Automotive radars at the Terahertz (THz) frequency band have the potential to be compact and lightweight while providing high (nearly-optical) angular resolution. In this paper, we propose a bistatic THz automotive radar that employs the recently proposed orthogonal chirp division multiplexing (OCDM) multi-carrier waveform. As a standalone communications waveform, OCDM has been investigated for robustness against interference in time-frequency selective channels. The THz-band path loss, and, hence, radar signal bandwidth, are range-dependent. We address this unique feature through a multicarrier wideband OCDM sensing transceiver that exploits the coherence bandwidth of the THz channel. We develop an optimal scheme to combine the returns at different ranges/bandwidths by assigning weights based on the Cramér-Rao lower bound on the range and velocity estimates. Numerical experiments demonstrate improved target estimates that can be obtained using our proposed combined estimation from measurements with varied attenuation at THz bands.

We consider a bistatic vehicular integrated sensing and communications (ISAC) system that employs the recently proposed orthogonal chirp division multiplexing (OCDM) multicarrier waveform. As a stand-alone communications waveform, OCDM has been shown to be robust against the interference in time-frequency selective channels. In a bistatic ISAC, we exploit this property to develop efficient receive processing algorithms that achieve high target resolution as well as high communications rate. We derive statistical bounds for our proposed Sequential symbol decoding and radar parameter estimation (SUNDAE) algorithm and compare its competitive performance with other multicarrier waveforms through numerical experiments.

We derive non-random and Bayesian Cramer-Rao lower bound (CRLB) for pilot-aided joint estimation of angle-of-arrival (AoA), angle-of-departure (AoD), and small scale channel gain in millimeter-wave (mmW) communication networks, in which transmitter and receiver are equipped with uniform planar antenna (UPA) arrays. Numerical results reveal that Bayesian CRLB decreases with an increase in Rice factor. Furthermore, using the derived Bayesian CRLB, we also observe that uniform design of beamforming and beamcombining codebooks, in which the angles are uniformly quantized, yield better performance than other types of codebook design.

In this paper, we consider physical layer security in wireless sensor networks (WSNs) using distributed co-phasing (DCP)-based transmissions. For this protocol, we first analyze the achievable ergodic secrecy rate of a single stream DCP system in the presence of one or more eavesdroppers. We show that the coherent combining gain offered by DCP leads to the signal-to-interference-plus-noise-ratio (SINR) over the main channel increasing as the square of the number of SNs N and that over the eavesdropper channel increasing linearly with N. This results in a strictly positive ergodic secrecy rate that increases as log N. We then analyze the performance of multi-stream DCP and show that using K data streams in DCP leads to a K -fold increase in the achievable secrecy rate at high SNRs. We also discuss an alternative power allocation scheme for multi-stream DCP, such as distributed maximal ratio transmission with a per-user power constraint and show that this improves the achievable secrecy rates as compared to standard multi-stream DCP. Finally, we analyze the role of artificial noise in improving the achievable secrecy rates. We validate the accuracy of these derived results and illustrate the efficacy of DCP in ensuring secure data fusion in WSNs using Monte Carlo simulations.

In this paper, we present an analysis of the nonrandom and the Bayesian Cramer-Rao lower bound (CRLB) for the joint estimation of angle-of-arrival (AoA), angle-of-departure (AoD), and the multipath gain in the millimeterwave (mmWave) wireless networks. Our analysis is applicable to multipath channels with Gaussian noise and independent path parameters. Numerical results based on uniform AoA and AoD in [0, π), and Rician fading path gains, reveal that the Bayesian CRLB decreases monotonically with an increase in the Rice factor. Further, the CRLB obtained by using beam forming and combining code books generated by quantizing directly the domain of AoA and AoD was found to be lower than those obtained with other types of beam forming and combining code books.

In this paper we consider performance of an integrated beam acquisition and tracking scheme for channel estimation in the millimeter-wave (mmWave) wireless networks. By assuming a block based transmission scheme in which pilot symbols are interspersed along with data slots we propose a two stage acquisition scheme namely successive interference cancellation plus iterative regularized least squares (SIC+IRLS) scheme that can be used for acquiring/estimating angle-of-arrival (AoA), angle-of-departure (AoD) and multi-path gains at the pilot slots. To facilitate channel tracking in data slots we also propose a particle filter (PF) based algorithm. Our simulation results demonstrate the superior performance of the integrated (SIC+IRLS)-PF approach as against that of the (SIC+IRLS)-Kalman filter (KF) approach, especially in fast varying conditions.

It is known that the capacity of the discrete-time memoryless noncoherent Rayleigh fading channels (DTM-NRFC) is achieved by a discrete constellation with finite number of mass points and when one of the mass points is located at the origin [1]. In this paper, we present the maximum likelihood detection (MLD) error performance on DTM-NRFC for a discrete constellation with coding and spatial diversity. In the absence of outer coding, the error probability with MLD is derived in a surprisingly simple closed-form. On the other hand, with coding and diversity, our error probability expressions can be evaluated via saddle-point approximation techniques.

In this paper, we design and analyze pilot-assisted Distributed Co-Phasing (DCP) schemes for information fusion in a wireless sensor network. First, using a cutoff rate analysis, we show that higher order constellations significantly improve the throughput performance of DCP in comparison with the binary constellation considered in past work. However, using a higher order constellation in the DCP setting requires estimation of the composite channel from the sensors at the Fusion Center (FC), which is not available in current DCP schemes. We propose two blind algorithms for channel estimation, namely, a power method and a modified K-means algorithm. In particular, the latter is computationally efficient and converges significantly faster and more accurately than the conventional K-means algorithm. We derive closed-form expressions for the probability of symbol error and study the performance of DCP both analytically and through simulations. Our simulation results show that even at moderate to low SNRs, the modified K-means algorithm achieves a probability of error comparable to that achievable with a perfect channel estimate at the FC. The proposed DCP and blind channel estimation schemes are thus a promising technique for energy-efficient data fusion in wireless sensor networks.

Due to the fine delay resolution in ultra-wideband (UWB) wireless propagation channels, a large number of multipath components (MPC) can be resolved; and the first arriving MPC might not be the strongest one. This makes time-of-arrival (ToA) estimation, which essentially depends on determining the arrival time of the first MPC, highly challenging. In this paper, we consider non-coherent ToA estimation given a number of measurement trials, at moderate sampling rate and in the absence of knowledge of pulse shape. The proposed ToA estimation is based on detecting the presence of a signal in a moving time delay window, by using the largest eigenvalue of the sample covariance matrix of the signal in the window as the test statistic. We show that energy detection can be viewed as a special case of the eigenvalue detection. Max-eigenvalue detection (MED) generally has superior performance, due to the following reasons: 1) MED collects less noise, namely only the noise contained in the signal space, and 2) if multiple channel taps fall into the time window, the MED detector can collect energy from all of them. Simulation results confirm that MED outperforms the energy detection in IEEE 802.15.3a and 802.15.4a channels. Finally, the selection of the threshold of the MED is studied both by simulations and by random matrix theory.

In this paper, a multi-antenna two-way relaying protocol is proposed whereby two source nodes wishing to exchange information via a relay node additionally send private messages intended solely for the relay. In particular, we investigate the performance of this bidirectional relaying protocol over fading channels when the relay and source nodes are equipped with multiple antennas thus enabling them to leverage diversity and/or multiplexing gains. Specifically, provided enough antennas are available at the relay, the latter may opt for a demodulate-and-forward approach whereby it demodulates all incoming streams before broadcasting solely the messages to be exchanged between the source nodes or it may opt for a generalized analog network coding approach whereby it only demodulates the private messages destined for the relay's own sake while treating the messages to be exchanged between the source nodes as colored noise, subtracting the demodulated information from the overall received signal and then broadcasting the remaining part of the received signal. We compare how the two approaches fare when coupled with different multiple-input multiple-output (MIMO) detection techniques thus striking suitable tradeoffs between performance and implementation complexity for the generalized multi-antenna two-way relaying channel under consideration.

We develop a recursive least-squares (RLS) algorithm which employs L1-Lqregularized sparse regressions to estimate a sparse channel matrix in frequency-and-time selective fading for multi-input multi-output (MIMO) wireless communications. We propose an improved sparse RLS by using an order extension technique for rapid fading channels. Simulation results demonstrate that the proposed sparse RLS algorithm offers a significant improvement over the conventional RLS algorithm.

In a multiple-input multiple-output (MIMO) system, cross-polarized antenna selection yields significant reduction in cost and hardware size. However, actual benefits of the technique are dependent on the propagation characteristics including channel polarization. To accurately characterize the target 2 GHz-band MIMO channels, the authors conduct 2 GHz cross-polarized channel measurement campaigns. Based on the measured data, novel channel models specifically for the 2 GHz bands are established. In addition, we evaluate the performance improvement obtained with cross-polarized antenna selection using the channel models. Simulation results reveal that antenna selection is particularly useful in the low SNR regime, and that the system capacity at cell edges can be increased up to 13%.

In this paper, we study the impact of uncertain channel state information (CSI) on the performance of demodulate-and-forward relaying protocols with higher order modulation formats such as pulse-amplitude modulation (PAM) and rectangular quadrature-amplitude modulation (QAM). Assuming a single source and a single destination node assisted by $N$ relay nodes, we study the average bit error probability (BEP) performance of $M$-ary PAM and rectangular QAM constellations with Gray code mapping and imperfect CSI at the relay nodes as well as the destination. The main contributions of this paper are the derivation of closed-form expressions for $a)$ the cumulative distribution functions of the demodulator test statistics, $b)$ the transition probability of error at a given relay, and $c)$ the average BEP for independent and not necessarily identically distributed Rayleigh fading channels with imperfect receiver CSI.

Consider L independent and identically distributed exponential random variables (r.vs) X1, X2,...,XLand positive scalars b1, b2,...,bL. In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Σ(j=1)LXj)2/(Σ(j=1}LbjXj). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii) M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

In this paper, we are concerned with the design and analysis of joint source-channel coding schemes for block fading channels with relay-assisted distributed spatial diversity. Assuming a progressive image coder with a constraint on the transmission bandwidth, we formulate a joint source-channel rate allocation scheme that maximizes the expected source throughput. Specifically, using Gaussian as well as BPSK inputs on flat Rayleigh fading channels, we lower bound the average packet error rate by the corresponding mutual information outage probability, and derive the average throughput expression as a function of channel code rates as well as channel SNR for both a frequency-division multiplexing-based baseline system without relaying, and a half-duplex relay system with a decode-and- forward protocol. At high signal-to-noise ratio (SNR), for the systems considered in this paper, we show that our rate optimization problem is a convex function of the channel code rates, and we show that a known recursive algorithm can be used to predict the performance of both systems.

This paper addresses the design and analysis of practical distributed beamforming techniques for the uplink communication over a wireless sensor network. Since the conventional frequency-division duplexing techniques require a large feedback overhead, we focus on a time-division duplexing approach, and exploit the channel reciprocity to reduce the channel feedback requirement. We consider periodic broadcast of known pilot symbols by the fusion center, and maximum likelihood estimation of the channel phase by the sensor nodes for the subsequent uplink co-phasing transmission. For simplicity, we study binary signaling over frequency-flat fading channels, and quantify the system performance such as the expected gains in the received signal-to-noise ratio (SNR) and the average probability of error at the fusion center, as a function of the number of sensor nodes and the pilot overhead. Our results show that a modest amount of accumulated pilot SNR is sufficient to realize a large fraction of the maximum possible beamforming gain.

In this paper, we analyze the performance of transmit beamforming on multiple-antenna Rayleigh fading channels with imperfect channel feedback. We characterize the feedback imperfections in terms of noisy channel estimation, feedback delay, and finite-rate channel quantization. We develop a general framework, that is valid for an arbitrary two-dimensional linear modulation, to capture the aforementioned imperfections and derive the symbol and bit error probability expressions for both M-PSK and M-ary rectangular QAM constellations with Gray code mapping. We show that the proposed analytical formulation is valid for a frequency-domain duplexing system with/without finite-rate channel quantization and a time-domain duplexing system. We validate the accuracy of the analysis through simulations, and assess the relative effects of channel estimation inaccuracy, feedback delay, and finite-rate quantization on the symbol and bit error performances for various constellations.

It is well-known that opportunistic transmission schemes are sum-capacity optimal, in the Shannon sense, for symmetric cellular networks with single-antenna transceivers. However, for a practical system operating at non-negligible error probability, the correctly delivered throughput (or spectral efficiency) is a more useful figure-of-merit. In this paper, we present a mathematical model for the average throughput of a practical wireless system with channel-aware user scheduling in a symmetric Rayleigh fading cellular system. By employing an accurate model for the block error probability with turbo coding, and accounting for channel estimation errors, channel feedback quantization, and feedback delay, we present closed-form expressions for the average spectral efficiency of the downlink scheduler.

We analyze the performance of transmit beamforming on multiple-antenna Rayleigh fading channels with imperfect channel feedback. The feedback imperfections are characterized by noisy channel estimation, feedback delay, and finite rate channel quantization. We develop a general framework, valid for an arbitrary two-dimensional linear modulation, that captures the aforementioned imperfections, and derive the average symbol and bit error probability expressions for M- PSK constellation. We show that the proposed analytical formulation is valid for frequency-domain duplexing system with/without finite rate channel quantization and time-domain duplexing system. The simulation results show accurate agreement with the analytical expressions.

We are concerned with transmit power optimization in a wireless relay network with various cooperation protocols. With statistical channel knowledge (in the form of knowledge of the fading distribution and the path loss information across all the nodes) at the transmitters and perfect channel state information at the receivers, we derive the optimal power allocation that minimizes high signal-to-noise ratio (SNR) approximations of the outage probability of the mutual information (MI) with amplify-and-forward (AF), decode-and-forward (DF) and distributed space-time coded (DSTC) relaying protocols operating over Rayleigh fading channels. We demonstrate that the high SNR approximation-based outage probability expressions are convex functions of the transmit power vector, and the nature of the optimal power allocation depends on whether or not a direct link between the source and the destination exists. Interestingly, for AF and DF protocols, this allocation depends only on the ratio of mean channel power gains (i.e., the ratio of the source-relay gain to the relay-destination gain), whereas with a DSTC protocol this allocation also depends on the transmission rate when a direct link exists. In addition to the immediate benefits of improved outage behavior, our results show that optimal power allocation brings impressive coding gains over equal power allocation. Furthermore, our analysis reveals that the coding gain gap between the AF and DF protocols can also be reduced by the optimal power allocation.

In this paper, we consider the design and bit-error performance analysis of linear parallel interference cancellers (LPIC) for multicarrier (MC) direct-sequence code division multiple access (DS-CDMA) systems. We propose an LPIC scheme where we estimate and cancel the multiple access interference (MAI) based on the soft decision outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation. In order to choose these weights optimally, we derive exact closed-form expressions for the bit-error rate (BER) at the output of different stages of the LPIC, which we minimize to obtain the optimum weights for the different stages. In addition, using an alternate approach involving the characteristic function of the decision variable, we derive BER expressions for the weighted LPIC scheme, matched filter (MF) detector, decorrelating detector, and minimum mean square error (MMSE) detector for the considered multicarrier DS-CDMA system. We show that the proposed BER-optimized weighted LPIC scheme performs better than the MF detector and the conventional LPIC scheme (where the weights are taken to be unity), and close to the decorrelating and MMSE detectors.

Generalized diversity combining (GDC), also known as hybrid selection/maximal ratio combining or generalized selection combining, is a low-complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining. In this paper, we analyze the performance of GDC on time-correlated Rayleigh fading channels with noisy channel estimates. We derive expressions for the probability of error for various linear modulation schemes with coherent detection, and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures. Throughout the paper, using a fundamental approach to obtain the decision statistic at the combiner output, a number of new expressions for the error probabilities are obtained in a rigorous way, along with a presentation of their performance with channel estimation errors. The final expressions have roughly the same complexity of evaluation as that for the channel with only additive Gaussian noise. Our results correct various inaccuracies in the literature, and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss.

In this paper, we develop first-order Markov models that characterize the packet error processes on Rayleigh fading channels considering binary DPSK/NCFSK modulation. Such models available in the literature so far consider only the fading process ignoring the underlying modulation used. Our contribution in this paper is that we consider first-order Markov models for binary DPSK/NCFSK modulation. To derive the Markov model parameters, we first derive expressions for the second-order statistics of the channel error process (specifically, the auto-correlation function of the bit error process as well as the packet error process), and obtain the Markov model parameters, in closed-form, as a function of normalized Doppler bandwidth, average received SNR and packet length. We also verify the accuracy of the proposed Markov model by deriving closed-form expressions for the mutual information of the channel error process

In this paper, we present the design and bit error performance analysis of weighted linear parallel interference cancellers (LPIC) for multicarrier (MC) DS-CDMA systems. We propose an LPIC scheme where we estimate (and cancel) the multiple access interference (MAI) based on the soft outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation; these weights are so chosen to maximize the signal-to-interference ratios at the individual subcarrier outputs. For this weighted LPIC scheme, using an approach involving the characteristic function of the decision variable, we derive exact bit error rate (BER) expressions for different cancellation stages. Using the same approach, we also derive exact BER expressions for the matched filter (MF) and decorrelating detectors for the considered MC DS-CDMA system. We show that the proposed weighted LPIC scheme performs better than the MF detector and the conventional LPIC (where the weights are taken to be unity), and close to the decorrelating detector

Recently, Cao and Beaulieu presented an insightful analysis on the bit-error performance of 16-quadrature amplitude modulation (QAM) scheme on Rayleigh fading channels with maximal ratio combining diversity and channel estimation errors. Unfortunately, although exact, the results presented in that paper are based on a complicated parabolic cylinder function, and a two-dimensional numerical integration has to be performed to evaluate the average probability of bit error. In this letter, we present a surprisingly simple expression for the average probability of error in a well-known closed form. We point out that the error rates for any N-ary square/rectangular QAM constellation with Gray mapping can also be expressed in this form. Furthermore, we show that the presented results can also be modified, in a simple fashion, for a generalized selection combining scheme in the presence of channel estimation errors.

In this letter, we derive analytical expressions for the bit error rate (BER) of space-time block codes (STBC) from complex orthogonal designs (COD) using quadrature amplitude modulation (QAM) on Rayleigh fading channels. We take a bit log-likelihood ratio (LLR) based approach to derive the BER expressions. The approach presented here can be used in the BER analysis of any STBC from COD with linear processing for any value of M in an M-QAM system. Here, we present the BER analysis and results for a 16-QAM system with i) (2-Tx, L-Rx) antennas using Alamouti code (rate-1 STBC), ii) (3-Tx, L-Rx) antennas using a rate-1/2 STBC, and iii) (5-Tx, L-Rx) antennas using a rate-7/11 STBC. In addition to being used in the BER analysis, the LLRs derived can also be used as soft inputs to decoders for various coded QAM schemes, including turbo coded QAM with space-time coding as in high speed downlink packet access (HSDPA) in 3G.

In this paper, we consider the design and bit error performance analysis of linear parallel interference cancellers (LPIC) for multicarrier (MC) DS-CDMA systems. We propose an LPIC scheme where we estimate (and cancel) the multiple access interference (MAI) based on the soft decision outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation. In order to choose these weights optimally, we derive exact closed-form expressions for the bit error rate (BER) at the output of different stages of the LPIC, which we minimize to obtain the optimum weights for the different stages. We show that the proposed BER-optimized weighted LPIC scheme performs better than the MF detector and the conventional LPIC scheme (where the weights are taken to be unity), and close to the decorrelating detector

In this paper, we present the optimum selection combining (SC) scheme for M-QAM which minimizes the average bit error rate (BER) on fading channels. We show that the selection combining scheme, where each bit in a QAM symbol selects the diversity branch with the largest magnitude of the log-likelihood ratio (LLR) of that bit, is optimum in the sense that it minimizes the average BER. In this optimum SC scheme, different bits in a given QAM symbol may select different diversity branches (since the largest LLRs for different bits may occur on different diversity branches), and hence its complexity is high. However, this scheme provides the best possible BER performance for M-QAM with selection combining, and can serve as a benchmark to compare the performance of other SC schemes (e.g., selection based on maximum SNR). We compare the BER performance of this optimum SC scheme with other SC schemes where the diversity selection is done based on maximum SNR and maximum symbol LLR.

For a fixed total bandwidth expansion factor, we consider the problem of optimal bandwidth allocation among the source coder, the channel coder, and the spread-spectrum unit for a direct-sequence code-division multiple-access system operating over a frequency-selective fading channel with narrowband interference. Assuming a Gaussian source with the optimum scalar quantizer, and a binary convolutional code with soft-decision decoding, and further assuming that the self-interference is negligible, we obtain both a lower and an upper bound on the end-to-end average source distortion. The joint three-way constrained optimization of the source code rate, the channel code rate, and the spreading factor can be simplified into an unconstrained optimization problem over two variables. Upon fixing the channel code rate, we show that both upper and lower bound-based distortion functions are convex functions of the source code rate. Because an explicit solution for the optimum source code rate, i.e., one that minimizes the average distortion, is difficult to obtain, computer-based search techniques are employed. Numerical results are presented for the optimum source code rate and spreading factor, parameterized by the channel code rate and code constraint length. The optimal bandwidth allocation, in general, depends on the system and the channel conditions, such as the total number of active users, the average jammer-to-signal power ratio, and the number of resolved multipath components together with their power delay profile.

In this paper, we study the optimality of bit detection for coherent M-ary phase-shift keying (PSK) and M-ary quadrature amplitude modulation (QAM), and noncoherent M-ary frequency-shift keying (FSK) signal sets. For M-PSK and M-QAM signal constellations, we employ Gray mapping, consider 8-PSK and 16-QAM signal sets as representative of the general results, and derive the log-likelihood ratio (LLR) for each bit forming the symbol. Using the LLRs, we derive the average bit-error probability (BEP) for the individual bits, and show that the decision regions and the corresponding average BEP for the case of M-PSK coincide with those obtained with the optimal symbol-based detector, whereas, in general, this is not the case for both M-QAM and M-FSK.

In this letter, we study the performance of binary signaling on generalized fading channels with maximal ratio combining (MRC) and imperfect channel estimates. With the assumption of the channel estimate being corrupted by a complex Gaussian random variable, an expression for the average probability of error is provided in the form of a simple single integral which involves the moment generating function of the normalized signal-to-noise ratio corresponding to the case of ideal MRC. Various examples are given to illustrate the usefulness of the derived expression under various fading conditions with different distributions, and with a possible correlation between the diversity branches.

In this paper, we analyze the error probability performance of maximal-ratio combining (MRC), equal-gain combining (EGC), selection combining (SC), and generalized-selection combining (GSC) diversity schemes with coherent binary phase-shift keying (BPSK) signaling on Rayleigh fading channels with Gaussian channel-estimation errors. We first show that, with weighting errors, averaging the conditional probability of error with the density function of the instantaneous signal-to-noise ratio (SNR) at the output of the combiner yields a lower bound on the exact probability of error. Later, we derive the exact probability of error for MRC, EGC, SC, and GSC diversity schemes and show that, for the case of nonnegative values of the in-phase correlation coefficient between the actual and the estimated channel gains, the exact probability of error with weighting errors is the same as that of the case with perfect channel estimation, but with the average SNR per diversity branch /spl gamma/~, for the case of perfect channel estimation, replaced by the effective SNR /spl gamma/~/sub /spl rho//, due to weighting errors. The effective SNR is a function of both /spl gamma/~ and /spl rho/, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as /spl rho//spl rarr/0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity-combining rule.

We derive analytical expressions for the bit error rate (BER) of space-time block codes (STBC) from complex orthogonal designs (COD) with quadrature amplitude modulation (QAM) on Rayleigh fading channels. We take a bit log-likelihood ratio (LLR) based approach to derive the BER expressions. We first derive the LLRs for the various bits forming the QAM symbol and use these LLRs to derive analytical expressions for the error rate of the individual bits forming the QAM symbol and hence the average BER of the system. The approach presented in this paper can be used in the BER analysis of any STBC from COD with linear processing, for any value of M in a M-QAM system. Here, we present the BER analysis and results for a 16-QAM system with i) (2-Tx, L-Rx) antennas using Alamouti code (rate-1 STBC), ii) (3-Tx, L-Rx) antennas using a rate-1/2 STBC and iii) (5-Tx, L-Rx) antennas using a rate-7/11 STBC. The LLRs derived can also be used as soft inputs to decoders for various coded QAM schemes, including turbo coded QAM with space-time coding.

In this paper, we investigate the effect of fade correlation and the level of imbalance in the mean signal strength on the capacity of Rayleigh fading channels with dual antenna receive diversity. We consider maximal ratio combining (MRC), equal gain combining (EGC) and selection combining (SC) diversity schemes and derive expressions for the average and the outage capacities of the channel. For the case of MRC and SC schemes we obtain closed-form expressions for the average and the outage capacities, whereas efficient Gauss-Hermite quadrature rule-based expressions are provided for ECG diversity. Numerical results are provided to illustrate the capacity degradation due to channel correlation and unbalanced diversity branches.

The optimum selection combining (SC) scheme, proposed recently by Kim, requires estimation of complex channel fades on every diversity channel for minimizing the average probability of error. In this paper, we quantify the effect of imperfect channel estimation on the performance of the optimum SC receiver. By modeling the estimation errors as independent Gaussian random variables, we obtain a simple closed-form expression for the average probability of error. We also analyze a simple sub-optimum SC scheme, based on the output of the coherent matched filter alone, without requiring the knowledge of the fade amplitudes, in the presence of channel estimation errors. Finally, we provide some numerical results to illustrate the comparative performances of various SC receivers with pilot-aided minimum mean-square error (MMSE) channel estimation.

In this paper, we provide an analytical performance comparison of various selection combining (SC) schemes for binary noncoherent frequency-shift keying (NCFSK) signals operating on independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. With this motivation, we first derive the receiver structure for the optimum SC scheme, which combines one out of the available L diversity branches so as to minimize the probability of bit error. We show that the optimum SC scheme chooses the diversity branch having the largest magnitude of the logarithm of the a posteriori probability ratio (LAPPR) of the transmitted information bit. We also show that: 1) the optimum noncoherent diversity receiver, for binary NCFSK signals, is equivalent to combining the LAPPRs of all the diversity branches; 2) the SC scheme proposed by Neasmith and Beaulieu is a special case of the optimum SC scheme for independent and identically distributed (i.i.d.) Rayleigh fading; and 3) for i.n.d. fading with dual diversity (i.e., L=2), the performance of the optimum SC scheme is the same as that of the optimum noncoherent diversity receiver, whereas the Neasmith and Beaulieu SC scheme gives the performance of the suboptimum equal gain combining receiver. Bit-error rate (BER) results show that, at 10/sup -4/ BER, for i.i.d. Rayleigh fading, the proposed optimum SC scheme performs better than the existing SC schemes by 0.5-0.9 dB for L=3 and by 0.8-1.5 dB for L=5, and performs within 0.3 dB of the optimum noncoherent diversity receiver for L=3,5, and for i.n.d. Rayleigh fading with L=5, the optimum SC scheme gives an additional gain of about 2.0 dB over the Pierce SC scheme. Further, for i.i.d. Rayleigh fading, we derive the bit-error probability expression for a (3,L) selection scheme which combines three branches whose LAPPR magnitudes are the largest among the available L branches. Numerical results for this (3,L) selection scheme show that for L=5 at a BER of 10/sup -4/, combining the three branches with the largest LAPPR magnitudes yields almost the full performance of the optimum noncoherent diversity receiver, whereas, for L=7, it is just about 0.2 dB away from the latter.

In this paper, we develop analytical tools for the performance analysis of coded, coherent communication systems on independent and identically distributed Nakagami-m fading channels with selection combining (SC) diversity. First, we derive an exact expression for the moment generation function (MGF) of the signal-to-noise ratio (SNR) of a code symbol at the output of the selection combiner. Next, based on Gauss-Chebyshev quadrature and Gauss-Laguerre quadrature rules, we propose a simple to compute, yet accurate, numerical solution for the pairwise error probability (PEP) of coded M-phase-shift keying (PSK) signals. Using the PEP expressions, we present the union bound-based bit-error performance of trellis-coded modulation schemes and turbo codes. Finally, we derive an exact expression for the computational cutoff rate of a coded system with M-PSK signaling and SC diversity, and show that the cutoff rate expression is a simple function of the MGF of the SNR at the output of the diversity combiner.

In this paper, we present a log-likelihood ratio (LLR) based approach to analyze the bit error rate (BER) performance of quadrature amplitude modulation (QAM) on Rayleigh fading channels without and with transmit diversity. We derive LLRs for the individual bits forming a QAM symbol both on flat fading channels without diversity as well as on channels with transmit diversity using two transmit antennas (Alamouti's scheme) and multiple receive antennas. Using the LLRs of the individual bits forming the QAM symbol, we derive expressions for the probability of error for various bits in the QAM symbol, and hence the average BER. In addition to being used in the BER analysis, the LLRs derived can be used as soft inputs to decoders for various coded QAM schemes including turbo coded QAM with transmit diversity, as in high speed downlink packet access (HSDPA) in 3G.

In this paper, we propose and analyze the bit error performance of a generalized selection combining (GSC) receiver for M-ary non-coherent frequency shift keying (NCFSK) signals on i.i.d. Rayleigh fading channels with L antennas at the receiver. For each of the M hypotheses, the receiver combines the K largest outputs among the L available square-law detector outputs before proceeding to the bit detection process. We derive a closed-form expression for the bit error probability of the proposed (K, L) GSC receiver, and present numerical results to illustrate the bit error performance of this receiver for different values of M, K, and L. We also show that our generalized (K, L) GSC scheme and analysis encompass the previously reported schemes/analyses by Chyi et al. and Hahn a special cases for K = 1 and K = L, respectively.

In this paper, we derive a new selection combining (SC) scheme for noncoherent binary FSK signals on independent (but not necessarily identically distributed) Rayleigh fading channels with L-antenna diversity reception. With this combining scheme, we choose the diversity branch having the largest magnitude of the logarithm of the ratio of the a posteriori probabilities (log-APP ratio - LAPPR) of the transmitted information bit. We show that this scheme minimizes the probability of bit error, thus proving the optimality. We also show that a) the traditional square-law combining of all L diversity branches is equivalent to combining the LAPPR of all the L diversity branches, and b) the SC scheme proposed by Neasmith and Beaulieu (1998) is a special case of the proposed optimum SC scheme for independent and identically distributed (i.i.d) Rayleigh fading. Bit error probability results show that, at 10/sup -4/ BER, a) for i.i.d Rayleigh fading, the proposed optimum SC combining scheme performs better than the existing SC schemes by 0.5 dB for L = 3 and 1.5 dB for L = 5, and performs within 0.5 dB of the scheme which square-law combines all the L diversity branches, and b) for independent Rayleigh fading, the proposed optimum SC scheme gives an additional gain of 2.0 dB over the SC schemes of Pierce (1958) and Chyi et al. (1989).

In a previous paper, we derived the optimum selection combining (OSC) scheme for binary noncoherent FSK (NCFSK) signals on independent (but not necessarily identically distributed) Rayleigh fading channels with L-antenna diversity reception. In the OSC scheme, the diversity branch having the largest magnitude of the logarithm of the ratio of the a posteriori probabilities (log-APP ratio - LAPPR) of the transmitted information bit is chosen. In this paper, we derive the bit error performance of a (3, L) selection combining scheme for binary NCFSK signals which combines the three branches whose LAPPR magnitudes are the largest among the available L branches in i.i.d Rayleigh fading. Numerical results for this (3, L) selection scheme show that, for L=5, combining the three branches with the largest LAPPR magnitudes yields almost the full performance of the square-law combining of all the L=5 branches. For L=7, the performance of combining the three branches with the largest LAPPR magnitudes is just about 0.2 dB worse from the performance of square-law combining of all the L=7 branches. We also compare the performance of the proposed (3, L) selection scheme with the (3, L) selection combining scheme of Chyi et al. (1989).

In this paper, we analyze the performance of trellis coded modulation (TCM) schemes with generalized selection combining (GSC) on fading channels. We first derive the computational cutoff rate, R/sub 0/, for coherent TCM schemes on i.i.d. Rayleigh fading channels with (K, L) GSC diversity which combines the K paths with the largest instantaneous SNR among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. The cutoff rate results show that, at a cutoff rate of 1 bit/sec/Hz, 8-PSK modulation with (1, 3) GSC requires about the same E/sub b//N/sub 0/ as QPSK modulation with (2,3) GSC. Also, at 1.5 bits/sec/Hz, 8-PSK with (1, 3) GSC and QPSK with (3,3) GSC require about the same E/sub b//N/sub 0/. This illustrates that in TCM schemes with GSC diversity, the modulation complexity (i.e., alphabet size, M) and the GSC receiver complexity (i.e., the number of combined diversity paths, K) can be traded off to achieve a desired performance. Next, we derive the union bound on the bit error probability of TCM schemes with (K, L) GSC reception in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.

We propose a first-order Markov model for generalized Nakagami-m (1960) flat fading channels. Using a moment generating function (MGF) approach, we derive the parameters of the proposed model for any value of the fading severity index m /spl ges/ 0.5. The proposed model is a generalized version of the one proposed earlier by Zorzi et al. (1995) for flat Rayleigh fading channels. For m = 1, we show that our generalized model gives the same parameter values obtained using Zorzi's approach. Our generalized model thus encompasses Zorzi's model as a special case. We illustrate the usefulness of our proposed Markov model by applying it to the analysis of the throughput and energy efficiency performance of a link layer (LL) protocol with backoff on wireless fading links with different values of the m-parameter (= 0.5,1,4).

We propose an online signal-to-noise ratio (SNR) estimation scheme for Nakagami-m (1960) fading channels with L branch equal gain combining (EGC) diversity. We derive the SNR estimate based on the statistical ratio of certain observables over a block of data, and use the SNR estimates in the iterative decoding of turbo codes on Nakagami-m fading channels with L branch EGC diversity. We evaluate the turbo decoder performance using the SNR estimate under various fading and diversity scenarios (m = 0.5, 1, 5 and L = 1, 2, 3) and compare it with the performance using perfect knowledge of the SNR and the fade amplitudes.

We are concerned with the performance of turbo codes on Rayleigh fading channels when noncoherent detection is employed. Performance of turbo codes with noncoherent detection on AWGN channels has been analyzed by E.K. Hall and S.G. Wilson (see Proc. IEEE Commun. Theory Mini-Conf, p.66-70, 1997). They compared the performance of turbo codes with the achievable information theoretic channel capacity for noncoherent detection on AWGN channels. We derive the information theoretic channel capacity for noncoherent detection on Rayleigh fading channels, and show that the noncoherent turbo decoder achieves performance close to this theoretical capacity (within 1.5 dB). We further show that the performance of noncoherent turbo decoder without the knowledge of channel fades is quite close (within 0.5 dB at 10/sup -5/ BER) to that with perfect knowledge of the channel fades. Optimum decoding of turbo codes requires the knowledge of channel SNR. With this requirement in mind, we propose online SNR estimation schemes, based on the ratio of certain observables at the output of the noncoherent detector, which when used in the turbo decoder gives performance very close to that with perfect knowledge of channel SNR.

We derive bit error performance bounds for turbo codes on Nakagami fading channels with diversity combining. We first derive the average pairwise error probability expressions for turbo codes with maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) on Nakagami fading channels. Using the pairwise error probability expressions and the union bounding technique, we then obtain bounds on the bit error probability of turbo codes for MRC, EGC, and SC diversity schemes. We present the modified log-MAP turbo decoder for MRC, EGC, and SC, and compare the analytical bounds with simulation results for the special case of 2-antenna diversity with Nakagami parameter m=1 (i.e., Rayleigh fading). Results indicate that the EGC scheme with turbo coding performs close to MRC scheme for i.i.d Rayleigh fading.

We propose an online SNR estimation scheme for generalized fading channels. We derive the SNR estimate based on a statistical ratio of observables over a block of data, when the channel undergoes Nakagami fading. An online SNR estimator for AWGN channels has been derived by Summers and Wilson (see IEEE Trans. Commun., vol.46, no.4, p.421-23, 1998). Our SNR estimation scheme in this paper is for a general Nakagami fading channel, where the SNR estimates in Rayleigh fading and AWGN can be obtained as special cases corresponding to the Nakagami parameter m=1 and m=/spl infin/, respectively. As an example, we use our SNR estimate in the iterative decoding of turbo codes on both i.i.d and correlated Rayleigh fading channels. We show that the turbo decoder performance on Rayleigh fading channels using our SNR estimate is close to the performance using perfect knowledge of the fade amplitudes and the SNR.