Amplitude phase shift keying (APSK) modulation signals are of low peak average power ratio and are generated to fight against the potentially non-linear high power amplifier in satellite communication. The benchmark maximum log-likelihood maximum a posteriori probability (max-log-MAP) detector requires to compute the distance squared between the received signal and each APSK constellation point for the extrinsic bit log-likelihood ratio (LLR) information. To overcome this major challenge of high detection complexity, we propose in this paper to partition and order all the APSK constellation points into rings of ordered phase shift keying (PSK) constellation points. We also propose to apply and tailor the iterative search strategies, originally used to detect multiple input multiple output (MIMO) quadrature amplitude modulation (QAM) signals, to search over the ordered irregular PSK constellation points. Compared with previously reported APSK detectors, our proposed detector achieves exactly the max-log-MAP detection, requires very low computational complexity, and is able to detect APSK signals modulated from the APSK constellation with arbitrary number of constellation points, arbitrary phase offsets, and arbitrary ring radii.

Full-duplex (FD) technology holds the potential for twice the spectral efficiency compared to half-duplex (HD) communication. However, simultaneous transmission and reception in the same frequency band may be subject to severe self-interference (SI). Therefore, mitigating the impact of SI becomes a key issue in realizing FD wireless communications. In this paper, we propose a hybrid beamforming design that effectively suppresses SI while maintaining superior communication quality for FD millimeter wave (mmWave) communication systems. Simulation results demonstrate that the designed hybrid transceivers exhibit exceptional resistance to the SI, leading to a significant improvement in spectral efficiency compared to conventional HD communications.

We present an enhanced informed dynamic scheduling (IDS) strategy to avoid propagations of unreliable messages in the residual belief-propagation (RBP) algorithm for decoding low-density parity-check (LDPC) codes. To reduce the resource needed for updating the degree-one variable nodes (VNs) in an RBP-based algorithm for decoding 5G New Radio (NR) LDPC codes, we further introduce a process consisting of several simple procedures for managing the resource consumption. Simulation results demonstrate that our RBP algorithm based on the proposed IDS strategy outperforms existing RBP-based algorithms at the early decoding iterations. By using our degree-one VN resource managing approach, the performance of both the proposed and the existing decoders is significantly improved in decoding the 5G NR codes.

Belief propagation (BP) decoding of low-density parity-check (LDPC) codes with various dynamic decoding schedules have been proposed to improve the efficiency of the conventional flooding schedule. As the ultimate goal of an ideal LDPC code decoder is to have correct bit decisions, a dynamic decoding schedule should be variable node (VN)-centric and be able to find the VNs with probable incorrect decisions and having a good chance to be corrected if chosen for update. We propose a novel and effective metric called conditional innovation (CI) which serves this design goal well. To make the most of dynamic scheduling which produces high-reliability bit decisions, we limit our search for the candidate VNs to those related to the latest updated nodes only. Based on the CI metric and the new search guideline separately or in combination, we develop several highly efficient decoding schedules. To reduce decoding latency, we introduce multi-edge updating versions which offer extra latency-performance tradeoffs. Numerical results show that both single-edge and multi-edge algorithms provide better decoding performance against most dynamic schedules and the CI-based algorithms are particularly impressive at the first few decoding iterations.

For a millimeter wave (mmWave) system consisting of a basestation (BS) and a mobile user-equipment (UE), the problem of signal-and-data detection is investigated, and a low complexity ML-MMSE receiver for mmWave beamforming, beamtracking, and data-symbols detection is proposed. Specifically, with a (practical) hybrid beamforming transceiver architecture at both the BS and UE, a multistage angle-of-arrival (AoA) estimation based beamtraining algorithm that provides fast acquisition of the best beam pairs for the BS-UE link is developed. In addition, a novel joint beamtracking and data-symbols detection algorithm, equipped with an adaptive equalizer, is also developed. The algorithm can simultaneously track the best receiving beams, and produce the data estimates that are easy to extract soft bit information for soft decoding; also, it can tackle the dynamic changes of the baseband effective channel. Analytical and simulation results show that the proposed receiver performs well over a broad range of SNR-it can rapidly acquire the most dominant AoAs for beamforming and constantly track the best moving beams due to UE's mobility or device rotation-and in particular, it achieves near-optimal spectral efficiency for a mobile UE with a single RF chain or very few RF chains.

In this paper, we establish a connection between length-compatible (LC) punctured/shortened polar codes and compound polar codes. Regarding an LC code as a compound code to be transmitted over two different channels, we propose four channel-coded bit mapping rules which generalize some known LC code constructing methods. Performance of the punctured and shortened codes constructed by applying different mapping rules can thus be predicted checking if the Bhattacharyya bound is minimized.

We consider a multi-carrier CDMA system based on carrier-interferometry (CI) sequences. The CI sequences are selected because of their outstanding cross-correlation property and are used to spread multi-stream data over transform (frequency) domain. The system is overloaded by allowing an user to transmit K data streams on N <; K orthogonal subcarriers or time-frequency units. This paper investigates the problem of multi-stream detection for such an overloaded system. Several suboptimal receiver structures are studied and their performance in uncoded and coded systems is investigated. We discuss the effects and usages of the channel state information on the performance of various receivers.

In this paper, we present a new type of Spatial Multiplexing (SMX) schemes based on the multiple signal constellation concept, which was recently introduced in the context of Spatial Modulation (SM) by the present authors. The proposed technique, which we refer to as Enhanced SMX or E-SMX, conveys information not only by the transmitted symbols, but also by the antenna and constellation combinations used. In addition to the primary constellation, these schemes make use of one or more specifically-designed secondary constellations, obtained through geometric interpolation in the signal constellation plane. We present the general concept and describe specific schemes for different numbers of transmit antennas and using 16QAM as primary modulation. Our analysis and the simulation results indicate that the proposed schemes provide a significant performance gain over conventional SMX.

In this paper, we present three new signal designs for enhanced spatial modulation (ESM), which was recently introduced by the present authors. The basic idea of ESM is to convey information bits not only by the index(es) of the active transmit antenna(s) as in conventional SM, but also by the types of the signal constellations used. The original ESM schemes were designed with reference to single-stream SM and involved one or more secondary modulations in addition to the primary modulation. Compared with single-stream SM, they provided either higher throughput or improved signal-to-noise ratio (SNR). In this paper, we focus on multi-stream SM (MSM) and present three new ESM designs leading to increasing SNR gains when they are operated at the same spectral efficiency. The secondary signal constellations used in the first two designs are derived through a single geometric interpolation step in the signal constellation plane, while the third design also makes use of additional constellations derived through a second interpolation step. The new ESM signal designs are described for MIMO systems with four transmit antennas out of which two are active, but we also briefly present extensions to higher numbers of antennas. Theoretical analysis and simulation results indicate that the proposed designs provide a significant SNR gain over MSM.

In this paper, we introduce a new signal design for the Enhanced Spatial Modulation (ESM) concept, which was recently proposed by the present authors. The basic idea of ESM is to convey information bits not only by the indexes of the active transmit antennas, but also by the types of the multiple constellations used. Design of the original ESM schemes involved one or more secondary modulations, which were derived using a single step of geometric interpolation in the signal constellation plane. In the new design, we go one step further in the interpolation process and derive additional modulations leading to a significant increase of the number of active antenna and modulation combinations used. A design example is given for 10 bits per channel use (bpcu) transmission using four transmit antennas two of which are active at a time. The new design is compared to conventional multi-stream spatial modulation (MSM) and to our previously proposed ESM scheme. The analysis and the simulation results confirm a signal-to-noise ratio (SNR) gain of 2.2 dB over MSM and 0.4 dB over ESM when the three schemes are operated at the same spectral efficiency.

Bit-flipping (BF) decoding of low-density parity-check codes is of low complexity but gives inferior performance in general. To improve performance and provide new BF decoder options for complexity-performance tradeoffs, we propose new designs for the flipping function (FF), the flipped bit selection (FBS) rule and the checksum weight updating schedule. The new FF adjusts the checksum weights in every iteration while our FBS rules take more information into account. These two modifications represent efforts to track more closely the evolutions of both check and variable nodes' reliabilities. Two selective update schedules are proposed to offer more performance and complexity tradeoffs. The combinations of the new FBS rule and known FFs result in new BF decoders with improved performance and a modest complexity increase. On the other hand, combining the new FF and FBS rule gives a new decoder with performance comparable to that of the normalized min-sum algorithm while if we use a much simpler FBS rule instead, the decoder suffers little performance loss with reduced complexity. We also present a simple decision-theoretical argument to justify the new checksum weight formula and a time-expanded factor graph model to explain the proposed selective weight-updating schedules.

In this paper, we introduce a new spatial modulation (SM) technique using one or two active antennas and multiple signal constellations. The proposed technique, which we refer to as Enhanced SM or ESM, conveys information bits not only by the index(es) of the active antenna(s), but also by the constellations transmitted from each of them. The main feature of ESM is that it uses a primary signal constellation during the single active antenna periods and some other secondary constellations during the periods with two active transmit antennas. The secondary signal constellations are derived from the primary constellation by means of geometric interpolation in the signal space. We give design examples using two and four transmit antennas and QPSK, 16QAM, and 64QAM as primary modulations. The proposed technique is compared to conventional SM as well as to spatial multiplexing (SMX), and the results indicate that in most cases, ESM provides a substantial performance gain over conventional SM and SMX while reducing the maximum-likelihood (ML) decoder complexity.

Interference cancellation is a key design concern for next-generation communication systems. One practical approach is the so-called interference rejection combining (IRC) scheme which treat interference as a stationary Gaussian process to simplify interference suppression design. However, this stationary assumption does not hold in practice; in particular, the statistics of the pilot and the data parts from an interfering eNodeB (eNB) are quite different. This considerably impacts the possible improvements of interference-aware receivers. In this paper, novel interference suppression schemes are proposed, which handle separately the interfering pilot and data signals. The proposed schemes take into account channel estimation errors and also the errors in covariance estimation of interference plus noise.

Co-channel interference suppression is a key design concern for next-generation communication systems. It is particularly challenging in the presence of frequency-selective fading as the covariance matrices of the interference plus noise vary across subcarriers. The moving average technique is an effective scheme for estimating the frequency- selective covariance matrices. But the problem of choosing the optimal window size is far from trivial. In this work, we propose a window selection scheme based on the mean square error (MSE) of the covariance estimate. It only requires information of the signalto-noise ratio (SNR) and signal-to-interference ratio (SIR) and is robust against variations of the interfering channel's power delay profile. Moreover, the results can be applied to time-varying channels by simply replacing the frequency correlation function by the time correlation function.

Interference rejection combining (IRC) is an effective technique to suppress the spatial interference in multiple input multiple-output (MIMO) systems. In general, more receive antennas result in better interference-suppression capability. However, as the number of receive antennas increases, the receiver becomes more complex and loses its scalability. Therefore, an increased attention was turned by industry to find efficient ways to enable the use of more receive antennas, e.g., scaling the number of receive antennas to increase interference rejection capability. In this paper, a baseband preprocessing scheme is proposed by maximizing the signal-to- interference-plus noise ratio (SINR). It involves minimum modification of the existing receiver structure when additional receive antennas become available. Substantial improvements are provided by exploiting the channel estimates or the SINR feedback from the original receiver. The main idea is to generate a new channel matrix for the original receiver such that the interference can be suppressed after the proposed processing. Since the proposed scheme does not rely on the receiver structure, it can be easily generalized to different kind of receivers.

Interference cancellation is a key design concern for next-generation communication systems. One practical approach is the interference rejection combining (IRC) scheme, which is already being considered as the base receiver for next-generation 3GPP specifications. IRC treats interference as a stationary Gaussian process to facilitate simple interference suppression. However, this stationary assumption does not hold in practice; for example, the variances of the pilot signal and of the data signal from the interfering base station (eNB) are quite different. This considerably impacts the possible improvements of an interference-aware receiver. In this paper, novel interference suppression schemes are proposed, which handle separately the interfering pilot and the interfering data signals. The proposed schemes take into account channel estimation errors and the errors in estimating the covariance of interference plus noise. The performance of the proposed schemes is validated by using realistic channel models and asynchronous scenarios for MIMO-OFDM systems.

In this paper, we propose three classes of systematic approaches for constructing zero-correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on the family size and the ZCZ width for a given sequence period. Our approaches can produce various binary and polyphase ZCZ families with desired parameters and alphabet size. They also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size. Furthermore, the constructed families have nested-like property that can be either decomposed or combined to constitute smaller or larger ZCZ sequence sets. We make detailed comparisons with related works and present some extended properties. For each approach, we provide examples to numerically illustrate the proposed construction procedure.

Energy-efficient scheduling problem in wireless communication system is investigated in this paper. We propose two near-optimal schedulers which have simple structures for the general hard delay constraint scenario. Both single-user and multiuser cases are considered. The first scheduler invokes Gaussian approximation while the second one is inspired by the inverse water-filling (IWF) approach. The scheduling policies consist of a channel-awareness term and a delay-awareness term. Numerical results show that the proposed policies achieve near optimal performance when the total required transmit bits, R, is large. For the multiuser scenario, our scheduling strategy consists of an initial resource (number of time slots) allocation and a slot-by-slot user selection and bit loading algorithm. The former depends on the rate requirement and a priori knowledge of user-dependent channel statistic while the latter use an order statistic based approach designed to minimize the expected total energy consumption.

This paper considers the problem of resource allocation for weighted sum rate maximization in a decode-and-forward (DF) based multi-hop MIMO-OFDMA systems. The optimal solution of joint subcarrier assignment (user and relay selections) and power allocation is obtained by solving a dual problem. We derive the necessary conditions for the optimal power allocation and propose a suboptimal algorithm with a closed-form based general power allocation solution. This suboptimal algorithm, as numerical results verify that, suffers from minor performance loss against that achievable by the optimal solution when SNR is high. It is observed that the corresponding closed-form power allocation yields 8% performance gain when compared with the equal power allocation.

We consider the problem of power allocation for capacity maximization in a decode-and-forward (DF) based multi-Hop MIMO-OFDM systems. We derive the necessary conditions for the optimal solution and propose an optimal power allocation algorithm for a 3-hop system, which can be easily extended to arbitrary number of relays. A suboptimal power allocation algorithm for a 3-hop system is also proposed. The suboptimal solution assumes equal power allocation over frequency domain and uses closed-form expressions for optimal power distribution over all hops for each subcarrier. Simulation results verify that, given the same transmit power, edge users are better served by a multi-hop relay scheme than by direct-link based scheme. Moreover, the proposed suboptimal power allocation yields an excellent sum rate performance which is close to the optimal performance.

We propose an optimal and a suboptimal resource allocation algorithms for sum rate maximization in an MISO-OFDMA based cognitive radio network subject to a primary user outage constraint. By converting the outage constraint into user and subcarrier dependent peak power constraints, we obtain the optimal joint subcarrier assignment and power allocation solution by applying Lagrange dual-decomposition method. We also propose a low-complexity, fast-convergent suboptimal algorithm which uses an opportunistic channel gain-to-noise ratio based subcarrier assignment and an efficient constrained power allocation scheme. The optimality of the latter power allocation scheme is verified as well. Numerical results demonstrate that, compared with the optimal solution, the suboptimal scheme suffers only minor performance loss. We also shown that the use of more transmit antennas by a cognitive base station not only yields better spectrum efficiency but also lessens the outage-induced peak power constraint.

In this paper, we present a joint antenna beamforming and power allocation technique to maximize the multiuser sum rate in an underlying microcellular system which reuses the same spectrum of a macrocellular system. One challenge in this kind of hierarchical cognitive radio (HCR) systems is to manage the interference between the macrocell and the microcell. The key contribution of this paper is to develop an optimization technique for antenna beamforming that can maximize the achievable sum rate of the underlying cognitive radio (CR) microcellular system and control the interference between the macrocell and the microcell with a satisfaction level. The proposed technique optimizes the sum rate performance by maximizing its lower bound and transfers the original non-convex problem into a convex optimization problem by introducing auxiliary variables to confine the intra-user interference power among the secondary system. Next, an iterative sum rate maximization (ISM) algorithm is developed to find the beamforming weights and the allocated power for each secondary user to simultaneously maximize system sum rate, coverage, and concurrent multiuser transmission probability in the HCR system. The developed joint design methodology provides valuable insights into the design of an optimal HCR system for various numbers of users as well as cell coverage, and can quantitatively optimize the performance tradeoffs in the hierarchical multiuser CR systems for current and future wireless communication applications.

This paper presents a general reduced-rank channel model and a corresponding low-complexity estimation scheme for wideband spatial-correlated multiple-input multiple-output (MIMO) systems. We focus on orthogonal frequency division multiplex (OFDM) based systems. The proposed reduced-rank model is useful for many post-channel-estimation applications such as channel state information (CSI) feedback, precoder design and user/channel selection. Our work is an extension of an earlier investigation on narrowband MIMO channels. Like the narrowband case, the proposed wide channel estimator also offer the advantage of rendering both channel coefficients and mean angle of departure (AoD) simultaneously. BY exploiting the time, frequency, and spatial correlations of the channel and with continuous-type pilot symbols, we found that, even with as high as a compression ratio of 1%, our channel estimator is capable of maintaining an acceptable mean squared errors (MSE) in highly correlated environments. Both mathematical analysis and computer simulation, based on some industry-approved standard channel models, indicate that our algorithm outperform the conventional least-square estimator within most range of interest.

We present a novel BCH code based sequences design method for generating large families of ranging sequences. The sequences can be used in an OFDMA network to offer sufficient ranging opportunities and guarantee low probability of false detection. Each derived sequence has low peak to average power ratio (PAPR) and cross-correlations with other sequences. These properties enable a mobile receiver to easily detect multiple ranging sequences and estimate the corresponding time offsets. Our approach leads to improved performance and enhanced robustness against multi-user interference and multi-path fading. Numerical results verify the effectiveness of the proposed method and its advantages over the class of pseudo-random binary sequences (PRBS)[2].

In this paper, we jointly design antenna beamforming and power allocation to maximize the sum rate for multiple users in a hierarchical cognitive radio (CR) system, where an underlying microcellular system adopts dynamic spectrum access techniques to reuse the same spectrum of a macrocellular system. One challenge in this kind of hierarchical CR systems is the interference management between the macrocell and the microcell. We suggest utilizing the antenna beamforming technique to overcome the interference between the macrocell and the microcell, while maximizing the achievable sum rate of the underlying CR microcellular system. We formulate an optimization problem to achieve the objective of maximizing sum rate subject to the constraints of the maximum allowable interference power to the primary system, the minimum required signal-to-interference plus noise power ratio (SINR) for the secondary users, and the maximum transmission power for the underlying CR base station (BS). An iterative rate maximization (IRM) algorithm is developed to find the optimal solution. This developed methodology provides an important insight into the design of an optimal hierarchical CR system for various numbers of users as well as cell coverage.

Capacity and coverage of a Frequency Division Multiple Access (OFDMA) network can be greatly enhanced by dynamically allocate the radio transmission resources. By including the radio resources of cooperative nodes and taking into account the fairness issue, we present a simple suboptimal solution to the problem of radio resource allocation in relaybased OFDMA cellular systems. We restrict our investigation to a single-cell system with several cooperative relay stations and mobile stations (MSs). An IEEE 802.16e-like TDD scenario is assumed and only the uplink transmission with the base station(BS) handling the resource allocation is of concern. We propose two suboptimal algorithms that assign power, subcarriers and cooperative relay stations to a group of MS's to meet their QoS and minimum rate requirements. Our low-complexity solutions maximize the sum rate and a fairness index while satisfies the QoS and total transmit power constraint. Numerical results show that the proposed algorithms provide robust fairness and achieve near optimal sum rate performance.

In this paper, we apply simulation-based optimization methods to detect quadrature amplitude modulated (QAM) MIMO signals. The first one is the so-called Cross-Entropy (CE) method which enables the corresponding CE-based detector to provide bit-error-rate (BER) performance close to that achievable by the maximum-likelihood (ML) detector when the signal-to-noise ratio (SNR) is relatively low. Unfortunately, the performance curves exhibit error floors in the high SNR region. To improve the performance in the high SNR region, we borrow the concept of Particle Swarm Optimization (PSO) and refer to the resulting iterative detector as the Particle-Swarm-driven Cross-Entropy (PSD-CE) MIMO detector. This detector gives a significant BER performance improvement in the medium-to-high SNR region. We also consider the case when the channel state information is imperfect and suggest a robust detector structure based on a modified score function.

The Multiple-Input Multiple-Output based Orthogonal Frequency-Division Multiple Access (MIMO-OFDMA) is a promising high rate air interface technology. It is well known that the capacity and coverage of such a system can be significantly enhanced by employing a proper resource allocation (RA) scheme. In this paper, a SVD based precoder and two corresponding adaptive RA algorithms for MIMO-OFDMA networks are proposed. The proposed centralized algorithms are designed to minimize the total required power while meeting each user's transmission rate and bit error rate requirements. Numerical results show that, for modest rate requirements, the proposed algorithms offer performance gain much larger than that of the existing RA algorithms.

Abstract—This paper presents two analytic correlated multiple-input multiple-output (MIMO) block fading channel models and their time-variant extensions that encompass the popular Kronecker model and the more general Weichselberger model as special cases. Both static and time-variant models offer compact representations of spatial- and/or time-correlated chan-nels. When the transmit antenna array is such that the associated MIMO channel has a small angle spread (AS), which occurs quite often in a cellular downlink, our models admit reduced-rank channel representations. They also provide compact channel state information (CSI) descriptions which are needed in feedback systems and in many post channel estimation applications. The latter has the important implication of reduced feedback channel bandwidth requirement and lower post-processing complexity. Based on one of the proposed channel models we present novel iterative algorithms for estimating static and time-variant MIMO channels. The proposed models make it natural to decompose each iteration of our algorithms into two successive stages that are responsible for estimating the correlation coefficients and the signal direction, respectively. Using popular industry-approved standard channel models, we verify through simulations that our algorithms yield good MSE performance which, in many practi-cal cases, is better than that achievable by a conventional least-square estimator. The mean-squared error (MSE) performance of our estimators are analyzed and the resulting predictions are consistent with those estimated by simulations. Index Terms—Channel estimation, space-time signal process-ing, spatial correlation. I.

A single-symbol based initial ranging signal structure and the associated signal detection and timing synchronization methods for OFDMA systems are presented. The proposed structure makes it feasible and flexible for a receiver to detect single and multiple ranging codes and estimate the corresponding timing offsets. Our approach offers improved performance and enhanced robustness against multi-user interference and multi-path fading. Numerical results verify the effectiveness of the proposed method and its advantages over existing alternatives.

In this paper, a complete solution to the initial synchronization for multi-cell OFDMA (orthogonal frequency division multiple access) systems is proposed. The proposed method consists of the following operations: timing synchronization, fractional carrier frequency offset (CFO) estimation, fractional CFO compensation, and joint integer CFO and preamble index estimation. To estimate multiple fractional CFOs with pseudo-periodic preamble, we suggest an over-sampling approach. An ill-condition detection and noise suppression algorithm is also presented. For joint integer CFO and preamble index estimation, we use a differential detection based cross-correlation method. Simulation results have shown that the proposed method gives satisfactory performance for a wide SNR range even when the mobile station (MS) is on the cell boundaries.

Sequences with desired autocorrelation (AC) and cross-correlation (CC) properties are often needed in many communication and radar system applications. In a multipath fading channel with a known delay spread bound, one needs a family of sequences that meets these desired correlation requirements only for those correlation lags that lie within a window called zero-correlation zone. This paper presents two classes of new systematic approaches-a transform domain method and a direct (time domain) synthesis method-for generating zero-correlation zone (ZCZ) sequences. The former approach generates sequence families that achieve the upper bounds on the family size and the zero-correlation zone width for a given sequence period. The latter unifies many existing construction methods and both provide more flexibilities in producing new families of sequences. We also suggest a modulation operation that is capable of transforming nonconstant modulus sequences into polyphase sequences.

Implementing a belief propagation (BP) based LDPC decoder requires high degrees of parallelism using many component soft-in soft-output (SISO) decoding units to perform message passing from variable nodes to check nodes or vice versa. An obvious complexity-reduction solution is to serialize the decoding process, i.e., dividing a decoding iteration into several serial sub-iterations in which a sub-iteration performs only part of the complete parallel message-passing operation. The group horizontal shuffled BP (GHSBP) and vertical shuffled BP (GVSBP) algorithms respectively partition the check and variable nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes new techniques to improve three key elements of a GHSBP decoding algorithm, namely, the grouping method, the decoding schedule and the log-likelihood updating formulae. The (check nodes) grouping method and decoding schedule optimize certain design criterion. The new normalized min-sum updating formula with a self-adjustable correction (scaling) factor offers better nonlinear approximation. Numerical performance of new GHSBP algorithms that include part or all three new techniques indicate that the combination of the proposed grouping and decoding schedule yields a faster convergence rate and our modified min-sum algorithm gives performance superior to that of the conventional min-sum and normalized min-sum algorithm and is very close to that of the sum-product algorithm.

Peak-to-average-power ratio (PAPR) is a key design concern of an OFDM system as it determines the system's power efficiency. Clipping is a simple and efficient way of reducing PAPR. A suboptimal recursive clipping and filtering (RCF) method was proposed in [5] to reduce PAPR. This paper presents an alternate RCF approach which selects an error (clipping) vector that minimizes the peaks in both I- and Q-channels while satisfying some time and frequency domain distortion bounds. We formulate the design problem as a constrained linear programming (CLP) problem and extend it to include the tonereservation option. Like the RCF method, our approach does not need side information and incurs no data rate loss. Since the error vector used in RCF has not been optimized, our approach offers improved PAPR reduction. It also provide tradeoff between PAPR reduction and bit error rate (BER) degradation.

We present a novel stochastic decoding algorithm for Reed-Solomon codes. We apply an iterative Monte Carlo based approach called the Cross-Entropy method to produce, in every iteration, a set of random error locator vectors, each indicatesn-kpossible erasure positions within a received word. We associate each error locator vector with a candidate codeword by erasures-only decoding the received word, using the error locator vector to locate the erasures. Each iteration results in a new elite set that contains the bestEcandidate codewords. To increase the search radius and enhance the decoder performance we use the randomly drawn samples to generate what we call virtual received words from which extra candidate codewords and thus candidate elite members can be obtained. The proposed algorithms offer both complexity and performance advantages over some existing algebraic decoding algorithms for high rate RS codes.

Fast and accurate spectrum sensing is crucial in realizing a reliable cognitive network. Cooperative spectrum sensing can help reducing the mean detection time and increasing the agility of the sensing process. However, when the number of cognitive users is large, the bandwidth need for the control channel that are used to report the secondary user nodes’ results to the fusion center may become excessively large. In this paper, we apply the sequential probability ratio test (SPRT) to control the average number of the reporting bits. It is shown that the proposed technique not only reduces the mean detection time and bandwidth but also outperforms its non-sequential counterpart. We derive the relationships amongst the global performance, miss probability and false alarm probability and show how to control the average number of reports by thresholding the distributed cognitive users.

Most investigations on the effect of channel memory on the performance of block codes use a two-state Gilbert-Elliott (GE) model to describe the channel behavior. As there are circumstances that the channel of concern can not be properly described by the GE model, there are some recent works on coded performance that characterize the channel behavior by a general finite-state Markov chain. This letter presents a new efficient systematic approach to analyze the performance of block codes in such a hidden Markov channel (HMC). An application example is given to predict codeword error probability performance of an RS-coded system in a channel with memory. Numerical results are also provided to validate our analytic results.

In this paper, we propose two novel generalized belief propagation (BP) algorithms to improve the convergence behavior of the conventional BP algorithm. By incorporating a dynamic temperature into the free energy formulation, message passing is performed on a dynamic surface of energy cost. The proposed cooling process helps BP converge to a stable fixed point with a lower energy value that leads to better estimations. For decoding turbo-like error correcting codes, we adopt a parametric Gaussian approximation to relax the binary parity check constraints and generalize the conventional binary networks as well. Both the computational complexity and the convergence rate of the proposed annealed BP algorithms are almost the same as those of the conventional BP algorithm. Simulated performance of the proposed algorithms when they are used to decode a low density parity check (LDPC) code and the (23,12) Golay code is presented to validate our proposals.

This paper presents an achievable codeword weight lower bound associated with weight-2 input sequences of a class of turbo codes. The class of codes has an interleaver structure that encompasses most practical interleavers used by turbo codes. It partitions the incoming information sequence into blocks of the same size and the interleaver performs intra-block and interblock permutations. Both pre- and post-permuted blocks are individually tail-biting encoded. Following [4], we refer to the codeword associated with a weight-2 input sequence as a weight- 2 error event. We apply a special permutation function that incorporates the separate encoding concept to derive a lower bound of the weight-2 error event This lower bound reveals that (i) a larger component code period gives better distance for the weight-2 error events, and (ii) separate encoding results in improved distance if the block length is suitably chosen and is large enough.

Transmit diversity through user cooperation is an attractive proposal for performance enhancement in a mobile communication network. Given the availability of multiple transmission channels from multiple users, we are concerned with the channel, power and rate assignment scheme that offers the maximum capacity while satisfying the multimedia multi-rate requirements. Earlier cooperative schemes often assume that a central processing device is available to find the optimal or suboptimal solution. The corresponding high computing complexity, however, makes the implementation of an energy-efficient cooperative transmission not very practical. In this paper, we present a simple resource allocation scheme that enables each participant user to easily and independently find a near-optimal channel assignment matrix and power allocation vector under certain constraints. Our solution can be used for both mono-rate and multi-rate applications. It is optimal for the former case and gives near-optimal performance for the latter case.

We study the decoding of product codes and a class of parallel concatenated product codes (PCPC). PCPC improves the minimum distance while retaining the merit of low decoding complexity of turbo product codes (TPC). We prove that using the Fibonacci interleaver does help increasing the minimum distance. The regularity of the interleaver also reduces the implementation complexity and makes parallel interleaving feasible. We show that Pyndiah's algorithm for decoding product codes produce an annealing effect similar to that of the so-called annealed belief propagation (ABP) algorithms which adjusts the "temperature" of an augmented cost surface. Decoding methods based on modified Pyndiah and annealed BCJR algorithms for both PC and PCPC are proposed and their performance is compared.

This paper presents a new turbo coding scheme for high data rate applications. It uses a special interleaver structure that is naturally suited for parallel processing and a multiple-round early stopping test involving both sign check and a CRC code. A memory (storage) management mechanism is included as a critical part of the decoder. The proposed coding scheme offers new design options and tradeoffs that are not available to conventional convolutional turbo codes (CTCs). In particular, it becomes possible for the decoder to employ an efficient inter-block collaborative decoding algorithm, passing the information obtained from stopping test proved blocks to other unproved blocks. It also becomes important to have a proper decoding schedule. The combined effect is improved performance and reduction in the average decoding latency. We show that the memory manager has a modular-like effect in that additional memory units render enhanced performance due not only to less forced early stopping but to possible increases of the interleaving depth. It also provides additional design tradeoff amongst performance, speed and required memory size. Depending on the decoding schedule, the degree of parallelism and other decoding resources available, the proposed scheme admits a variety of decoder architectures that meet a large range of speed and performance demands.

In this paper, we propose two simulation based maximum likelihood (ML) methods to estimate the direction of arrival (DOA) by a novel combination of the cross-entropy (CE) method and the polynomial parameterization scheme. The CE method is an efficient stochastic approximation method for solving both discrete and continuous optimization problems. We bridge the ML approach and the stochastic search algorithm by properly randomizing the desired parameters. Numerical results show that the proposed CE-based algorithms yield highly accurate DOA estimation with fast convergence rate while requiring only linear processing complexity. Compared with the conventional iterative quadratic maximization likelihood (IQML) method, the proposed algorithms can alleviate the error propagation effect in low signal to noise ratio (SNR) region and asymptotically approach the Cramer-Rao bound in high SNR region

This paper documents an initial effort in detecting frequency-hopped (FH) signals in a multiple access (MA) environment from a machine learning perspective. Although the off-line training might require very intensive computing power, the extracted information does has a concise representation, which then enables to detect a signal using only simple and low-power operations.Frequency-hopping is an attractive alternative multiple access technique for direct sequence based code division multiple access (CDMA) schemes. Other than the communication channel statistic, the capacity of an FHMA system is determined by two major related design concerns: waveform design and receiver structure. Given the FH waveform, one still has difficulty in designing an FHMA ML receiver due to the facts that our knowledge about the channel statistics is often incomplete and even if it is complete the associated conditional probability density function (pdf) does not render a closed-form expression.Regarding the FHMA/MFSK waveform as a time-frequency pattern, we convert the multiuser detection problem into a pattern classification problem and then resolve to the Support Vector Machine (SVM) approach for solving the resulting multiple-class classification problem. By using an appropriate kernel function,t he SVM essentially transforms the received signal space into a higher dimension feature space. We propose a SVM-based FHMA/MFSK receiver by applying the Sequential Minimization Optimization (SMO) and Directed Acyclic Graph (DAG) algorithms to find the optimal separating hyperplanes in the feature space. Simulation results indicate that our design does yield robust and satisfactory performance.

Many communication and radar systems necessitate the use of sequences with desired autocorrelation (AC) and cross-correlation (CC) properties. This paper presents a systematic method based on the transform domain characterization of the AC and CC constraints to generate new families of sequences that meet the requirements. We demonstrate that some existing families can easily be generated by our approach. Our approach, however, renders new families of sequences with less constraints. The proposed approach is elementary and can easily be extended to synthesize two-dimensional arrays or even higher dimensional waveforms that possess the desired multidimensional correlation properties. A preamble structure based on our new sequence family is suggested and performance of frequency offset and channel estimation algorithms for a multiantenna orthogonal frequency-division multiplexing (OFDM) system that uses such a preamble is given.

Many communication and radar systems necessitate the use of sequences with desired autocorrelation (AC) and crosscorrelation (CC) properties. This paper presents a systematic method based on the frequency (transform) domain characterization of the AC and CC constraints to generate new families of sequences that meet the requirements. We demonstrate that some existing families can easily be generated by our approach. But our approach is more general for it renders new families of sequences with less constraint on the sequence's AC period. The proposed approach is elementary and can easily be extended to synthesize two-dimensional arrays that possess the desired two-dimensional correlation properties.

In a Bluetooth piconet, the Master essentially controls the channel. Due to an absence of coordination between independent Masters while accessing the wireless medium, devices will encounter high packet interference if several piconets are simultaneously operating in the same area. Since even a headset and a mobile phone can be connected with a Bluetooth link forming a piconet, it may not be unusual to find tens of independent piconets in crowded places like airports, international conferences, shopping malls, and so on. Study of packet interference is important because interference affects the throughput of a piconet. Motivated by the fact that applications will benefit, in terms of higher available data rate in one direction, by using multiple-slot packets in an asymmetric manner, in this paper, we present an analytical model of packet interference in a cluster of piconets using multiple-slot packets. Also, considering that all the portable devices can have a Bluetooth interface and people are highly mobile these days, it will not be uncommon to find a cluster of piconets of both the 79-hop and the 23-hop types in the same area. We then present an analytical model of interference of multiple-slot packets in a heterogeneous cluster of Bluetooth piconets. By a heterogeneous cluster we mean some piconets are of the 23-hop type and the rest are of 79-hop type. We show how the aggregate throughput in a cluster of piconets degrade under various traffic scenarios, such as 1-slot, 3-slot, and 5-slot packets in symmetric and asymmetric modes in synchronous and asynchronous conditions of Master clocks. Our analytic model is based on the idea of probabilistic graphs, where a node denotes a piconet and an edge denotes the probability of interference between two nodes. Though the 23-hop system has been phased out, our work gives a general approach to model packet interference in multiple, frequency-hopping systems that need not be Bluetooth systems.

Study of packet interference is important because interference affects the throughput of a piconet. Motivated by the fact that applications will benefit, in terms of higher available data rate in one direction, by using multiple-slot packets in an asymmetric manner, in this paper, we present an analytical model of packet interference in a cluster of piconets using multiple-slot packets. Also, considering that all the portable devices can have a Bluetooth interface and people are highly mobile these days, it will not be uncommon to find a cluster of piconets of both the 79-hop and the 23-hop types in the same area. We then present an analytical model of interference of multiple-slot packets in a heterogeneous cluster of Bluetooth piconets. By a heterogeneous cluster we mean some piconets are of the 23-hop type and the rest are of 79-hop type. We show how the aggregate throughput in a cluster of piconets degrade under various traffic scenarios, such as 1-slot, 3-slot, and 5-slot packets in symmetric and asymmetric modes in synchronous and asynchronous conditions of master clocks. Our analytic model is based on the idea of probabilistic graphs, where a node denotes a piconet and an edge denotes the probability of interference between two nodes.

We present in this paper a novel model-based scheme for estimating MIMO block fading channels. The proposed method can be applied to estimate the conventional independent and identically distributed (i.i.d.) complex Gaussian as well as the more realistic spatial-correlated channels. Excellent mean squared identification error (MSIE) performance can be attained with proper designed system parameters. We also derive an adaptive least squares (RLS) version that can be used for estimating a static channel or tracking time-varying channels. Furthermore, when the angle spread (AS) at the transmit site is small and thus the correlations amongst the transmit antennas are high, we show that it is possible to extract the information about the transmitter's angle of departure (AOD) for potential postprocessing applications.

The bit error rate (BER) performance of a multicode CDMA RAKE receiver over band-limited fading channels is analyzed in this paper. We consider a pilot-assisted channel estimation mechanism and investigate, among others, the effect of imperfect channel estimation, Our analysis removes some idealized assumptions used in earlier efforts, taking multiple access interference, interchannel interference (ICI), and the effects of bandlimiting as well as time-varying correlated multipath fading all into account. As a result, we are able to obtain more accurate performance prediction and assess the impacts of some system parameters that have not been considered before.

Inter-block permutation (IBP) concept is a simple but effective technique to improve the performance of a conventional turbo code. On the other hand, proper early termination leads to reduced decoding latency without compromising the performance. For inter-block permuted turbo codes (IBP-TC), however, the termination time variation over blocks within the interleaving span necessitates a new design paradigm. We use both cyclic redundancy check (CRC) code and sign check to make a termination decision and generate soft information for unterminated neighboring blocks at the same time. The new decoder that combines the features of iterative decoding and variable stopping time not only yields less average decoding delay but also outperforms its fixed-stopping-time counterpart by 0.2 - 0.3 dB.

This paper considers the problem of blind joint channel estimation and data detection for orthogonal frequency-division multiplexing (OFDM) systems in a fading environment. Employing a regression model for a time-varying channel, we convert the problem into one that finds the data sequence x whose associated least-squares (LS) channel estimate z(x) is closest to the space of some regression curves (surfaces). We apply the branch-and-bound principle to solve the nonlinear integer programming problem associated with finding the curve that fits a subchannel in the LS sense. A recursive formula for fast metric update is obtained by exploiting the intrinsic characteristic of our objective function. The impacts of reordering the data sequence and selective detection are addressed. By employing a preferred order along with a selective detection method, we greatly reduce the detector complexity while giving up little performance loss. Both the complete and the reduced-complexity algorithms can be used for blind and semiblind detections of OFDM signals in a subchannel-by-subchannel manner. To further reduce the complexity and exploit the frequency-domain channel correlation, we suggest a two-stage approach that detects a few selected positions in some subchannels first, and then, treating the detected symbols as pilots, determines the remaining symbols within a properly chosen time-frequency block by a two-dimensional model-based pilot-assisted algorithm. The proposed methods do not require the information of the channel statistics like signal-to-noise ratio or channel correlation function. Performance of differential modulations like differential quaternary phase-shift keying and STAR 16-ary quadrature amplitude modulation are provided. Both blind and semiblind schemes yield satisfactory performance.

For orthogonal frequency-division multiplexing (OFDM) signals that suffer from frequency-selective fading, we derive the maximum-likelihood (ML) pilot-assisted carrier frequency offset (CFO) estimate and show that most proposals based on repetitive pilot symbols did not use the complete set of sufficient statistics. We convert the problem of obtaining the ML solution from searching exhaustively over the entire uncertainty range to that of solving a spectrum polynomial, thereby greatly reducing the computational load. By properly truncating the polynomial, we obtain a closed-form expression for the corresponding zeros so that the root-searching procedure is greatly simplified. The complexity of locating the desired root is further reduced at almost no expense of performance degradation by an alternate algorithm that uses the fact that the solution is related to the root of a special factor of the polynomial. This alternate method is very attractive for its simplicity and excellent performance that, even at low signal-to-noise ratios (SNRs), is very close to the corresponding Crame/spl acute/r-Rao lower bound. A detailed analysis of the mean-squared error performance is presented and the analysis is validated by simulations.

The desired properties of a medium access control (MAC) protocol in mobile ad hoc network (MANET) include: (1) meet quality of service (QoS) requirements for real-time nodes, (2) be decentralized, (3) achieve fairness from viewpoint of throughput or energy consumption, and (4) be immune to the hidden node problem. Though there have been numerous proposed MAC protocols for the IEEE 802.11 WLAN, few of them possess all of the four properties mentioned above. Our protocol can support real-time traffic and satisfy QoS requirements, and can achieve fairness among non-real-time nodes. Also, without using any centralized control, it can be easily deployed in MANET. An analytic model of the protocol's throughput has also been developed. We compare the protocol's throughput obtained from its analytic model and simulation to validate each other.

Turbo product codes (TPCs) possess the advantages of (relatively) low decoding complexity and excellent performance. They are very attractive candidate codes for packet communication systems using ARQ. We propose two TPC-based ARQ protocols and evaluate their performance in AWGN and Rayleigh fading channels. Numerical results show that the proposed protocols can achieve high throughput with minimum latency at high SNRs and acceptable delay and respectable packet error rate performance at low to middle SNRs.

Based on a Volterra-type channel model, we suggest a coded solution for compensating the nonlinear distortion of TDMA satellite waveforms. The resulting receiver for the coded system uses the iterated detection principle that iteratively equalizes the nonlinear channel and then decodes the equalized symbols. Computer simulation results show that significant improvement over conventional approach can be achieved.

This paper proposes a robust pilot-assisted channel estimation method for orthogonal frequency division multiplexing (OFDM) signals in Rayleigh fading. Our estimation method is based on nonlinear regression channel models. Unlike the linear minimum mean-squared error (LMMSE) channel estimate, the method proposed does not have to know or estimate channel statistics like the channel correlation matrix and the average signal-to-noise ratio (SNR) per bit. Numerical results indicate that the performance of the proposed channel estimator is very close to the theoretical bit error propagation lower bound that is obtained by a receiver with perfect channel response information.

Channel estimation is usually needed to compensate for the amplitude and phase distortions associated with a received orthogonal frequency-division multiplexing (OFDM) waveform. This paper presents a systematic approach for analyzing the bit-error probability (BEP) of equalized OFDM signals in Rayleigh fading. Closed-form expressions for BEP performance of various signal constellations [phase-shift keying (PSK), differential phase-shift keying (DPSK), quaternary phase-shift keying (QPSK)] are provided for receivers that use a linear pilot-assisted channel estimate. We also derive the optimal linear channel estimates that yield the minimum BEP and show that some previous known results are special cases of our general formulae. The results obtained here can be applied to evaluate the performance of equalized single-carrier narrowband systems as well.

The capacity of a fast frequency-hopped multiple access (FHMA) system is dictated by two major related design concerns: the hopping pattern and the receiver structure. This paper studies the impact of these two factors. We present a maximum likelihood (ML) diversity combiner for detecting asynchronous FHMA multilevel PSK (MPSK) signals in Rician fading channels and analyze the performance of a close approximation of the ML receiver. We compare systems using random hopping patterns and those using optimal hopping patterns of Einarsson (1980). Performance comparisons between chip-synchronous and chip-asynchronous systems are made as well. We propose and examine the effectiveness of a two-stage multiuser detector, in which the first stage makes an initial decision while the second stage tries to reduce multiple access interference (MAI) and resolve the ambiguity left by the first stage detector. The MAI caused by undesired users is constituted by a cochannel interference (CCI) contribution and an interchannel interference (ICI) contribution. This detector is of modest complexity and is capable of removing most of the CCI and part of the ICI. Two methods for mitigating MAI are also examined.

Cochannel interference is often the predominant factor that limits the capacity of a cellular mobile radio system. Power control is thus needed so that carrier-to-cochannel interference ratio (CIR) can be maintained within a tolerable bound. Many power control algorithms that require real-time CIR measurement have been proposed but there is very few mentioning the measurement method. This paper presents viable solutions for real-time CIR estimations under various channel conditions. These solutions are based on either the method of moments or the histogram matching concept. We provide numerical results to demonstrate the usefulness and to compare the performance of the proposed algorithms. It is found that the histogram matching method with a properly-designed nonuniform quantizer offers excellent CIR estimation.

The application of Reed-Solomon codes in slow frequency-hopped systems has been extensively studied. Earlier investigations assumed an infinite interleaving length and considered partial-band noise jammers only. This paper extends previous efforts by analyzing the effect of finite interleaving length and the impact of band multitone jammers. We also explain why two-threshold (2T) erasure-insertion methods (EIM) are needed and examine their performance. Numerical results are presented to compare the effectiveness of the EIM and jammer types and to study the relationships among the hop rate, the interleaver size, and the code rate. The use of 2T-EIM necessitates the estimation of several additional channel and signal parameters. Simple and effective estimation algorithms are provided as well.

The spectral efficiency of a cellular mobile radio system is enhanced through the reuse of the available spectrum. The resulting co-channel interference, however, also limits the system capacity. Power control is needed so that co-channel interference can be maintained within a tolerable bound. Therefore, co-channel carrier to interference ratio (CIR) is often used as a quality indicator for received signals. Various power control algorithms assume perfect CIR measurement have been proposed but there is no mentioning of the measurement method. This paper presents viable solutions for real-time CIR estimations under either additive white Gaussian noise (AWGN) or Rayleigh fading condition. A new algorithm that uses the concept of probability density function matching is also proposed to measure CIR in the presence of multiple interferers. Numerical results are provided to demonstrate the usefulness of the proposed algorithms.

The paper presents the bit error rate (BER) analysis of a GMSK system employing various forms of differential detection. The desired signal is assumed to experience Rician fading while multiple co-channel interference (CCI) suffer from Rayleigh fading. The effects of fading rate (fast or slow fading) and time and frequency dispersions are also examined.

It is well known that an adaptive filter with a large step size in the transient period and a small one in the convergence period gives small mean squared steady state error while achieving a fast convergence rate. Based upon this idea, we present two variable step size (VSS) blind equalizers. The first one employs an intersymbol interference (ISI) estimator to control the step size, the second algorithm uses a mean squared error (MSE) estimator to adjust the step size. Both accomplish what has been expected.

This paper studies the problem of diversity combining for frequency hopped multiple access (FHMA) systems that operate in a mobile satellite environment characterized by frequency-nonselective Rician multipath fading. The modulation scheme considered is the incoherent M-ary frequency-shift keying (MFSK). The optimal diversity combining rule is derived under the assumptions that the number of active users (K) in the system is known, all users are chip (hop)-synchronous, and each user employs a random FH address. We suggest practical implementations that are close approximations of the optimal rule and examine the effects of various system parameters on the resulting receivers. The bit error probability performance is analyzed and numerical examples are provided. The effects of the diversity order (L), the signaling size (M) and unequal received powers are examined and related system design concerns such as system capacity and spectral efficiency are evaluated as well.>

This paper studies the coded performance of multichannel MFSK and DPSK signalings in mobile satellite environments characterized by various kinds of multipath fading. Rician, Rician/lognormal, and a convex combination of Rician and Rician/lognormal or Rayleigh/lognormal distributions are used to model these communication channels. We investigate the minimum average signal-energy-to-noise ratio required to yield a cutoff rate that is greater than or equal to a given code rate. Also examined are system design issues such as the effect of quantization and metric conversion, the choice between binary codes and M-ary symbol codes, the optimization of the diversity order and the signal size, and the order of deinterleaving and diversity combining. Numerical examples are given to answer concerns raised by these issues.>

This paper presents two classes of adaptive blind algorithms based on second- and higher order statistics. The first class contains fast recursive algorithms whose cost functions involve second and third- or fourth-order cumulants. These algorithms are stochastic gradient-based but have structures similar to the fast transversal filters (FTF) algorithms. The second class is composed of two stages: the first stage uses a gradient adaptive lattice (GAL) while the second stage employs a higher order-cumulant (HOC) based least mean squares (LMS) filter. The computational loads for these algorithms are all linearly proportional to the number of taps used. Furthermore, the second class, as various numerical examples indicate, yields very fast convergence rates and low steady state mean square errors (MSE) and intersymbol interference (ISI). MSE convergence analyses for the proposed algorithms are also provided and compared with simulation results.>

Two iterated algorithms for evaluating the performance of a class of sequential tests are proposed. The goal is equivalent to computing the distribution function of the first passage time for a random walk to cross a one-sided barrier. Limitations on both algorithms are studied, and associated methods for eliminating those limitations when possible are derived. These algorithms are applied to a pseudonoise code acquisition system and a range-sampled radar searching problem. Related computational problems are discussed, and numerical results are given.>

The performance of four algorithms using pseudonoise matched filters (PNMFs), for direct-sequence spread-spectrum systems, is analyzed. They are: parallel search with fix dwell detector (PL-FDD), parallel search with sequential detector (PL-SD), parallel-serial search with fix dwell detector (PS-FDD), and parallel-serial search with sequential detector (PS-SD). The operation characteristic for each detector and the mean acquisition time for each algorithm are derived. All the algorithms are studied in conjunction with the noncoherent integration technique, which enables the system to operate in the presence of data modulation. Several previous proposal using PNMF are seen as special cases of the present algorithms.>