Task-oriented semantic communication, leveraging learning-based joint source-channel coding (JSCC), has emerged as a key paradigm for low-latency, high-precision edge-assisted Internet of Things systems. However, the direct mapping of source data to continuous channel symbols in JSCC poses a great challenge in compatibility with existing digital systems. To address this, we propose a digital semantic communication scheme, i.e., an AdaptiveSemanticCompression with jointResourceAllocation andModulation (Adaptive-SCRAM) optimization scheme for multi-user image classification. This scheme, with the semantics quantized by a compressed codebook, enables the discrete semantic transmission with adaptive modulation, while achieving high accuracy and low latency with transmission resources optimized in multi-user classification task. Specifically, we first design a vector quantized-variational autoencoder-based digital JSCC framework with regional quantization, by jointly maximizing the semantic entropy and minimizing the codebook training loss with various SNRs and modulation orders considered in Rayleigh fading. Then based on the well trained end-to-end architecture, we mathematically fit the classification accuracy with respect to the effects of both compressed codebook size and received SNR under different modulation orders, providing an effective premise for the task performance optimization. Finally, we consider to maximize the overall multi-user classification accuracy under the transmission delay constraint, by optimizing the compression, modulation, power and bandwidth allocation for each user. To address the highly non-convex issue, we develop a dual-layer optimization algorithm. The outer-layer problem, which optimizes the compressed codebook size and modulation order, is solved by a cross-entropy-based learning algorithm. While for the inner-layer problem, a successive convex approximation method is used to optimize the power and bandwidth allocation. Simulation results show that our JSCC framework significantly reduces the semantic codebook size without compromising the classification accuracy, which is applicable to practical digital transmission systems. More importantly, compared to most existing comparable optimization schemes for image classification, our Adaptive-SCRAM optimization scheme with adaptive compression, modulation, and resource allocation can achieve much higher classification accuracy for multi-user tasks, while guaranteeing the transmission efficiency.

Phase noise is one of the fundamental impairments in radar, communications, and even the integration of sensing and communications, which is necessary to be suppressed to guarantee the system performance for high-order modulations. In order to obtain precise phase estimation or effectively track phase noise, many estimation algorithms rooted in digital signal processing operate under the premise that the variance of the phase noise is known. However, in practical applications, the receiver side can hardly get the premise knowledge of the phase noise variance. Thus, accurate estimation of the phase noise variance is significantly important for not only carrier recovery, but also performance monitoring. This paper proposes a maximum likelihood (ML)-based Wiener phase noise variance estimation scheme, based on the amplitude and phase-form of the noisy received signal model for$M$-ary phase-shift keying ($M$PSK) modulated systems. Specifically, by making full use of the explicit statistics of the received phase after raising to the Mth power, the closed-form expressions for ML estimation of the incremental phase noise and the Wiener phase noise variance are derived. The estimated mean square error is both theoretically and numerically analyzed to validate the unbiased ML estimator. Numerical results are given to verify the estimation accuracy in terms of varing signal-to-noise ratio and memory length. The proposed ML estimator is demonstrated to have precise estimation performance with low computational complexity.

Cooperative spectrum sensing (CSS) plays a crucial role in this era of explosive Internet of Things with scarce spectrum resources, since it can effectively enhance the sensing accuracy with the cooperation of secondary users (SUs). However, most existing CSS algorithms primarily focus on increasing the cooperative detection accuracy, while neglecting the computational complexity or sensing latency. Therefore, we propose a deep learning (DL) driven CSS scheme with the consideration of dynamic multi-model selection and suitable resource allocation. Specifically, we first derive the closed-form expressions to fit and characterize the detection and false alarm probabilities of three popular DL models, including the convolutional neural network, the long short-term memory (LSTM) network and the hybrid convolutional LSTM network. Then, the problem of minimizing the cooperative sensing error is formulated under the constrains of limited computational resource and sensing latency. Finally, the cross-entropy algorithm is employed to dynamically select the most suitable cooperating SU set and their correspondingly matched models, to balance the sensing accuracy and computational complexity. Simulation results demonstrate that our CSS scheme are much more robust and computationally efficient compared to some well-known CSS algorithms, especially in achieving extremely high sensing accuracy at low transmit power or low received signal-to-noise ratio.

The performance of modern communication and radar systems can suffer severe performance degradation from oscillator phase noise. Existing receivers commonly assume that the carrier phase is a constant over a window of a few symbol intervals and average the received signals over these intervals to obtain an estimate of the carrier phase for data demodulation. For mmWave/THz wireless and optical communications with fast time-varying phase noise, this quasi-static carrier phase assumption will no longer be applicable to ensure optimum estimation and compensation for the unknown carrier phase. We present here an Mth-power receiver for$M$-ary phase-shift keying ($M\text{PSK}$) modulation and a Wiener process carrier phase model that is applicable in many situations, especially in optical communications. The receiver can eliminate the$M$-ary phase modulation by raising the received signal samples (one sample per symbol interval) with noise to the power of$M$. The resulting unmodulated phase samples then enable the receiver to perform joint maximum likelihood estimation and maximum a posteriori probability estimation of the unknown initial carrier phase and Wiener carrier phase noise process. The estimation performance improves with a relatively small data block length for any given signal-to-noise ratio and Wiener phase noise variance, and this leads to better error probability performance in data detection. Simulation results are obtained for the estimation mean square error of the noisy carrier phase and the error probability of the detected$M\text{PSK}$symbols.

We derive approximate bit error probability (BEP) expressions for binary differential phase shift keying (BDPSK) and quadrature differential phase shift keying (QDPSK) signals in free-space optical communication system over exponentiated Weibull (EW) fading channel. By using the cumulative distribution function of EW channel and integration by parts, the conventional BEP expressions with the integral over an infinite interval are transformed to the integral over a finite interval. Based on the novel BEP expressions, we derive new, closed-form, approximate BEP expressions that involve only a gamma function, which reduce the computational complexity. The approximate BEP expressions are compared with theoretical BEP expressions under weak, moderate, and strong turbulence regimes, where the maximum gaps between the approximate and theoretical BEP expressions are 0.33 dB and 1.36 dB for BDPSK and QDPSK signals, respectively. The approximate BEP expressions are also used to analyze the loss of signal-to-noise ratio in EW fading channel.

In conventional approach, the bit error probability (BEP) expressions of$M$-ary phase-shift keying (MPSK) signals over additive white Gaussian noise (AWGN) channel are derived by averaging error probabilities for all bits of MPSK symbol. The closed-form BEP expressions of MPSK signals over AWGN channel can also be derived by using the weighted conditional symbol error probability (SEP) expressions, which has not been reported. In this paper, we derive the conditional SEP expressions of MPSK signals in terms of Gaussian$Q$and Owen's$T$functions by changing the domain of integration from a plane bounded by two rays into a quadrant. By weighting the conditional SEP expressions according to average distance spectrum, the closed-form BEP expressions of MPSK signals over AWGN channel are obtained. Only two summations involving two parameters are required. The closed-form BEP expressions of MPSK signals over Nakagami-$m$fading channel are derived by using the BEP expressions over AWGN channel and the moment generating function-based approach. The approximate BEP expressions of MPSK signals over Nakagami-$m$fading channel are obtained by using elementary functions-based approximations of Gaussian$Q$and Owen’s$T$functions. The conciseness and computational complexity of our BEP expressions are verified by the comparison with existing results.

Maximum likelihood (ML) amplitude and noise variance estimation without having to jointly estimate the frequency and the phase and based only on information from the noisy received signal magnitude, is studied for a single sinusoid in complex additive white Gaussian noise. This estimation problem is equivalent to the classic problem of parameter estimation for the Rician distribution. While solving the likelihood equation is impossible in general, we propose a new approach based on a large argument approximation. For the case with known noise variance, a closed-form ML amplitude estimator is obtained, which outperforms the conventional root-mean-square estimator. For the case with unknown noise variance, the closed-form joint amplitude and noise variance estimators obtained do not require prior knowledge of one another.

Ambient Backscatter Communication (AmBC) is a promising technology for green IoT, which overcomes the energy, cost and spectrum resource shortage challenges. In AmBC, the weak backscatter link strength caused by the double-fading is a big challenge for IoT device symbol detection. This paper focuses on receiver design with the M PSK RF source symbol. Most previous works have not considered the issue of channel estimation that is very important for wireless communications. We focus on precisely estimating the channels at each of the AmBC receiving antennas, in particular on resolving the quadrant ambiguities in the channel estimates. The proposed channel estimator makes use of both the pilot and the data symbols of the RF source to eliminate quadrant ambiguity and enhance the estimation accuracy. We propose a novel distance detector (DD) that makes its decision in each IoT symbol interval based on which of the calibrated channel estimates the current channel estimate is closer to in Euclidean distance. What is more, we propose two modified distance detection methods to enhance the bit error rate (BER) performance. Finally, extensive numerical results show that the proposed distance detection method achieves performance comparable to that of the optimal detector with perfect channel state information (CSI).

We consider the uplink channel estimation problem in a millimeter wave (mmWave) system with large-scale antenna arrays. Unlike many existing works which estimate the channel assuming that the number of channel paths is known a priori, we address the problem of channel estimation with an unknown number of channel paths. The spatial channel is transformed into the beamspace channel by the discrete Fourier transform (DFT). Based on the sparsity property of the beamspace channel, we propose three algorithms to estimate the number of paths, direction of arrivals (DoAs) and path gains. The first one is the Spectrum Weighted Identification of Signal Sources (SWISS) for the case when the channel statistics are unknown, which introduces a weight vector to amplify the desired signal and suppress the noise. The second one is the Neyman-Pearson criterion based-Detector (NPD) based on the Rician channel model, which adopts the Neyman-Pearson criterion to decide whether there exists a path on each DFT point. In practice, the DoAs are continuously distributed, leading to the power leakage problem. We solve this leakage problem by proposing the combined algorithm with leakage (CAL). Simulation results show that the proposed algorithms perform better than the conventional spatial smoothing.

Non-orthogonal multiple access (NOMA) is envisioned to be a key technology to enhance the spectrum efficiency for 5G cellular networks. Meanwhile, ambient backscatter communication (AmBC) is considered as a promising solution to Internet-of-Things (IoT), due to its high spectrum- and power-efficiency. In this paper, we are interested in an integrated system of cellular and IoT networks, and propose a backscatter-NOMA system, which incorporates a downlink NOMA system with backscatter devices. In this system, the base station (BS) transmits information to two cellular users according to the NOMA protocol, while a backscatter device transmits its information over the BS signals to one cellular user using passive radio technology. We derive the closed-form expressions of the outage probabilities and analyze the diversity orders of all relevant transmissions in the proposed system. Finally, we provide numerical results to verify the theoretical analysis.

This paper considers the channel estimation problem in millimeter-wave (mmWave) systems where a single-antenna user communicates with a massive multiple-input multiple-output (MIMO) base station (BS) in the uplink. Unlike many existing works which estimate the channel gain under the assumption that the number of channel paths is given a priori, we address first the problem of path-number identification. By taking the weighted discrete Fourier transform (WDFT) of the received noisy signal, we formulate an optimization problem to determine the optimum combination of DFT components in this weighted spectrum that leads to a time-domain reconstructed signal (the channel vector) that is at the minimum Euclidean distance from the received signal. Our algorithm, called SWISS (Spectrum Weighted Identification of Signal Sources), is an accurate and computationally efficient means for identifying the paths in the channel vector, providing the information needed for BS beamforming. Once the paths are identified, their individual directions-of-arrival (DoAs) and complex fading gains can be obtained easily. Simulation results for the case of no power leakage in the DFT are presented to demonstrate the effectiveness of SWISS.

Superposed multicarrier transmission is a potential solution to the spectra overcrowding problem in wireless communications. Powerful FEC coding using a turbo code is one way to overcome the increased noise power due to the interference. Reliable decoding of turbo codes requires accurate knowledge of the channel coefficients and the power of the interference if it is present. This paper presents soft-decision-aided, joint MAP estimation of these parameters, which requires only a small pilot overhead. A novel superposed band detection method is also proposed. The accuracy of the estimators and the effectiveness of the superposed band detection are demonstrated via simulations.

In this paper, we derive the analytical expressions for the secure outage probability in a single-input single-output (SISO) system over fading, in which both the main and eavesdropper channels are subject to κ-μ fading. Many authors have analyzed the secrecy performance of such a SISO system over various fading models. More recently, a lower bound on the secure outage probability over κ-μ fading has been reported. However, the exact analytical expression of secure outage probability over κ-μ fading has not been obtained. The problem with using the lower bound is that we are not sure about the tightness of the bound. Our result is an exact expression which is verified by Monte-Carlo simulations. Furthermore, it enables us to examine the behavior of the secure outage probability as a function of the fading parameters of both the main and eavesdropper channels for given values of the average signal-to-noise power ratio (SNR) over these channels. Exact expressions for the case of Nakagami-m and Rician fading models for both the main and eavesdropper channels are also obtained and verified by simulations.

In this paper, we investigate the secrecy performance of single-input single-output (SISO) system over fading, such that the main channel and the eavesdropper channel are subject to Rician/Nakagami-m fading or Nakagami-m/Rician fading, and derive the analytical expressions of the probability of the existence of the non-zero secrecy capacity and the outage probability of secrecy capacity. Although many authors have analyzed the secrecy performance of SISO system over various fading, the secrecy performance in the cases we assume has not been clarified. Furthermore, the simulation and numerical results show that the results using the approximation between Rician and Nakagami-m fading is insufficient in evaluating those probabilities because of only approximation to main bodies of the probability density function, and that our analyses are valid.

We consider frequency-flat time-varying fading channels with no channel model information (CMI). By introducing the smoothness function to measure the extent of channel fluctuation, we derive a robust soft-decision-aided (SDA) channel estimator based on Pareto optimality of the double-objective optimization of the likelihood function of the received signal sequence and the smoothness constraint of the channel estimates. Compared with the conventional maximum-likelihood-based channel estimators derived under the block-fading assumption, the newly derived SDA-Pareto estimator gives more freedom to the channel estimation process, allowing channel estimates to have controlled variations to track the time-varying channel more closely. Compared with estimators derived based on the maximum a posteriori probability or the minimum mean-square error criterion which require explicit acquisition of the CMI, the SDA-Pareto estimator significantly simplifies the channel measurement process by requiring only a suitable regularization parameter to balance the trade-off between the likelihood function and the smoothness condition. An adaptive algorithm is proposed to adjust the regularization parameter adaptively, enabling an efficient and effective implementation of the SDA-Pareto estimator in practical applications. Simulation studies are provided to demonstrate the advantage of the SDA-Pareto estimator over the conventional estimators in both channel estimation accuracy and error-rate performance.

This paper presents the simultaneous data detection and parameter estimation receiver. The receiver performs simultaneous ML detection of the data sequence and joint channel estimation and carrier synchronization. The explicit structure of the joint amplitude, frequency offset and unknown phase estimator enables us to evaluate explicitly the ML estimates of the fading amplitude, frequency offset and unknown phase corresponding to each hypothesized data sequence. This then allows us to evaluate explicitly for each hypothesized data sequence the maximum value of the likelihood function. By comparing these maximum values among all possible data sequences, the optimal ML detection of the data sequence can be obtained.

This paper analyzes the error performance of M-ary amplitude phase-shift keying (M-APSK) signals with annular-sector (AS) detection over the channel where both additive white Gaussian noise and oscillator phase noise exist. This AS detector performs ring detection and phase detection separately, and leads to the circular decision boundaries in the middle of rings. We derive a unified, closed-form expression for the symbol error probability (SEP) of M-APSK with phase reference error (PRE) due to imperfect phase estimation, based on our previously proposed additive observation phase noise model. The SEP result is analytically tractable and consists of products of Gaussian Q-functions. An accurate, unified approximation to the error floor is directly obtained as a sum of Gaussian Q- functions. Within a wide range of PRE variances, our approximations agree very well with the Monte Carlo simulation for all signal-to-noise ratio (SNR) values of interest. We show that as the PRE variance or the SNR or both increase, the AS detector outperforms the conventional minimum Euclidean distance detector. Moreover, our results provide explicit insight into how the parameters affect the error performance, and facilitate the optimization of M-APSK constellations in phase noise. Examples of ring radii optimization have been given.

We consider iterative decoding of repeat- accumulate (RA) codes over frequency-flat, quasi- static fading channels. A soft-input, soft-output decoder is proposed for the inner convolutional decoding, which fuses the decoding approach of the soft-output Viterbi algorithm and the estimation approach of the maximum-likelihood sequence detector. The decoder deploys trellis search algorithm based on the generalized likelihood ratio test, whereby the channel state information is acquired implicitly using both the pilot and data signals during the decoding process. Through simulations, we show that the RA decoding with the proposed decoder has much better error performance than standard RA decoding with pilot-symbol- assisted channel estimation, while having approximately the same computational complexity. Compared with the conventional scheme of iterative channel estimation and decoding, the proposed decoder has much simpler structure and requires significantly less computational power, although it incurs some loss in error performance.

Accurate channel state information (CSI) is crucial for reliable decoding over fading channels. In many existing works, the CSI acquisition relies greatly on accurate knowledge of the channel model information (CMI), which includes, in particular, the power spectrum of the fading process and the statistical distribution of the fading gain. In practice, it may be difficult to obtain or keep track of the CMI accurately. In this paper, we consider the decoding of Reed- Solomon convolutional concatenated (RSCC) codes over the quasi-static fading channel, and propose a robust, decision-directed, soft-output convolutional decoder which does not require explicit CSI acquisition. Simulation result shows that the proposed decoder has a lower bit-error rate for convolutional decoding than the conventional soft-output Viterbi algorithm and the BCJR algorithm with pilot-symbol-assisted channel estimation. The advantage of the former in terms of the accuracy of soft-decision output is demonstrated by the superiority of word-error performance in the RSCC decoding.

We consider the differential phase-shift keying modulation over the flat Rician fading channel with perfect channel model information (PCMI), and derive the two-symbol-observation-interval log-likelihood ratio (LLR) metric from first principles. The work generalizes the previous LLR derivations in [16]-[19], and demonstrates the necessity of the knowledge of the statistical channel model in the exact LLR computation. Assuming the channel is slowly time-varying, we also propose a simple approximate LLR metric based on the generalized likelihood ratio test (GLRT), which requires only the information of the noise spectral density. The advantage of the newly derived PCMI-LLR metric over the approximate metric and the other LLR metrics in the literature is explained from the information-theoretic perspective via the generalized mutual information. Computer simulations are also provided to demonstrate the superiority of the PCMI-LLR metric in both error rate performance and convergence speed for iterative decoding of turbo and low-density parity-check codes in practical systems. This paper aims to present the fundamental principles of LLR computation, emphasizing the importance of selecting the appropriate metric for iterative decoding over fading channels.

The paper investigates the signal-to-noise ratio (SNR) threshold effect in estimating the frequency and phase of a single sinusoid over the additive white Gaussian noise. This is done by making use of the results on the time-domain, phase-based estimator and the additive observation phase noise (AOPN) models developed in the work of Fu and Kam (2013). Specifically, the relationship between the threshold SNR and the similarity/dissimilarity of the Tikhonov distribution model of the AOPN to the corresponding Gaussian approximation is studied from three different but relevant aspects, namely, the series convergence, the Kullback-Leibler (KL) divergence and the AOPN variance. The interconnection that exists among these three aspects is revealed. In comparison to the mean-square-error-based approach, the AOPN-based approach proposed here has an advantage that it can lead to an analytical result on the performance of threshold SNR.

We consider transmissions over the frequency-nonselective time-selective fading channel and derive the soft-decision-aided maximum a posteriori probability (SDA-MAP) channel estimator that utilizes the entire received signal sequence, including both pilot signals and data signals, and the a priori statistical information of the transmitted data symbols. This paper theoretically demonstrates how the soft data decisions should be incorporated into the channel estimation process. An iterative implementation of the SDA-MAP estimator is proposed, which uses the feedback of earlier soft decisions and the feedforward of later soft decisions to estimate the current channel gain. This approximate SDA-MAP implementation is similar in structure to the expectation-maximization algorithm. Simulation results show that the receiver using this iterative SDA-MAP estimator outperforms the conventional pilot-symbol-assisted modulation receiver in which the channel estimates are obtained from only the pilot signals. An application to iterative decoding using the LTE turbo code is also provided.

This paper is concerned with detector design and performance analysis for spectrum sensing of phase-modulated signal in cognitive radio systems. Under the maximum a posteriori probability criterion, the optimal detector which outperforms the popular energy detector is derived, and its detection and false-alarm probabilities that describe the receiver operating characteristic (ROC) are analyzed. These probabilities are obtained as explicit, closed-form expressions, which show analytically ROC behavior as a function of various system parameters such as the signal-to-noise ratio and the number of data samples. The theoretical analysis and results are validated by computer simulations.

This paper aims at providing explicit, closed-form solutions to the error probability performance analysis of digital communications over fading channels. This is achieved by first deriving a family of new upper bounds on the Gaussian Q-function Q(x), which is given by a sum of products of the exponential function and c/x where c is a constant. The bounds obtained can be made arbitrarily tight as the number of summation terms increases, and thus, can be used to approximate Q(x) accurately. Their applications to the performance analysis over fading are then presented to highlight the significance of the bounds derived. Both short-term fading and combined short-term and long-term fading are considered. It is shown that the new bounds can lead to better performance than the popular exponential-type upper bounds.

This paper is concerned with performance analysis (in terms of bounds and approximations to the average symbol error probability (ASEP)) of a product and power of Gaussian Q-functions over Nakagami-m fading. The results are valid for arbitrary product/power order. This is done by first deriving a family of new, simple lower bounds on the Gaussian Q-function, which is obtained as a sum of products of an exponential function and cx where c is a constant. These lower bounds can be made arbitrarily tight as the number of summation terms increases, and thus, can be used to approximate the Gaussian Q-function accurately. Their applications to the evaluation of the ASEP are then presented. Some advantages of the results derived here over those given in the literature are briefly discussed.

We consider a differential amplify-and-forward transmission scheme for a two-user cooperative system with a single relay. We propose a new analytical approach based on first principles, and obtain a closed-form expression for the exact bit error probability (BEP) in Rayleigh fading. This result involves only a single exponential integral function. It applies generally to the case where the channel statistics on different links are non-identical. As expected, the BEP decreases monotonically with the source transmission energy, or the relay transmission energy. The explicit BEP result allows us to study optimum energy allocation between the source and the relay, given a total transmission energy. By lower bounding the exact BEP expression via Jensen's inequality, we obtain analytically a closedform approximate optimum energy allocation solution between the source and the relay. Numerical results show that the BEP bound and the approximate optimum energy allocation solution are very tight.

We propose to use the probability of instantaneous bit error outage (IBEO) as a new performance measure in the design of an actual feedback power control system. It is defined as the probability that the instantaneous bit error probability (IBEP) exceeds an IBEP threshold. We propose the IBEO-based power control law where the transmitted power is adjusted according to the variations of the channel such that the IBEO probability is kept within some quality of service (QoS)-specified threshold. It ensures that in the long term, no more than a certain fraction of received bits would have IBEP exceeding some IBEP threshold. Therefore, the instantaneous QoS is guaranteed. Based on a practical system model with channel estimation and prediction, we develop the traditional average bit error probability (ABEP)-based power control law and the new IBEO-based power control law. For both laws, we derive explicit ABEP and IBEO probability results. The IBEO-based law shows a remarkable gain over the ABEP-based law in terms of IBEO probability, and sacrifices only a little in the ABEP performance.

This paper presents the theoretical foundation for time-domain, phase-based estimation of the frequency and phase of a single sinusoid in additive white Gaussian noise (AWGN), analogous to the theoretical foundation provided by Rife and Boorstyn for frequency-domain, Fourier-transform-based estimation. It is shown from the maximum a posteriori probability (MAP) and the maximum likelihood (ML) estimation principles that with the additive observation phase noise (AOPN), due to the AWGN, being described by its a posteriori distribution conditioned on the received signal magnitude, the received signal phase is a sufficient statistic for estimating the single-sinusoid angle parameters. Using a geometric approach, the exact statistical model for the AOPN is derived, where the a posteriori probability density function (pdf) and the corresponding a priori pdf are given by explicit, closed-form expressions that are valid for arbitrary signal-to-noise ratios (SNRs). The a posteriori pdf is Tikhonov, and is of particular interest as it establishes the AOPN model for phase-based frequency/phase MAP/ML estimation in the time domain. It is further illustrated that the results derived can yield various AOPN models as special cases, and the underlying physical insights and interconnections that exist among these models are revealed. It is shown that the model derived by Tretter is an ultimate specialization in the high SNR limit of the AOPN models developed here. For high SNR, the a posteriori Tikhonov pdf can be accurately approximated by a Gaussian distribution, which leads to the best linearized AOPN model. The applications of these AOPN models to the design of linear estimators, including the linear minimum mean square error (LMMSE) estimator, the linear minimum variance estimator, and the LMMSE implementation of the weighted phase averager are presented, and their estimation performances are compared through computer simulations, with the Cramer–Rao lower bound (CRLB) and the Bayesian CRLB as the benchmark. To facilitate estimator design, the a priori statistical models of the frequency and phase are proposed from the information-theoretic perspective, and an improved phase unwrapping algorithm over that given by Fu and Kam is presented. It is shown that by incorporating all the information available in the AOPN, the estimation accuracy can be much improved.

With the prior knowledge that the primary user is highly likely idle and the primary signals are digitally modulated, we propose an optimal Bayesian detector for spectrum sensing to achieve higher spectrum utilization in cognitive radio networks. We derive the optimal detector structure for MPSK modulated primary signals with known order over AWGN channels and give its corresponding suboptimal detectors in both low and high SNR (Signal-to-Noise Ratio) regimes. Through approximations, it is found that, in low SNR regime, for MPSK (M > 2) signals, the suboptimal detector is the energy detector, while for BPSK signals the suboptimal detector is the energy detection on the real part. In high SNR regime, it is shown that, for BPSK signals, the test statistic is the sum of signal magnitudes, but uses the real part of the phase-shifted signals as the input. We provide the performance analysis of the suboptimal detectors in terms of probabilities of detection and false alarm, and selection of detection threshold and number of samples. The simulations have shown that Bayesian detector has a performance similar to the energy detector in low SNR regime, but has better performance in high SNR regime in terms of spectrum utilization and secondary users' throughput.

The problem of estimating the frequency of a single sinusoid observed in additive, white, Gaussian noise is addressed. An explicit, sample-autocorrelation-function-based, approximate maximum likelihood (ML) frequency estimator which does not require numerical search is derived. The structure of this estimator reveals that both the magnitude and the angle of the autocorrelation function should be utilized in estimation processing. Simulation results show that the estimator derived attains the Cramer-Rao lower bound at high signal-to-noise ratio, and has better performance than the planar filtered estimator developed in [22, 23] and the time-domain, approximate ML, received-signal-based estimator in [20, 21]. A new phase unwrapping algorithm is presented to faciliate an efficient, recursive implementation of the estimator. To have a better understanding on the sample-autocorrelation-function-based estimator, a geometric interpretation on the autocorrelation function is introduced. This interpretation allows us to propose a further simplified frequency estimator that resorts to the autocorrelation function angle increments to avoid phase unwrapping. By using the autocorrelation function expression, an alternative form to the frequency estimator of [20, 21] is derived.

Automatic repeat request (ARQ) schemes with cyclic redundancy check (CRC) codes are designed specifically for additive white Gaussian noise channels based on average performance measures. Average performance measures are known to be inadequate for high data rate wireless communication where the channel gain varies randomly in time, because they do not reflect the poor QoS in deep fades. The instantaneous accepted packet error outage (IAPEO) probability is a more meaningful performance measure. Therefore, we examine the IAPEO of conventional ARQ and observe that, to achieve a certain IAPEO performance, the system must operate above a minimum signal-to-noise ratio (SNR), which may be too high to achieve. This motivates us to propose ARQ with channel gain monitoring (CGM), in which a packet is only demodulated and checked for errors when the channel gain exceeds a threshold; otherwise retransmission is requested. We show that it does not have a minimum SNR requirement. The average performance measures of ARQ-CGM with selective-repeat, go-back-n and stop-and-wait retransmission protocols, i.e. the average accepted packet error probability, throughput and goodput, are also obtained as functions of the pilot length and the CRC code length. The allocation of bandwidth and energy between channel estimation and CRC coding is studied.

We consider the iterative decoding of low-density parity-check codes with M-ary phase-shift keying transmission and pilot-symbol-assisted channel estimation over time correlated Rayleigh fading channels. We present the correct conceptual approach for deriving the log-likelihood ratio (LLR) expression for a general q-ary code. Its bit-error probability (BEP) performance is compared with that of the conventional metric which does not take into account the information concerning the channel estimation accuracy. Simulation results show that this LLR metric outperforms the conventional metric in both BEP performances and average number of decoding iterations required for convergence. The work here demonstrates the importance of incorporating the knowledge of the channel estimation accuracy in the iterative decoding process.

This paper presents new bounds on the Marcum Q-function Q1(a, b). First, new, simple, arbitrarily tight, exponential lower bounds on the zeroth-order modified Bessel function of the first kind Io(x) and the Gaussian Q-function Q(x) are derived. Due to their elegant features, these new bounds are fundamental in their own rights. Then, when they are applied to the Marcum Q-function that is expressed as a function of lo(x) and Q(x), various new exponential-type lower and upper bounds are developed.

The probability of instantaneous accepted packet error outage (IAPEO) is proposed as a performance measure for packet transmission with automatic-repeat-request (ARQ) schemes over wireless channels. It is defined as the probability that the instantaneous accepted packet error probability (IAPEP) exceeds an IAPEP threshold. We obtain a closed-form upper bound expression for IAPEO of a pure ARQ over Rayleigh fading, and observe that, in order to satisfy a system design requirement of maximum tolerable IAPEO, the system must operate above a minimum SNR value. We next propose an ARQ scheme by incorporating channel gain monitoring (ARQCGM), such that the IAPEO requirement can be satisfied at any SNR value with the right channel gain threshold. The IAPEO performance of ARQ-CGM with selective repeat retransmission protocol is related to the conventional performance measures, i.e. average accepted packet error probability, throughput and goodput.

We propose an iterative decoding scheme for low density parity check codes concatenated with binary differential phase shift keying (BDPSK) in additive white Gaussian channels with unknown phase offset by viewing the BDPSK modulator as the encoder of a rate-one convolutional code. To assist this iterative scheme, a new log-likelihood ratio (LLR) metric based on three consecutive received symbols is derived. This metric takes a priori information of other coded bits into account and therefore applicable to the proposed iterative scheme. We show that the proposed iterative scheme has better performance than systems using other LLR metrics for noncoherent detections. The performance of the proposed scheme under signal-to-noise ratio estimation error is also investigated.

Using the convexity property of the exponential function, we obtain a family of exponential lower bounds on the Gaussian Q-function using the Jensen's inequality. The tightness of the bounds can be improved by increasing the number of exponential terms. The coefficients of the exponentials are constants, allowing easy averaging over the fading distribution using the moment generating function method. This method is also applied to the symbol error probability of M-ary phase shift keying and M-ary differential phase shift keying over additive white Gaussian noise and fading channels. The tightness of the bounds is demonstrated.

Based on the high probability that primary user is idle in cognitive radio networks, we propose an optimal Bayesian detector structure for spectrum sensing. Although the optimal detector by Neyman-Pearson theorem maximizes the detection probability for a given false alarm probability, Bayesian detector can achieve a higher overall spectrum utilization and SU throughput and at the same time the primary user is well protected from secondary user's interference. For BPSK modulated primary signals we show that the optimal Bayesian detector can be reduced to an energy detector in lower SNR regime, and it can be approximated to a detector employing the sum of received signal magnitudes in high SNR regime to detect primary signals. We give the analysis for optimal Bayesian detector and the corresponding suboptimal detector structure in both low and high SNR regimes, and verify the performance of the detector with simulation results.

The ergodic capacity is a key performance parameter of a multiple-input-multiple-output (MIMO) fading channel. We would like to determine the optimal number of transmit antennas to be used for a given signal-to-noise ratio (SNR) and a given total number of antennas in the system. Thus, we obtain here three simple and tight bounds on the ergodic capacity of the MIMO Rayleigh fading channel, which show explicitly the dependence of the ergodic capacity on the SNR and the number of transmit and receive antennas.

This paper presents a geometric-view-based evaluation for the generalized Marcum Q-function Q_m(a,b), which is interpreted as the probability that a random Gaussian point whose mean vector has an Euclidean norm a≥, lies outside of an N-dimensional sphere/hypersphere of radius b≥0, centered on the origin point O, where N=2m≥3. By using the geometric symmetry of the sphere/hypersphere and the symmetry property of the joint Gaussian probability density function as well as a proper selection for the center point of the transformed spherical/hyperspherical coordinates, a direct, simpler evaluation approach is presented which leads to several new, compact, finite-integral representations of Q_m(a,b). The new representations are given in an unified form in the sense that they are valid for both an integer m and a non-integer m. Their application to error performance analysis of digital communications is illustrated.

We consider phase-based estimators for chirp parameters due to their high computational efficiency for implementation. Their performances can approach the Cram\'{e}r-Rao lower bound for high signal-to-noise ratio (SNR). One challenge for the phase-based estimators is the performance loss at low SNR because the reliability of phase unwrapping and the accuracy of the phase noise model decrease seriously at low SNR. We here propose a signal recovery method to enhance the SNR for phase-based estimators. The method first uses an adaptive filter to recover the chirp signal from the noisy received signals. Then, the reconstructed chirp signal is used as the input to the traditional phase-based estimators for parameter estimation. The significantly enhanced SNR at the output of the filter brings much improved estimation performance. A robust algorithm is also proposed to achieve good performance over a range of values of chirp parameters of interest. Our simulation results show that significantly improved performance can be obtained by using the signal recovery method for the phase-based estimators.

Phase-based frequency estimators over frequency-selective fading channels are examined. The implementation complexity of phase-based estimators is low due to their explicit structures which require no numerical search. The statistical information of the measurement phase noise (MPN) is crucial for phase-based estimators. The exact probability density function of the MPN over frequency-selective fading channels is first derived. Then, two approximations are proposed to further reduce the computational complexity of the estimators. In our new phase models, the magnitudes of received signal samples enter in determining the covariance of the MPN, and give adaptive weights to the phase measurements. In contrast, only phase information is exploited in the traditional phase-based frequency estimators due to the approximate MPN model used. Our simulation results demonstrate that better performance can be achieved by using our improved MPN models over frequency selective fading channels. Finally, the effects of the periodic length of the training sequence on the performance of frequency estimation are studied.

We derive the log-likelihood ratio for iterative decoding of low-density parity-check codes transmitted using binary phase-shift-keying (BPSK) with pilot-symbol-assisted modulation. This is done with the aid of a reference phasor formed from the received pilot signals. We compare our metric with the existing Gaussian metric for differential BPSK transmission and also show that our metric converges to that for coherent BPSK transmission in the limit as the size of the pilot reference set becomes large. Simulation results verify our analysis and study the effects of carrier phase noise and signal-to-noise ratio mis-estimation on the performance of the metric.

We propose to use the probability of instantaneous symbol error outage (ISEO) as a performance measure for digital communication over wireless channels. It is defined as the probability that the instantaneous symbol error probability (ISEP) exceeds an ISEP threshold. We analyze the impact of imperfect channel state information (CSI) on the ISEO probability over Rayleigh fading channels. A simple, but tight, closed-form upper bound on the ISEO probability is obtained as a function of the channel estimation mean square error (MSE). It is shown that the ISEO performance improves rapidly with decreasing MSE, when MSE drops below a certain value, which is determined partly by the ISEP threshold chosen. As CSI is commonly obtained by pilot-symbol-assisted channel estimation in packet transmission, we obtain the optimum allocation of pilot and data energy in a frame that minimizes the ISEO probability, which also minimizes the instantaneous packet error outage probability.

The generalized Marcum Q-function of order m, Qm(a, b), is interpreted geometrically as the probability of a 2m-dimensional, real, Gaussian random vector Z2m, whose mean vector has a Frobenius norm of a, lying outside of a hyperball BO,b2mof 2m dimensions, with radius b, and centered at the origin O. Based on this new geometric view, some new representations and closed-form bounds are derived for Qm(a, b). For the case that m is an odd multiple of 0.5, a new closed-form representation is derived, which involves only simple exponential and ERFC functions. For the case that m is an integer, a pair of new, finite-integral representations for Qm(a, b) is derived. Some generic exponential bounds and ERFC bounds are also derived by computing the probability of Z2mlying outside of various bounding geometrical shapes whose surfaces tightly enclose, or are tightly enclosed by the surface of BO,b2m. These bounding shapes consist of an arbitrarily large number of parts. As their closeness of fit with BO,b2mimproves, our generic bounds approach the exact value of Qm(a, b). The function Qm(a, b) is proved to be an increasing function of its order when 2m is a positive integer. Thus, Qm+0.5(a, b) and Qm-0.5(a, b) can be used as tight upper and lower bounds, respectively, on Qm(a,b). Their average is a good approximation to Qm(a, b). An application of our new representations and bounds is also given.

In this paper, differential modulation and demodulation in a multiple relay system using either the decode-and-forward (DF) protocol or the selection relaying (SR) protocol, are investigated. For the DF protocol, the detectors at the destination take the average bit error probabilities (BEPs) of all the source-relay transmissions into account. For a DF single relay system, the exact BEP and its approximation at high signal-to-noise ratio (SNR) are obtained. The approximation of the BEP at high SNR shows explicitly the diversity order and the different effects of the source-relay link and the relay-destination link on the end-to-end error performance. For a DF multiple relay system, a Chernoff upper bound on the BEP and a high SNR approximation for the BEP are obtained. For the SR protocol, some computational complexity is shifted from the destination to all the relays. Each relay computes the instantaneous BEPs of the source-relay transmissions, and uses the instantaneous BEPs to decide whether to transmit or remain silent. The destination performs simple maximal ratio combining (MRC) reception whose error performance is analyzed at high SNR. It shows from an error probability perspective that the SR protocol offers a space diversity order equal to the number of all the potential cooperating nodes.

With imperfect channel state information (CSI) acquired by channel estimation at the receiver, the performances of automatic-repeat-request (ARQ) systems are evaluated as a function of the accuracy of channel estimation. A link between network-layer performances and physical-layer parameters is therefore established. We study in particular the good-put and the accepted packet error rate as a function of the channel estimation mean square error (MSE) and the factors which affect the MSE. The results enable us to analyze the optimum allocation of energy for data transmission and energy for pilot channel estimation so as to maximize the good-put.

We develop an approach to compare different log-likelihood ratio (LLR) metrics for iterative soft decoding. We show that an LLR metric for a function of the received signals is a sufficient statistic to this function about the binary channel input. We also prove that when the function belongs to a set of specific mappings, the corresponding LLR metric can feed the maximal mutual information to the decoder. For decoding low density parity check codes with the belief-propagation decoder, we develop a method to estimate the minimal average number of iterations. The results are applied to compare the Gaussian metric in and the two-symbol-observation-interval LLR metric in. The latter is shown to be superior.

The exact statistical models for the observation phase noise (OPN) and their approximations in time-domain, phase-based estimation of the frequency and phase of a noisy single sinusoid are summarized, and the underlying physical interconnections are highlighted. The application of the various OPN models to the design of the weighted phase averager (WPA) estimator is developed. Simulation results show that using the time-varying OPN variance information which can intelligently indentify those phase samples with large errors, the performance of the WPA estimators can be improved, especially for low SNR.

We propose a MAC for wireless ad hoc cognitive radio networks where secondary users employ cooperative spectrum sensing to mitigate the degradation of the channel between primary transmitter and secondary users. The sensing reports and fused decisions are transmitted based on random access of CSMA/CA and 802.11e EDCA on the control channel, whose access scheme determines the overall achievable throughput among the multi-channels. We propose several schemes and derive the upper bound of overall throughput. The saturation problem is also studied to address the optimization of the channel selection and the trade-off between cooperative sensing gain and channel reuse efficiency.

A rate adaptation scheme requires channel state information (CSI), which can be acquired at the receiver by inserting pilot symbols in the transmit signals. We have developed a rate adaptation scheme that takes account of both channel estimation and prediction errors. The transmitter adapts transmission rate relative to the predicted channel state and a utilization factor. In turn, this utilization factor is optimized so as to achieve a maximum goodput.

We derive the exact log-likelihood ratio (LLR) for iterative decoding of low-density parity-check codes for pilot-symbol-assisted BPSK transmission over flat Rayleigh fading channels. The bit-error rate (BER) performances of this metric are studied for various interleavers and different pilot spacings. We further compare this metric with the approximate metric, which has been commonly used in the literature. Simulation results show that the newly derived LLR metric results in better BER performances. In addition, the effect of signal-to-noise ratio estimation error is investigated and our new LLR shows more robustness.

In we developed a Viterbi algorithm for efficient detection ofM-ary phase-shift keyed (MPSK) sequences received over the additive, white, Gaussian noise (AWGN) channel with an unknown carrier phase. Its performance approaches that of coherent detection, but the observation interval for forming the decision metric is fixed and chosen based on prior statistical knowledge of the carrier phase characteristics. Thus, the metric is non-adaptive, and cannot be optimized when a priori statistical knowledge of the carrier phase is not available. The work here renders it adaptive by developing a recursive metric that is adapted on-line based on the received signal, without prior knowledge of the carrier phase characteristics. An adaptive filter is used to generate the phasor reference on-line, by extending that in to sequence detection for generalM-ary quadrature amplitude modulation (MQAM). Comparison between the proposed adaptive, recursive metric and those in the literature is provided. Simulation results using a random-walk carrier phase model show the superior performance of the adaptive sequence detector over the original nonadaptive sequence detector of.

Iterative decoding of low-density parity-check codes transmitted over noncoherent channels using pilot-symbol- assisted binary phase-shift keying (BPSK) is studied. The log- likelihood ratio of the two values of each transmitted code bit is derived using the joint probability density function of the received signal that carries that bit and a set of reference pilot signals. We establish the relationship of our metric with that derived for differential BPSK transmission and also prove that our metric converges to that for coherent BPSK transmission. The theoretical analysis is further verified through simulation studies. In addition, two approximations of the metric that yield lower computational cost with negligible performance losses are introduced. Finally, we study the effects of signal-to-noise ratio estimation error on the performance of these metrics.

In cognitive radio networks, the secondary users (SUs) are allowed to use the spectrum originally allocated to primary users (PUs) as long as the PUs are not using it temporarily. This operation is called opportunistic spectrum access (OSA), and it is assisted through spectrum sensing. In distributed OSA, the SUs sense the channel independently; once the channel is available, they contend for channel access on a frame-by-frame basis. In this paper, we study the random medium access control (MAC) in conjunction with the sensing protocol design. In particular, we are interested in the design of frame duration, sensing time and MAC random access to maximize the secondary network throughput performance while protecting the PUs from the interference of secondary users' operations. We formulate the nonlinear constrained optimization problems for the described system model with cross-layered and layered approaches. Simulations show that the cross-layered approach performs much better than layered approach especially when the frame duration is small.

A new approach is presented for analyzing the bit error probability (BEP) of square, multilevel, quadrature amplitude modulation over a nonselective Rayleigh fading channel, with imperfect channel estimation employing pilot-symbol-assisted-modulation. It is much simpler and more powerful than those in the literature, and the average BEP is obtained by calculating the BEP for each individual bit. The results are given in simple, exact, closed-form expressions that do not require any numerical integration. These expressions show explicitly the behavior of the BEP as a function of various system parameters. Three channel estimation schemes are investigated. It is shown that existing channel estimation schemes using sinc interpolation and Gaussian interpolation can be improved.

Many existing works on space-time block codes (STBC) assume the channels are block-wise constant, but this assumption does not always hold. In the more general case of time-selective channels, the channel matrix is no longer orthogonal, so inter-symbol interference (ESI) is generated and the performance is greatly reduced. Several decoders have been proposed to eliminate the ESI, but it remains unclear how and to what extent the performance is affected by the ISI. In this paper, we introduce an approach to analyze the performance of STBC over time-selective channels, with arbitrary numbers of antennas for which orthogonal STBC's are defined. Exact error performances are obtained in closed form. Furthermore, the analysis reveals the relationship between the ISI and the structure of STBC matrices. ConsideringGisystems, we then propose one proposition and two design criteria, following which it is easy to design or search for better STBC's that have less ISI compared with the original code matrix.

We consider the maximum likelihood (ML) receiver design, performance analysis and code design for space-time trellis codes (STTC) over non-identical, rapid fading channels with imperfect channel state information (CSI). The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. A new code design criterion exploiting the statistical information of the channel estimates is proposed, which can minimize the performance loss caused by channel estimation error. New codes are obtained via an iterative search algorithm with reduced complexity. Under actual channel estimation conditions, our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels, and perfect CSI at the receiver. More performance gain can be achieved by our codes when the degree of imbalance among the links is higher.

In a fading environment, the statistical distribution of the mutual information of a multiple-input multiple-output (MIMO) system depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant and the trace of a Wishart matrix. Based on the obtained distributions, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the mutual information of a MIMO system in Rician fading environments. The bounds obtained on the CCDF of mutual information provide further insights into the channel mutual information, and show the effects of the system parameters on the mutual information distribution explicitly. In addition, results for the Rayleigh channels are obtained as a special case.

Assuming the channel gains associated with different receive antennas are not identically distributed, we study the orthogonal space-time block codes over non-identical channels with channel estimation. It is shown that the non-identical statistics lead to non-identical channel estimation errors, which make the conventional optimum decoder sub-optimum in this case. A new optimum decoder is derived. We show that it can be simplified to a symbol-by-symbol decoder under certain conditions. Analytical and simulation results show that our new decoder substantially outperforms the conventional decoder.

We analyze the average bit error probability (BEP) of orthogonal space-time block codes (STBC) over time-selective channels. Exact BEP results are obtained in closed form. Through the analysis, we reveal the relationship between the inter-symbol interference (ISI) and the row positions in a STBC matrix. We then introduce one proposition and two design criteria for code search/design. Optimum/near-optimum codes are found/designed with reduced ISI.

We analyze the capacity of a multiple-input single- output system over Rayleigh fading channels. The channels are assumed to be independent and non-identically distributed. Simple, explicit and closed-form expressions of ergodic mutual information and outage probability are obtained. Moreover, two suboptimal but efficient analytical power allocation schemes for mutual information maximization and outage minimization are derived, respectively. In specific, for mutual information maximization, more power is assigned to those channels with higher channel variances, while for outage minimization the power allocation scheme follows the water-filling principle.

Cooperative space-time coding (STC) is a distributed way to exploit the spatial diversity. With the help of relay nodes, STC can be applied among several single antenna users, where the relay nodes can either decode-and-forward (DF), or amplify-and-forward (AF) the received signal. In this paper, we analyze the performance of cooperative space-time block codes with AF strategy. Exact bit error probabilities (BEP) are derived in closed form for three existing protocols. We show that our exact BEP results are more reliable than the existing asymptotic results. A performance comparison of the three protocols is also provided.

The exact statistical models for the measurement phase noise in estimating the frequency and phase of a single sinusoid over the additive white Gaussian noise channel are derived. The a posteriori probability density function (PDF) and the a priori PDF of the phase noise derived are given by explicit, closed-form expressions that are valid for arbitrary signal-to-noise ratios. It is shown that as far as estimating the single sinusoid angle parameters is concerned, the phase of the received signal samples alone is a sufficient statistic, provided that the phase noise is modeled by the a posteriori PDF, which has a Tikhonov distribution. Furthermore, we illustrate that the results derived can yield various phase noise models as special cases, and the underlying physical insights and interconnections that exist among these models are revealed. The application of these models to the design of linear minimum variance estimator is presented, and their estimation performances are compared through computer simulations.

We extend the study in Fu and Kam (2006) of estimating the frequency and carrier phase of a noisy sinusoid. We show that when the improved observation model is used, the linear regression estimator developed in Tretter (1985) is suboptimal. Two generalized least-squares estimators, namely, the weighted least-squares estimator and the linear minimum variance estimator, are then formulated. To avoid phase unwrapping, we propose two new frequency estimators by using the differenced phase. The first is based on the ML estimator derived in (Fu and Kam). The second is based on the approach in Kay (1991) but incorporates our improved observation model.

This paper is concerned with receiver design for digital communications with linearly modulated signals over the additive, white Gaussian noise channel with unknown carrier frequency and phase offset. The modulation techniques examined are phase shift keying with and without differential encoding and M-ary quadrature amplitude modulation. Two types of receiver structures are proposed, namely, the symbol-by-symbol receiver with pilot-symbol assisted-modulation and the simultaneous data detection and carrier frequency/phase offset estimation receiver. Both receivers incorporate the use of the maximum likelihood frequency/phase estimator of a single sinusoid in noise that we recently derived in the work of Fu and Kam (2007 and 2006) to estimate and compensate for the effects of the unknown carrier frequency and phase offset. The error performance of the proposed receivers are examined via computer simulations.

Cooperative space-time block codes (STBC) can be applied to exploit the spatial diversity among several single antenna users. Because of its simplicity, amplify-and-forward strategy is often used at relay. In such cases, the additive noise at the relay is also forwarded to the destination. Therefore, it will degrade the received signals from both the relay and the source, due to the receiver structure of STBC. In this paper, we examine the effect of the forwarded noise and propose a condition, under which the relay should stop forwarding the signal. Based on this condition, adaptive cooperative STBC schemes are proposed. The performances of these schemes are studied and the exact bit error probabilities are obtained in closed form.

Iterative decoding of low-density parity-check codes transmitted over noncoherent channels using binary differential phase-shift keying modulation is examined. Using the joint estimation approach and the averaged likelihood function approach, the log-likelihood ratios of the two values of each bit, based on two contiguous received signal samples that convey the bit, are derived. In addition, a simplified approximate metric is introduced and shown to yield similar performance to the two metrics. Simulation results also show that these metrics derived here outperform the existing Gaussian metric. The performances of these metrics in the presence of phase noise and signal-to-noise ratio estimation error are also studied.

We derive a decision-feedback channel estimation receiver for independent and non-identically distributed (i.n.d.) Rayleigh fading channels. The receiver has memory to store signals received over the past several symbol intervals, and then use them to adaptively estimate instantaneous channel gains. The receiver adapts its decision rule based on estimates of the varying channel gains, and hence it is partially coherent. We also obtain the bit error rate (BER) of the channel estimation receiver for binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) modulations. The BER results are obtained in simple forms which explicitly show the effects of system parameters on the BER. In addition, our results are applicable to the cases where all the branches have arbitrary fade rates.

A geometric interpretation of the first-order Marcum Q-function, Q(a,b), is introduced as the probability that a complex, Gaussian random variable with real mean a, takes on values outside of a disk CO,bof radius b centered at the origin O. This interpretation engenders a fruitful approach for deriving new representations and tight, upper and lower bounds on Q(a,b). The new representations obtained involve finite-range integrals with pure exponential integrands. They are shown to be simpler and more robust than their counterparts in the literature. The new bounds obtained include the generic exponential bounds which involve an arbitrarily large number of exponential functions, and the simple erfc bounds which involve just a few erfc functions, together with exponential functions in some cases. The new generic exponential bounds approach the exact value of Q(a,b) as the number of exponential terms involved increases. These generic exponential bounds evaluated with only two terms and the new simple erfc bounds are much tighter than the existing exponential bounds in most cases, especially when the arguments a and b are large. Thus, in many applications requiring further analytical manipulations of Q(a,b), these new bounds can lead to some closed-form results which are better than the results available so far.

We present a symbol-by-symbol channel estimation receiver for an orthogonal space-time block coded system, and derive its analytical performance on a slow, nonselective, Rayleigh fading channel. Exact, closed-form expressions for its bit error probability (BEP) performance for M-ary phase shift-keying modulations are obtained, which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error. Our BEP expressions show explicitly the dependence of BEP on the mean square error of the channel estimates, which in turn depend on the channel fading model and the channel estimator used. Tight upper bounds are presented that show more clearly the dependence of the BEP on various system parameters. Simulation results using various fading models are obtained to demonstrate the validity of the analysis.

In this paper, a decode-and-forward (DF) single relay model in a Rayleigh fading environment is considered. The outage probability and ergodic rate for this model are derived. With the objective of either minimizing the outage probability or maximizing the ergodic rate, optimal and approximately optimal transmission strategies are developed through selecting appropriate transmit signaling and/or spatial power allocation. The derived transmission strategies only require the knowledge of the second-order statistics of the channels at the transmitters, which can be readily acquired in practice. Simulation results demonstrate that the optimal transmit signaling and/or spatial power allocation can offer considerable performance improvements over the equal power allocation strategy.

The generalized Marcum Q-function, Qm(a,b), can be interpreted geometrically as the probability of a 2m- dimensional, real, Gaussian random vector z2m, whose mean vector has a Frobenius norm of a, lying outside of a hyperball B2mO,bof 2m dimensions, with radius b, and centered at the origin O. Based on this geometric view, we propose some new generic exponential bounds on Qm(a, b) for the case where m is an integer. These generic exponential bounds are obtained by computing the probability of z2mlying outside of some bounding geometrical shapes whose surfaces tightly enclose, or are tightly enclosed by the surface of B2mO,bldr The bounding geometrical shapes used in the derivation consist of an arbitrarily large number of parts. As their closeness of fit with B2mO,bimproves, the generic exponential bounds obtained approach the exact value of Qm(a,b). These generic exponential bounds only involve the exponential function, and thus, are easy to handle in analytical computations. Our numerical results show that when evaluated with a few terms, these generic exponential bounds are much tighter than the existing exponential bounds in the literature for a wide range of arguments. For the case of a > b, our generic upper exponential bound is the first upper exponential bound on Qm(a,b).

We derive the correct log-likelihood differential detection metric for iterative decoding of LDPC codes transmitted with BDPSK modulation over Rayleigh fading channels. This metric does not require estimation of the amplitudes of the complex channel gains, showing that existing metrics in the literature that require estimation of amplitudes of channel gains are suboptimum. Simulation results confirm that an intentional SNR underestimation further improves BEP.

We consider about a multiple relay system operating under amplify-and-forward (AF) protocol and non-coherent modulation and demodulation. When the relays are under long-term power constraints, a near-maximum likelihood (ML) receiver and a diversity combining receiver are proposed. Both the near- ML receiver and the diversity combining receiver are expressed in simple closed forms and only rely on the second order statistics of the fading coefficients. Moreover, both of the proposed detectors outperform a non-cooperative system which only has a direct link with non-coherent ML detection in a Rayleigh fading environment. However, when the relay output is under a short-term power constraint, the ML detector derived here for the non-coherent AF relay performs the same as the non-cooperative system.

In this paper, we derive an optimal spatial power allocation strategy that maximizes the achievable rate of the decode-and-forward (DF) relay channels in a Rayleigh fading environment. Different from prior work, the derived strategy only requires the knowledge of the variances of the channels at the transmitters, which does not require frequent updates. Furthermore, we demonstrate that the optimal spatial power allocation strategy leads considerable performance improvements over the equal power allocation one.

Most of the existing works on space-time block codes (STBC) assume the channels are quasi-static, i.e., they remain invariant within one block. This assumption is not always true. In a more general case of time-selective channel, the channel matrix is no longer orthogonal. If conventional linear decoder is applied as it is in the quasi-static channel, it will introduce an irreducible error floor. In order to improve the performance, we can use zero-forcing decoder, which completely removes the interference. In this paper, we analyze the average bit error performance for BOTH conventional linear and zero-forcing decoders in the time-selective channels. The closed-form average bit error probabilities are obtained for both decoders, together with the irreducible error floor for the conventional linear decoder. Asymptotic analysis and numerical examples are also provided.

Distributed space-time coding (STC) gives rise to nonidentical channels between different transmit and receive antennas, which are not co-located. Therefore, the performance and the optimum power allocation strategy for distributed STC is different from conventional STC. In this paper, we derive the exact bit error probability for distributed space-time block codes over nonidentical Ricean channels, with an arbitrary number of relays. Based on the closed-form BEP results, we investigate the optimum power allocation strategies between different nodes and symbols.

This paper is concerned with optimum diversity receiver structure and its performance analysis of differential phase shift keying (DPSK) with differential detection over nonselective, independent, nonidentically distributed, Rayleigh fading channels. The fading process in each branch is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth, but to have distinct, asymmetric fading power spectral density characteristic. Using 8-DPSK as an example, the average bit error probability (BEP) of the optimum diversity receiver is obtained by calculating the BEP for each of the three individual bits. The BEP results derived are given in exact, explicit, closed-form expressions which show clearly the behavior of the performance as a function of various system parameters.

A linear, two-dimensional state-space model involving the instantaneous signal frequency and carrier phase is formulated. This enables Kalman filtering to be used for estimating the frequency and phase. Two Kalman filters are presented here, one based on the old observation model of Tretter (1985) and the other based on our newly proposed model by H. Fu and P.Y. Kam (2006). The Kalman filter for the old observation model requires knowledge of the signal amplitude and the noise variance, while for the new observation model, only knowledge of the noise variance is required. Their mean square estimation error performances are compared using simulations, and it is shown that the filter based on the new observation model performs better, especially at low signal-to-noise ratio. Kalman filtering also allows the incorporation of prior knowledge of the interval of distribution of the frequency to improve the estimation performance.

This paper provides a comprehensive study on the error performance of noncoherent orthogonal M-ary frequency-shift-keying (FSK) signals with various diversity combining schemes over fading channels. The diversity branches are assumed to be independent and non-identically distributed (i.n.d) Rayleigh fading. Closed-form expressions for the symbol error probability with an arbitrary diversity order and any modulation level are obtained for optimal combining (OC), equal gain combining (EGC) and log-likelihood ratio based selection combining (SC-LLR). Our analytical results show that EGC performs closely to OC over slightly unbalanced channels, whereas for highly unbalanced channels SC-LLR performs more closely to OC than EGC.

This paper is concerned with the error-performance analysis of binary and quadrature differential phase-shift keying with differential detection over the nonselective, Rayleigh fading channel with combining diversity reception. The diversity channels are independent, but have nonidentical statistics. The fading process in each channel is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. Both optimum diversity reception and suboptimum diversity reception are considered. Results available previously apply only to the case of second-order diversity, and require numerical integration for their actual evaluation. Our results are more general, in that the order of diversity is arbitrary. Moreover, the bit-error probability (BEP) result is obtained in an exact, closed-form expression which shows the behavior of the BEP as an explicit function of the one-symbol-interval fading correlation coefficient at the matched-filter output, the mean received signal-to-noise ratio per symbol per channel, and the order of diversity

The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.

We propose the generalized quadratic receivers (GQRs) for unitary space--time modulation over flat Rayleigh fading channels. The GQRs realize the performance improvement potential, known to be approximately 2--4 dB, between the quadratic receiver (QR) and the coherent receiver (CR), by performing channel estimation without the help of additional training signals that consume additional bandwidth. They are designed for various unitary space--time constellations (USTC) in which signal matrices may or may not contain explicit inherent training blocks, and may be orthogonal or nonorthogonal to one another. As the channel memory span exploited for channel estimation increases, the error probability of the GQRs reduces from that of the QR to that of the CR. The GQRs work well for both slow and fast fading channels, and the performance improvement increases as the channel fade rate decreases. For a class of USTC with the orthogonal design structure, the GQR is simplified to a form whose complexity can be less than the complexity of the QR or even that of the simplified form of the QR.

We propose the generalized quadratic receivers (GQRs) for unitary space-time modulation over flat Rayleigh fading channels. The GQRs realize the performance improvement potential, known to be approximately 2-4 dB, between the quadratic receiver (QR) and the coherent receiver (CR), by performing channel estimation without the help of additional training signals that consume additional bandwidth. They are designed for various unitary space-time constellations (USTC) in which signal matrices may or may not contain explicit inherent training blocks, and may be orthogonal or nonorthogonal to one another. As the channel memory span exploited for channel estimation increases, the error probability of the GQRs reduces from that of the QR to that of the CR. The GQRs work well for both slow and fast fading channels, and the performance improvement increases as the channel fade rate decreases. For a class of USTC with the orthogonal design structure, the GQR is simplified to a form whose complexity can be less than the complexity of the QR or even that of the simplified form of the QR.

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semiidentical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are nonidentically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit-error probabilities (BEPs) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semi-identical channel statistics degrade the error performance of differential OSTBC, compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels, the two detectors have similar performances

In this paper, we investigate the performance of differentially detected differential phase-shift keying (DPSK) modulation with postdetection maximal ratio combining, in nonselective Rayleigh fading channels with multiple asynchronous cochannel interferers. The approach is based on an analytical technique we have presented earlier in the literature. Exact bit-error probability (BEP) results for binary DPSK and quaternary DPSK are derived. More specifically, we look into the effects of symbol-timing offsets between the interfering signals and the desired signal on the error performance. Our results show that when all the interfering signals are synchronous with the desired signal, the impairment caused by the cochannel interference to the desired user is maximum. On the other hand, when all the interfering signals are half-symbol-duration-delayed with respect to the desired user, they introduce the minimum impairment. Based on these findings, upper and lower bounds on the BEP are derived in simple closed form. Our explicit BEP results also show that the error probabilities of different transmitted symbols of the desired user are affected differently by the interfering signal

We develop in this paper an Alamouti-type space- time (ST) block code that employs orthogonalM-ary FSK (MFSK) modulation. It is demonstrated that every transmitted symbol in the proposed ST-MFSK scheme can be treated as an implicit pilot symbol, and consequently the receiver can attain close to ideal coherent bit-error performance even in the absence of an explicit channel sounding signal. In addition to employing the popular block-wise static fading model for performance evaluation, we also study the implications of a more realistic fading model whereby the fading gains are allowed to vary from one subinterval to another within a ST code block. It was discovered that an iterative channel estimation strategy has to be adopted to mitigate the cross-talk associated with this refined channel model. The iterative channel estimator, in conjunction with a companion minimum mean square error detector, or a companion maximum likelihood detector, enable the receiver to obtain a bit-error performance similar to that obtained under the block-wise static fading model. In comparison with differential ST-MPSK, the two approaches yield similar error performance in a static fading environment. However, the error performance of differential ST-MPSK deteriorates rapidly as the fade rate increases whereas the performance of ST-MFSK is almost independent of the fade rate. In terms of implementation complexity and delay of the receiver, the proposed coherent ST- MFSK scheme and differential ST-MPSK are very similar, as both approaches employ digital filters of similar lengths. The findings in this paper suggest that despite its larger bandwidth requirement, ST-MFSK is a very attractive alternative space-time signaling format.

The problem of estimating the frequency and carrier phase of a single sinusoid observed in additive, white, Gaussian noise is addressed. Much of the work in the literature considers maximum likelihood (ML) estimation. However, the ML estimator given by the location of the peak of a periodogram in the frequency domain has a very high computational complexity. This paper derives an explicit structure of the ML estimator for data processing in the time domain, assuming only reasonably high signal-to- noise ratio. The result of this approximate ML estimator shows that both the phase and the magnitude of the noisy signal samples are utilized in the estimator, and the phase data alone as assumed is not a sufficient statistic. The sample-by-sample iterative processing nature of the estimator enables us to propose a novel, recursive phase-unwrapping algorithm that allows the estimator to be implemented efficiently. To facilitate the performance analysis, an improved, linearized observation model for the instantaneous signal phase that is more accurate than is proposed. This improved model explains physically why the phase data are weighted by the magnitude information in the ML estimator.

A new approach for analyzing the bit error probability (BEP) of square, multilevel, quadrature amplitude modulation (QAM) over a nonselective Rayleigh fading with imperfect channel estimation employing pilot-symbol-assisted-modulation is presented. The analytical approach here is much simpler and more powerful than that in the existing literature. The average BEP is obtained by calculating the BEP for each individual bit. The results derived are given in simple, closed-form expressions which show the behavior of the BEP as an explicit function of various system parameters, without requiring any numerical integration.

We consider the bit error performance of orthogonal space-time block codes (STBC) over independent, non- identically distributed, Rayleigh/Ricean, block fading channels with perfect channel state information. With symbol-by-symbol detection, we derive the expressions for the exact bit error probability (BEP) in both Rayleigh and Ricean fading channels. The results are applicable to any number of transmit and receive antennas for which orthogonal STBC's are defined. A simple but insightful upper bound on the BEP is also obtained. From the expressions of the BEP, we find that in Rayleigh channels, the nonidentical distributions degrade the performance. However, for Ricean case, the nonidentical distributions can have different effects on the performance.

The first-order Marcum Q-function, Q(a,b), can be interpreted geometrically as the probability that a complex, Gaussian random variable Z with real mean a, takes on values outside of a circular region CO,bof radius b centered at the origin O. Bounds can thus be easily obtained by computing the probability of Z lying outside of some geometrical shapes whose boundaries tightly enclose, or are tightly enclosed by the boundary of CO,b. In this paper, the bounding shapes are chosen to be a set of sectors or angular sectors of annuli to generate generic exponential bounds, and to be a set of rectangles to generate generic erfc-bounds. These generic exponential bounds and erfc-bounds involve an arbitrarily large number of exponential functions and erfc functions, respectively, and are shown to approach the exact value of Q(a, b) as the number of terms involved increases.

We consider a multi-antenna system using space- time trellis codes (STTC) over independent, non-identically distributed, rapid, Rayleigh fading channels with pilot-symbol- assisted-modulation channel estimation. The maximum likelihood (ML) receiver structure that incorporates the imperfect channel state information (CSI) from the pilot channel measurements, is derived. The exact pairwise error probability (PEP) and PEP bounds for the ML receiver are obtained. Using the explicit PEP bounds obtained, a new pilot power allocation scheme is proposed to improve the performance of STTC at no additional cost of bandwidth or power.

The distribution of the capacity of multiple input multiple output (MIMO) fading depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant of a Wishart matrix. Based on the distributions of the determinant and the trace of the Wishart matrix, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the capacity of MIMO Rayleigh fading channels. The new bounds on capacity CCDF provide further insights into the channel capacity, and show the effects of the system parameters on the capacity distribution explicitly. These bounds can be used to evaluate the mean capacity as well.

We propose the generalized quadratic receivers (GQRs) for orthogonal and general nonorthogonal unitary space-time constellations, respectively, over the flat Rayleigh fading channel. The GQRs exploit the performance improvement potential, known to be approximately 2-4 dB, between the noncoherent quadratic receiver (QR) and the coherent receiver (CR), without wasting bandwidth resources for additional training signals. For both the cases of orthogonal and nonorthogonal unitary space-time constellations, as the channel memory span exploited for channel estimation increases, the error probabilities of the GQRs reduce from that of the QR and approach that of the CR. The GQRs are shown to be effective for both slow and fast fading channels, and the performance improvements increase as the channel fade rate decreases.

In this paper, we present transmit antenna selection (TAS) for wireless communication systems with space-time block codes (STBC). In coherent STBC systems, channel estimation is necessary at the receiver for decoding. In the proposed scheme, the transmitter selects the one or several antennas with best estimated channel gain for STBC transmission. Exact closed-form bit-error probability expression is derived for two specific scenarios. The TAS systems achieve full diversity provided by the total number of transmit and receive antennas.

We study the performance of differential orthogonal space-time block codes over independent and semi-identically distributed Rayleigh fading channels. In this semi-identically distributed fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are non-identically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit error probabilities (BEP) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas and any number of transmit antennas for which orthogonal space-time block codes exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. A Chernoff bound on the BEP of optimal detection for any number of transmit antennas is also derived.

The geometric interpretation of the first-order Marcum Q-function, Q(a, b), has been shown as the probability that a complex, Gaussian random variable Z with real, nonzero mean a takes on values outside of a circular region CO,bof radius b centered at the origin O. Based on this interpretation, many new, simple, tight, upper/lower exponential bounds on Q(a, b) are easily obtained by computing the probability of Z lying outside of some simple geometrical shapes, such as circular regions, semicircular regions, sectors, and angular sectors of annuli, whose boundaries tightly enclose, or are tightly enclosed by the boundary of CO,b. The new bounds presented here only involve two exponential functions, and the best of them are in most cases much tighter than the best existing exponential bounds. In addition to these bounds, more new bounds can be obtained by using similar methods. Even some bounds in the literature can also be obtained via this geometric approach

The generalized Marcum Q-function, Qm(a,b), is here explained geometrically as the probability of a 2m-dimensional, real, Gaussian random vector, whose mean vector has a Frobenius norm of a, lying outside a hypersphere of 2m dimensions, with radius b, and centered at the origin. Based on this new geometric interpretation, a new closed-form representation Qm(a,b) is derived for the case where m is an odd multiple of 0.5. This representation involves only the exponential and the erfc functions, and thus is easy to handle, both numerically and analytically. For the case where m is an even multiple of 0.5, Qm+0.5(a,b) and Qm-0.5(a,b), which can be evaluated using our new representation mentioned above, are shown to be tight upper and lower bounds on Qm(a,b), respectively. They are shown in most cases to be much tighter than the existing bounds in the literature, and are valid for the entire ranges of a and b concerned. Their average is also a good approximation to Qm(a,b)

Independent, frequency nonselective, fast, Rayleigh diversity fading channels with nonidentical branch statistics are assumed. The optimum combining receiver structure for differential phase shift keying (DPSK) with differential detection is derived based on the maximum a posteriori probability criterion. Both explicit, closed-form bit error probability (BEP) expressions for 2-4-and 8-DPSK and simple Chernoff upper bounds to these BEP's are obtained for arbitrary order of diversity.

A geometric interpretation of the first-order Marcum Q-function, Q(a, b), is introduced as the probability that a complex, Gaussian random variable with real, nonzero mean a, takes on values outside of a circular region Cbof radius b centered at the origin. This interpretation engenders a fruitful approach for deriving new representations and tight, upper/lower erfc-bounds on Q(a, b). The new representations involve finite-range integrals that facilitate analytical and numerical computations, and are simpler than similar ones in the literature. The new, simple erfcbounds are easily obtained by using simple geometrical shapes that tightly enclose, or are tightly enclosed by the circle Cb. They involve only a few terms of erfc and exponential functions, and are close to, or even tighter than the existing bounds that involve the modified Bessel function.

In this paper, we provide a new, practical design criterion for space-time trellis codes over rapid fading channels with imperfect channel state information (CSI) at the receiver. This criterion exploits the statistical information of the channel estimates in code design. The minimum error performance can be achieved by optimally distributing the symbol-wise Euclidean distance based on the variances of the channel estimates. New codes designed with imperfect CSI are obtained using an iterative algorithm with reduced complexity. Simulation results show that in the presence of channel estimation errors, the codes designed based on our criterion assuming imperfect CSI have improved bit error probability performance compared with existing codes that were designed under the perfect CSI assumption. It is also shown that the effect of channel estimation on code design increases with the channel fade rate and the number of transmit antennas

Unitary space-time modulation is a transmit diversity technique for the nonselective Rayleigh fading channel. It was proposed for noncoherent detection without any channel state information (CSI) at the receiver. However, with perfect CSI at the receiver, the performance improvement is known to be approximately 2-4 dB. In order to exploit this improvement potential and keep the merit of not wasting bandwidth resources for additional training signals, we propose a generalized quadratic receiver (GQR) for a class of unitary space-time constellations with orthogonal design over the Rayleigh fading channel. As the channel memory span exploited by this GQR for channel estimation increases, the error probability of the GQR reduces from that of the conventional quadratic receiver to that of the coherent receiver. This performance improvement increases as the channel fade rate decreases. In addition, the complexity of the simplified GQR can be less than that of the noncoherent receiver.

Explicit closed-form expressions of the bit error probabilities are obtained for space-time block codes based on generalized orthogonal designs with differential encoding and differential detection utilizing 2/sup b/-ary phase shift keying mapping. The frequency non-selective, block-wise constant Rayleigh fading channel is considered here. The results are applicable to any arbitrary Doppler spectrum and any number of transmit and receive antennas, where the number of transmit antennas is dictated by the available coding schemes.

This paper is concerned with the error performance analysis of binary differential phase shift keying with differential detection over the nonselective, Rayleigh fading channel with combining diversity reception. Space antenna diversity reception is assumed. The diversity branches are independent, but have nonidentically distributed statistics. The fading process in each branch is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. Both optimum diversity reception and suboptimum diversity reception are considered. Results available previously apply only to the case of first and second-order diversity. Our results are more general in that the order of diversity is arbitrary. Moreover, the bit error probability (BEP) result is obtained in an exact, closed-form expression which shows the behavior of the BEP as an explicit function of the one-bit-interval fading correlation coefficient at the matched filter output, the mean signal-to-noise ratio per bit per branch and the order of diversity. A simple, more easily computable Chernoff bound to the BEP of the optimum diversity detector is also derived.

We investigate in this paper an Alamouti-type space-time block code (STBC) using orthogonal M-ary frequency-shift-keying (MFSK). The signal is coherently detected using the channel estimates derived from the unmodulated (or implicit pilot) component of the orthogonal signal. An exact bit error probability expression for BFSK and tight union bound for MFSK are derived for the proposed coherent ST-FSK receiver. It is observed that the receiver can maintain close to ideal coherent performance even at very fast fading rates. In comparison with differential STBC, the two approaches yield similar error performance in a static fading environment. However, the error performance of differential STBC deteriorates rapidly as the fade rate increases. In terms of implementation complexity and delay, the proposed coherent ST-FSK receiver is similar to differential STBC, as both approaches employ digital filters of similar lengths. The findings in this paper suggest that despite its larger bandwidth requirement, ST-FSK is a very attractive alternative space-time signaling format.

Explicit closed-form expressions of the bit-error probabilities are obtained for space-time block codes based on generalized orthogonal designs with differential encoding and differential detection using 2/sup b/-ary phase-shift keying mapping. The frequency-nonselective, block-wise constant Rayleigh fading channel is considered here. The results are applicable to any number of transmit and receive antennas, where the number of transmit antennas is dictated by the available coding schemes.

This paper is concerned with the error performance analysis of binary differential phase shift keying (DPSK) with differential detection over the nonselective Rayleigh-fading channel with selection diversity reception and with an additive, correlated, Gaussian interference process in each diversity channel. The fading process is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The selection schemes investigated are: 1) the selection combining (SC) scheme based on signal-to-noise power ratio (SNR); 2) the SC scheme based on signal-plus-noise (S+N); and 3) the SC scheme based on maximum output (MO). New, exact, closed-form bit-error probability (BEP) expressions are derived, and a performance comparison among the three SC schemes and combining diversity reception is given. The results obtained reduce to previously known results when the correlated interference process is absent, and when the fading process does not fluctuate over the duration of several symbol intervals. The results indicate that the performance of each scheme depends on the tradeoff between the number of diversity branches, the SNR, the interference level, and the correlation of the interference process. However, the SC-(S+N) scheme generally performs worse than the SC-SNR scheme, the SC-MO scheme and combining diversity reception scheme. The findings presented here are not only of fundamental theoretical value, but are also of practical interest to the designers of future mobile communication systems.

A coherent symbol-by-symbol (SBS) diversity receiver for m-ary phase-shift keying (MPSK) and differentially encoded MPSK (MDPSK) signals transmitted over a nonselective Rayleigh fading channel is presented. It incorporates a new adaptive filter for channel estimation that does not require any prior knowledge of the fading process model. It estimates the fading gains through decision-feedback and recursive least squares adaptation of the filter coefficients. A novel forgetting-factor adaptation algorithm that enables the filter to react quickly to randomly changing fading statistics caused by shadowing and acceleration/deceleration is introduced. Simulations show that the receiver performs better than that of Adachi's ( IEEE Trans. Veh. Technol. vol. 47 p. 909, 1998), either without shadowing or under slow lognormal shadowing.

Orthogonal space-time block codes utilize transmit diversity and allow the receiver to have a simple maximum-likelihood decoder. Normally, channel state information is not readily available at the receiver. Hence, channel estimation is necessary for coherent detection. We present analytical bit error rate (BER) expressions as well as the tight Chernoff bound for orthogonal space-time block coded systems employing M-PSK modulation. The results show directly the BER dependence on the transmit diversity and the mean square error of the channel estimator. Simulation results show the accuracy of our BER predictions.

An adaptive version of the optimum, decision-aided, symbol-by-symbol receiver obtained in our previous works for M-ary phase shift keying over the Gaussian channel with unknown carrier phase characteristics is considered. It uses a first-order adaptive filter for carrier reference tracking, and the filter gain is adapted on-line based on the observed signal samples using a least-mean-square-error criterion. The phase tracking performance of the filter in the steady-state tracking mode is analyzed using a linearized model. The phase tracking error variance is minimized due to the risk function used in designing the filter gain adaptation algorithm. The bit-error probability for quadrature phase shift-keying is obtained, both analytically and via computer simulations.

The bit-error probabilities (BEPs) of matched-filtered differentially detected two differential phase-shift keying (2DPSK) and 4DPSK over the nonselective Rician-fading channel are studied using the upper bound in Kam (1994). The bound coincides with the exact error probability result in the binary case and provides very accurate estimates of the BEP in the quadriphase case, especially for high signal-to-noise ratio (SNR) and small K-factor. The bound provides a simple analytical handle for studying the behavior of the error probability as a function of the Doppler spectrum, the Doppler bandwidth, and the K-factor. A new result is obtained for the irreducible error-rate floor. The results are useful for the design of digital mobile radio communication systems.

A new analytical approach is presented for deriving the bit error probability results for 2 and 4DPSK with differential detection over the nonselective Rayleigh fading channel with diversity reception and with an additional additive, correlated, Gaussian interference process in each diversity channel. The approach differs from that in a previous paper, and is based on a well-known result in the literature. The results are new, and reduce to known results when the correlated interference is absent. They show that the correlated interference behaves like an additional component of the information-bearing signal, and affects the error probabilities of the various transmitted symbols differently, irrespective of its statistical distribution. Its Gaussian statistical distribution is essential only for the analysis of the bit error probability.

An efficient algorithm is presented for the estimation of continuous phase modulation (CPM) sequences over the Gaussian channel with unknown carrier phase. It operates on the excess phase trellis like the Viterbi algorithm, except that it is not a maximum-likelihood (ML) estimator. Its decision metric for survivor selection at each node is chosen so that it achieves the node error event probability of coherent ML estimation in the limit as the carrier phase remains constant over a long interval, so that the observation interval for forming the metric can be made large. It is shown for the case of minimum-shift-keying (MSK) that the bit-error probability (BEP) of perfectly coherent ML estimation is attained.

A Viterbi-type algorithm for the efficient estimation of a convolutionally/trellis coded, or uncoded M-PSK sequence over the Gaussian channel with unknown carrier phase is presented. It performs coherent detection of M-PSK sequences with no explicit recovery of coherent references. The metric computations involve only linear operations. Theoretical and simulated performance results are presented for various carrier phase processes. The algorithm is called the suboptimum ML estimator (SMLE). Its BER in the presence of a time invariant carrier phase is obtained analytically. The simulation results for the BER with time-invariant as well as time-varying carrier phase processes allow a comparison of the performance of the SMLE with other sequence estimation algorithms, and enable the applicability of the SMLE to burst mode TDMA communications to be ascertained.>

This paper presents a fundamental approach for deriving the bit error probability of BDPSK and QDPSK over the nonselective Rayleigh fading channel for a receiver with an arbitrary IF filter, and for a fading process with an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small Doppler bandwidth compared to the symbol rate. This allows the error probability to be studied in the presence of varying degrees of ISI due to the bandlimitation of the received signal by the IF filter, and in the presence of fading fluctuations of various rates. The analytical approach presented is simple, and yet powerful in that it can handle the case of diversity reception. This is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval. The bit error probability results apply to both conventional BDPSK and QDPSK, as well as /spl pi//2-2DPSK and /spl pi//4-4DPSK, and allow the irreducible bit error probability as well as the SNR at which this irreducible value sets in to be studied as a function of the Doppler bandwidth and IF filter bandwidth. The computed results are applicable to the design of digital cellular mobile communication systems.

The orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated (pilot tone) component which can be used for channel measurement. Starting from this point of view, the quadratic receiver for orthogonal signals over the Gaussian channel with unknown phase/fading has been shown to be equivalent to a detector-estimator receiver. The estimator makes an optimum estimate of the unknown complex channel gain based on the channel measurement provided by the unmodulated component of the received signal. This channel estimate then forms a (partially) coherent reference for the detector in detecting the data carried by the antipodal signaling component of the received signal. This paper exploits this detector-estimator structure of the quadratic receiver, and generalizes it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of signals received over all the signaling intervals or a subset of these intervals. The generalized quadratic receiver is just as simple to implement as the conventional quadratic receiver, and theoretical and simulation results show that it can achieve substantial performance gains over the conventional receiver. A theory is presented to show that the generalized quadratic receiver is an implementable approximation to the optimum symbol-by-symbol receiver for uncoded orthogonal signals over the Gaussian channel with unknown phase/fading. The theory shows that the structure provides a unified and systematic approach to the design of coherent symbol-by-symbol receivers, and shows that the conventional carrier-loop-type receivers are ad hoc.>

Consider the classic problem of evaluating the probability that one Rician random variable exceeds another, possibly correlated, Rician random variable. This probability is given by Stein (1964) in terms of the Marcum's Q-function, which requires numerical integration on the computer for its evaluation. To facilitate application in many digital communication problems, we derive here tight upper and lower bounds on this probability. The bounds are motivated by a classic result in communication theory, namely, the error probability performance of binary orthogonal signaling over the Gaussian channel with unknown carrier phase. Various applications of the bounds are reported, including the evaluation of the bit error probabilities of MDPSK and MPSK with differential detection and generalized differential detection, respectively. The bounds prove to be tight in all cases. Further applications will be reported in the future.>

A theory of optimum receiver design for symbol-by-symbol detection of an uncoded digital data sequence received over the Gaussian channel with unknown carrier phase is presented. Linear suppressed-carrier modulation is assumed. The work here aims at laying a conceptual foundation for optimum symbol-by-symbol detection, and rectifies existing approaches to the problem. The optimum receiver structure is obtained explicitly for an arbitrary carrier phase model, but its computational requirements are too heavy in general for any practical implementation. In one important special case, namely, the case in which the carrier phase can be treated as a constant over some K+1 symbol intervals, the optimum receiver can be approximated by a readily implementable decision-feedback structure at high SNR. Simulated error performance results are presented for this latter receiver for PSK modulations, with various carrier phase models. Since a decision-feedback receiver can encounter a "runaway", a variation of this receiver is developed which uses feedforward of tentative decisions concerning future symbols. This modified receiver does not have any "runaway" problem, and has been shown to yield good error performance via simulations.>

A simple tight upper bound on the BEP of 2DPSK over the AWGN channel with phase noise in the received signal is obtained. The phase is modeled as a Gaussian random process which is slowly varying compared to the bit rate so that a piecewise-constant approximation can be made. The bound is verified by computer simulations, and it provides good estimates of the error probability. It shows that for high SNR the error probability decreases as the reciprocal of the square-root of the SNR. The results are applicable in particular to heterodyne optical communications.>

Orthogonal signaling over the slow nonselective Rician fading channel is considered. Previous receiver designs have all assumed the amplitude and phase of the specular component of the received carrier to be known completely, but this assumption is entirely unrealistic. The problem is reformulated with unknown random amplitude and phase of the specular component. The optimum maximum likelihood receiver is obtained for equally likely equal-energy orthogonal signals and is shown to be identical to the quadratic receiver for the purely unknown phase channel and the pure Rayleigh fading channel. The error probability performance is analyzed for a fixed known specular amplitude. When specialized to the binary signaling case this error probability result exhibits a performance that is very close to and asymptotically approaches that of the conventional coherent-specular-component case for high SNR. Thus, knowledge of the specular component phase is not important to the optimum receiver.>

Approximate results for the bit error probability (BEP) of binary phase shift keying (BPSK) in the presence of a noisy carrier phase reference are presented. The results show correctly the behavior or the BEP as a function of SNR. The accuracy of the approximations is verified by simulations and numerical integration of the BEP formulas. The results are compared with existing bounds.>

The authors consider minimum error probability detection of a data sequence transmitted using linear-suppressed carrier modulations, specifically phase-shift keying (PSK), over the Gaussian channel with slow nonselective Rayleigh fading. Complete channel interleaving/deinterleaving and diversity reception are assumed. The problem is considered with application to Viterbi decoding in particular. It is first shown that the two presently available receivers, namely, the conventional maximum likelihood (ML) receiver and the simultaneous estimation receiver, do not perform adequately for this problem. A two-stage receiver is proposed in which the unknown channel fading gains are estimated in the first stage prior to data sequence estimation in the second stage. This receiver is shown to perform adequately, and leads to an efficient receiver/decoder for Viterbi decoding of convolutionally trellis-coded sequences. The issue of optimum estimation of channel fading gains is clarified. The bit error probability of the receiver/decoder is analyzed, and numerical performance results are presented.>

Based on the criterion of minimum symbol error probability, an analysis is made of symbol-by-symbol detection of a sequence of digital data transmitted using linear suppressed-carrier modulation over L independent diversity channels with AWGN (additive white Gaussian noise) and slow nonselective Rayleigh fading. The optimal receiver is derived, but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length. Suboptimal decision-feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers. The exact bit error probabilities of these suboptimal receivers are obtained. Tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal-to-noise ratio and order of diversity. A main conclusion of this work is that optimal data detection on a fading channel should be performed using MMSE (minimum mean squared error) estimates of the quadrature amplitudes of the channel fading processes as a coherent reference.>

Data transmission using M-ary differential phase shift keying (MDPSK) over the nonselective Rayleigh fading channel with diversity reception is considered. While previous studies on error probability mostly assume no fading fluctuation, the author considers, exclusively, the case in which the fading process fluctuates from one symbol interval to the next. Exact bit error probability results for 2, 4, and 8 DPSK as well as tight upper bounds are derived. Some applications of the results are discussed.>

ML estimation of carrier phase for coherently orthogonal continuous-phase frequency-shift-keying (COCPFSK) signals is considered. Although the estimator, in general is nonimplementable, its high and low signal-to-noise-ratio approximations both lead to linear readily implementable receiver structures. The high SNR approximation yields a DA receiver, whereas the low SNR approximation yields an NDA receiver. The performance of both receivers in term of bit error probability is analyzed. The existence of an unmodulated component in the sufficient statistical representation of a COCPFSK signal is pointed out, and it is shown how this component enters directly into maximum-like carrier recovery. This leads to interpretation of the NDA receiver as a generalization of the conventional matched-filter envelope-detector receiver. The insights gained here are useful to the problem of ML carrier recovery for Viterbi decoding of continuous phase modulation signals.>

The problem of binary orthogonal signaling over a Gaussian noise channel with unknown phase/fading is considered. By viewing the problem in a rotated coordinate system, the orthogonal signal structure is considered as the combination of an antipodal signal set and a pilot tone for channel measurement. For data detection the optimum matched-filter envelope-detector is shown to be identical to a novel detector-estimator receiver in which the detector performs partially coherent detection, using an absolute coherent reference generated by the estimator from the channel measurement provided by the pilot-tone component of the orthogonal signal structure. This detector-estimator interpretation shows that it is incorrect to refer to the optimum receiver as a noncoherent receiver. It also leads to the development of new approaches for analyzing the error probability of the receiver. An exponential Chernoff upper bound is obtained for the Rician channel.>

The authors consider maximum-likelihood (ML) detection of convolutionally coded data over the AWGN channel with unknown carrier phase. A receiver is developed for simultaneous ML data decoding and suboptimal ML carrier-phase estimation. The receiver is readily implementable and, for a circular signal constellation, it is totally linear. Computer simulations using two different models of the time-varying carrier phase indicate that the receiver provides good bit error probability performance.>

We consider here a new approach to PSK signal detection over a slow nonselective Rayleigh fading channel which does not require a carrier recovery loop. The receiver achieves coherent demodulation by making use of estimates of the quadrature amplitudes of the received PSK signals in its likelihood ratio test. The receiver is assumed to have a memory containing information on the past received signals which enables it to generate the estimates. The error rate of the receiver can be evaluated analytically and computer simulation results are presented to verify the predicted performance.