels, the hybrid channel using turbo codes is found to provide several dBs of gain in the signal-to-noise ratio (SNR) over an optical only link. A technique to jointly optimize puncturing and RF bit selection patterns for the hybrid channel is also presented. Results demonstrate significant BER performance improvement obtained from the proposed joint optimization approach.

This paper investigates the behavior of optical and hybrid optical/RF links over varying link distances. We first describe inclusion of various factors affecting the optical link, such as the atmospheric absorption, beam divergence and atmospheric turbulence. A technique to analyze outage probability of the hybrid link for low density parity check (LDPC) codes is presented. Our results show that the hybrid link can improve outage probability by orders of magnitude over an optical only link. In haze conditions, the hybrid link can extend the coverage distance of an optical only link by hundreds of meters by diverting a small fraction of the data through the RF link.

An analysis on the bit error rate performance of turbo codes for hybrid optical/RF channels is presented using the transfer function bounding technique. The optical channel includes the effects of atmospheric turbulence, which is represented using the gamma-gamma model. The effects of various turbulence conditions on the performance of the hybrid link is investigated. The role of the RF link in the hybrid channel is analyzed using the trade-offs between the RF and the optical signal-to-noise ratios.

A hybrid channel, consisting of a free space optical (FSO) link and a parallel radio frequency (RF) link, is considered. The FSO link carries most of the transmitted data while leaving only a small fraction of the data to be carried by the RF link. It is first shown that the capacity of the proposed hybrid structure is much higher than the capacity of a single FSO link. Next the performance of the hybrid channel is studied using a low density parity check code. A density evolution strategy for the hybrid channel is derived and a Gaussian approximation technique is presented. Using these techniques, the conditions for the convergence of the message passing algorithm in terms of minimum data carrying rate through the RF link are derived. Finally, numerical results showing the benefits of the hybrid channel under various channel conditions are presented.

A list based data detection algorithm is presented for long intersymbol interference channels. The algorithm first extracts bit reliabilities using a low complexity equalizer and then uses these reliabilities to generate lists of possible data vectors before making final bit decisions. It is shown through analysis that the detector can be designed to ensure a specific bit error rate performance with respect to a maximum likelihood sequence detector. The complexity advantage of the detector is described through analysis and simulation.

A hybrid channel, consisting of a free space optical (FSO) link and a parallel radio frequency (RF) link, is considered. Information bits are first encoded by a low density parity check (LDPC) code and the coded bits are transmitted through both the FSO and the RF links. A density evolution (DE) technique to analyze the convergence of the message passing algorithm at the detector is described for the hybrid channel, and a Gaussian approximation (GA) technique is presented. Numerical results showing the benefits of the hybrid channel are discussed.

A simple algorithm to implement a distributed version of the Alamouti diversity scheme is presented and its performance is studied. It is observed that the algorithm provides quick convergence, and a bit error rate (BER) performance quite close to the Alamouti's original localized scheme. The proposed algorithm has potential applications in providing diversity in co-operative communications, in poor scattering environments, and in hybrid channels consisting of optical and radio links.

Iterative detectors based on subset selection of candidate codewords are presented for turbo MIMO systems. The performance of the detectors is studied using turbo product codes as the constituent channel code. The proposed detectors are shown to perform close to capacity limits. They have low implementation complexity, and are able to outperform the existing detectors including the list sphere detector.

This paper investigates the effects of impulse noise on the performance of multidimensional parity check codes (MDPC) in additive white Gaussian noise and Rayleigh fading channels. The Bhattacharya upper bound is derived for impulsive noise and is found to closely match with the simulation results. It is observed that impulse noise can degrade the bit error rate performance by several dBs. Further, the use of incorrect impulse noise model in the receiver decoding algorithm is found to cause severe penalty in fading channels. Our results also show that MDPC codes outperform traditional convolutional codes in impulsive noise channels. The performance of MDPC codes is found to be slightly inferior to turbo codes, when the latter uses slightly lower code rate and higher complexity. The capacity limits for impulsive noise channels are also calculated

A constant envelope modulation technique called the smooth phase interpolated keying (SPIK) is investigated. The phase values of the symbols are computed to obtain a smooth phase function. A method to efficiently compute the phase function is described. An optimal receiver structure is outlined, and a near-optimal low complexity version is described. The bit error rate (BER) performance of SPIK is characterized analytically. It is observed that SPIK provides BER performance close to ideal QPSK, 8-PSK and 16-PSK constellations while providing better spectral and BER performance than enhanced Feher QPSK (EFQPSK).

A matching pursuit followed by cancellation (MPC) algorithm is investigated for time-varying multipath channel estimation in asynchronous CDMA. The algorithm has significantly low computational complexity and consists of two steps. In the first step, a basic matching pursuit algorithm that identifies the strongest channel taps, and successively cancels them, is used. The second step of the algorithm uses the already estimated channel taps to remove interference from the received vector in order to identify the channel coefficients more accurately. The performance of the algorithm is characterized in terms of mean squared identification error (MSIE). The convergence behavior of MPC is described. A method to terminate the MP step of the algorithm successfully is proposed and is shown to perform well. Our results show that MPC achieves performance close to the Cramer-Rao lower bound (CRLB).

The performance of an IEEE 802.11a wireless receiver, in the presence of multiple users transmitting ultra-wideband (UWB) interfering signals, is evaluated. The frequency band of interest for the 802.11a system is 5.21-5.23 GHz. The coexistence of the two systems is characterized in terms of 802.11a receiver's bit error rates and throughputs. Our simulations indicate that UWB interferers can cause severe degradation in the attainable throughput of the 802.11a system. However, as the UWB interferers move away from the 802.11a receivers, so does their negative effect on the throughput performance of the 802.11a system.

Estimation of fast fading channels with large possible delay spread is considered. The time-varying fading channel taps are explicitly modeled by polynomial basis functions, and the basis coefficients are obtained via a matching pursuit (MP) algorithm. It is shown that, in the case of sparse channels, this approach outperforms the conventional least squares (LS) estimation with polynomial basis functions as well as the conventional adaptive matching pursuit, while still providing significant savings in complexity. Moreover, the MP is used to identify the appropriate polynomial model orders for channel taps that vary at different rates. A new least squares algorithm using matching pursuit (LSMP) is proposed. It is shown that the LSMP performs well for both sparse and non-sparse time-varying channels.

This paper presents an adaptive iterative (turbo) receiver for coded asynchronous CDMA systems. This receiver consists of a soft-input soft-output (SISO) multiuser detector, which is implemented in the weighted least squares (WLS) sense with the BCJR algorithm, and a bank of SISO channel decoders. All parameters needed for the receiver are estimated or adaptively obtained. Simulation results show that in a multicellular environment the proposed adaptive turbo receiver outperforms the matched filtered turbo receiver in terms of bit error rate (BER) performance. It is observed that the turbo principle allows significant reduction in training overhead. As the SNR increases, the adaptive receiver's BER performance is found to approach the optimal WLS receiver's performance.

This paper investigates receiver structures for enhanced FQPSK modulation. A new receiver structure called the per waveform matched filter (PWMF) receiver is introduced. The bit error rate performance of averaged matched filter receiver, optimal linear MMSE receiver, PWMF receiver and the optimal receiver based on the Viterbi algorithm is studied for uncoded and coded EFQPSK signals with and without a nonlinear power amplifier. Our study shows that the various structures provide complexity performance trade off and their performance is little degraded due to the presence of the nonlinear amplifier. A low complexity receiver structure for Rayleigh frequency-flat fading channels is also investigated and is found to perform well.

An optimal multiuser detector in the weighted least squares (WLS) sense is derived. This detector, which includes the maximum likelihood multiuser detector as a special case, consists of two parts: a bank of linear fractionally chip spaced minimum mean squared error (MMSE) filters, and a nonlinear WLS metric minimizer. It is shown that the symbol spaced samples at the output of the MMSE filter bank provide a set of sufficient statistics for WLS detection. The relationship between the taps of a centralized decision feedback detector and the MMSE filter bank is derived. It is proven that all the necessary parameters for implementing the WLS detector can be realized by adaptively training a centralized decision feedback detector. Therefore, the WLS detector achieves optimal joint synchronization and data detection even in the presence of colored noise, such as narrowband interference, without any a priori knowledge of the users' signatures, multipath channel taps or statistics of the colored noise. Significant features of the WLS detector are that: (1) the WLS detector is a generalization of the maximum likelihood multiuser detector that employs a bank of matched filters; (2) it is implemented adaptively; and (3) it has structural flexibility in terms of implementation complexity.

This paper describes a new interpretation of the maximum-likelihood sequence detector metric for a linearly modulated signal and an unknown time-varying, dispersive, Rayleigh fading channel. The metric, which involves the channel and noise autocovariances, is transformed into the intuitive Mahalanobis distance (squared Euclidean distance in white noise) between the observations and a reference estimated from them. A novel estimator, called the autocovariance preserving estimator, is obtained that trades off increased estimation bias for reduced sequence-error probability.

The performance of equalizers depends on the discrete time model of the input signal and noise. The use of a higher sampling rate results in colored noise when the bandwidth of the noise-limiting prefilter is not sufficiently large. It is shown that the mean square error (MSE) performance of linear equalizers becomes sensitive to the decision delay when the input noise is colored, and by using the appropriate delay, a significant improvement in the MSE can be achieved. This is in contrast to the behaviour observed in the white noise case well known in the literature. This behaviour is explained in time domain by showing the contributions to the MSE from the columns of the channel convolution matrix and the noise eigenvectors. In the frequency domain, it is shown that the equalizer exploits the noise correlation to improve the MSE.

Several receiver structures for linearly modulated signals are proposed for time-varying frequency-selective channels. Their channel estimators explicitly model the time variation of the channel taps via polynomials. These structures are constructed from the following building blocks: (i) sliding or fixed block channel estimators; (ii) maximum likelihood sequence detectors (MLSDs) or decision feedback equalizers (DFEs); and (iii) single or multiple passes. A sliding window channel estimator uses a window of received samples to estimate the channel taps within or at the end of the window. Every symbol period, the window of samples is slid along another symbol period, and a new estimate is calculated. A fixed block channel estimator uses all received samples to estimate the channel taps throughout the packet, all at once. A single pass receiver estimates the channel and detects data once only. A multipass receiver performs channel estimation and data detection repetitively. The effect of the training symbol positions on the performance of the block multipass approach is studied. The bit error rate (BER) performance of the MLSD structures is characterized through simulation and analysis. The proposed receivers offer a range of performance/complexity tradeoffs, but all are well suited to time-varying channels. In fast fading channels, as the signal-to-noise ratio (SNR) increases, they begin to significantly outperform the per-survivor processing-based MLSD receivers which employ the least mean-squares (LMS) algorithm for channel estimation.

The well-known code division multiple access maximum likelihood receiver (MF-ML) uses a bank of matched filters as a generator of sufficient statistics for maximum likelihood detection of users transmitted symbols. In this paper, the bank of matched filters is replaced by a bank of adaptive minimum mean squared error (MMSE) filters as the generator of sufficient statistics. This formal replacement of the MF bank by the adaptive MMSE filter bank has significant conceptual consequences and provides improvement by several performance measures. The adaptive MMSE-ML receiver's digital implementation is significantly computationally simplified. The advantages of the proposed adaptive MMSE-ML receiver over the MF-ML receiver are: (1) ability to perform joint synchronization, channel parameter estimation, and signal detection where the signal is sent over an unknown, slowly time-varying, frequency-selective multipath fading channel; (2) increased information capacity in a multicellular environment; and (3) significantly improved bit error rate (BER) performance in a multicellular mobile communications environment. The information capacity and the BER of the proposed MMSE-ML receiver are analyzed. Numerical results showing the BER performance of the MMSE-ML receiver in a multipath channel environment are presented.

A receiver structure for unknown time-varying, frequency-flat, Rayleigh fading channels is proposed. Unlike the maximum-likelihood receiver structure, this receiver does not need any knowledge of the channel autocovariance or the received signal-to-noise ratio, and yet analytic and simulation results show, that its bit-error rate performance is close to the optimal structure. The receiver is applicable to signals with constant or approximately constant envelopes or to linearly modulated signals using Nyquist pulses.

A rectangular-windowed least-squares estimator using a polynomial model of the time-varying channel taps is proposed for estimating the impulse response of a frequency-selective fading channel. This method provides a significant improvement in mean square identification error (MSIE) over the conventional least mean squares (LMS) and the exponentially weighted recursive least squares (EW-RLS) algorithms without a polynomial model. A detailed study of the effects of channel parameters, such as the fading rate and the signal-to-noise ratio, on the proposed method is carried out. The performance of the method depends on the window size of the least squares estimator and the polynomial order being used. Algorithms to obtain the approximately optimal window size and polynomial order are proposed and are shown to perform well.

The performance of the adaptive MMSE maximum likelihood CDMA receiver is analysed. Instead of the matched filter (MF) bank as the generator of sufficient statistics for maximum likelihood detection (MF-ML), a bank of minimum mean squared error (MMSE) filters is used. It is shown that the proposed MMSE-ML receiver achieves increased information capacity in a multicellular environment. Numerical results showing the performance of the MMSE-ML receiver in a multipath channel environment are presented.

The performance and complexity of blind algorithms in a digital receiver is dependent on the prefilter prior to discretization of the received continuous time signal and the sampling rate. This paper shows that symbol spaced blind equalization algorithms are in general sub-optimal, since a matched filter cannot be used. We show that, for fractionally spaced equalizers, the prefilter can be a general low-pass filter and does not need to be matched to the unknown channel. This flexibility on choosing the prefilter can result in different discrete time models with different complexities for the signal processing algorithms to follow. As for example, a simpler whitening filter design which is needed for the success of several important blind equalization algorithms can be realized using this flexibility.