The channel estimation in a wide‐band orthogonal frequency division multiplexing (OFDM) system is different from the narrow‐band system, for the estimation parameters should include the Doppler scale factor, which is a particular parameter of the wide‐band system. The underwater acoustic OFDM system is a typical wide‐band system, and its channel has more than one scale factor usually. For this multi‐scale case, the common estimation method is a factor‐by‐factor process with repeated calculation of the reproduced waveform. This article proposes a factor‐graph‐based estimation method, which fully uses the restriction relationship among the parameters, and estimates the parameters simultaneously. To reduce the computation load, the modified Bayesian propagation (BP) algorithm is proposed. Comparing to the common BP algorithm, the modified BP algorithm simplifies the calculation of the condition probability in the summation. The simulation results of the mean squared error show that the proposed method is an effective estimation method for the multi‐scale wide‐band system. The bit error rate performance of the proposed method is very close to the result of the known channel‐state‐information, and outperforms the fractional Fourier transform (FrFT) and the modified particle swarm optimisation (MPSO) methods for well channel condition.

This study focuses on the reception strategy and the detection method of a wideband orthogonal frequency‐division multiplexing (OFDM) signal, which is passing through a Doppler channel. Most prior works regarded the Doppler effect as a reason of interchannel interference due to its destruction of the subcarrier orthogonality. Distinguishing from those works, the authors point out that the wideband OFDM signal is still an OFDM signal with subcarrier orthogonality after passing the channel with single Doppler scaling factor. Thus, the received OFDM signal passing the Doppler spreading channel is a linear superposition of a set of transmitted OFDM signals associated with different parameters. To make full use of the diversity gain offered by the superposition, the authors propose a strategy of diversity reception and a belief propagation detection method for the received wideband OFDM signal. The simulation results show that the proposed strategy improves the performance obviously with increase of the diversity order in a Doppler spreading channel. It offers different options for system demands. Furthermore, the proposed detection method can offer an acceptable performance even it combined with the conventional sampling process. It makes the conventional structure replacing the common resampling structure possible in a wideband OFDM system.

We investigate the problem of resource allocation in a downlink orthogonal frequency-division multiple access (OFDMA) broadband network with an eavesdropper under the condition that both legitimate users and the eavesdropper are with imperfect channel state information (CSI). We consider three kinds of imperfect CSI: (1) noise and channel estimation errors, (2) feedback delay and channel prediction, and (3) limited feedback channel capacity, where quantized CSI is studied using rate-distortion theory because it can be used to establish an informationtheoretic lower bound on the capacity of the feedback channel. The problem is formulated as joint power and subcarrier allocation to optimize the maximum-minimum (max-min) fairness criterion over the users’ secrecy rate. The problem considered is a mixed integer nonlinear programming problem. To reduce the complexity, we propose a two-step suboptimal algorithm that separately performs power and subcarrier allocation. For a given subcarrier assignment, optimal power allocation is achieved by developing an algorithm of polynomial computational complexity. Numerical results show that our proposed algorithm can approximate the optimal solution.

In this study, the authors investigate the energy‐efficient resource allocation in a multiuser downlink multiple‐input multiple‐output (MIMO) orthogonal frequency‐division multiple access system with block diagonalisation. Unlike the existing works in which one subcarrier is exclusively used, they consider the multiple user MIMO case on each subcarrier. An optimisation problem involving user selection, receive‐signal subspace selection and power allocation is formulated to maximise the system energy efficiency (EE). As optimising the orientation of the receive‐signal subspace is difficult, they considered two simpler resource allocation schemes, subspace selection scheme and user selection scheme. The two optimisation problems for the subspace and user selection schemes can be rewritten as a unified problem involving set selection and power allocation. By relaxing the combinatorial variables, they obtain an optimal joint set selection and power allocation solution, which can be directly applied to the original problem in most cases. To further reduce the complexity of the algorithm, they also develop a preselection technique for the user and received‐signal subspace on each subcarrier. Through simulations, they discuss the impact of different parameters on the EE for the two schemes and show that the proposed suboptimal algorithm can achieve a close performance to the optimal algorithm.

The performance of multiuser multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) systems can be significantly improved by using efficient resource allocation schemes. There are a lot of resource allocation schemes to maximize the system capacity. However, under a practical circumstance of employing a suboptimal MIMO detector, optimizing for maximum capacity may not be proper. In this paper, we investigate resource allocation schemes to minimize the bit error rate (BER) for various suboptimal detectors, including the zero forcing (ZF) detector, the successive interference cancellation (SIC) detector, the lattice reduction (LR) based ZF detector, and the LR based SIC detector. For the ZF and SIC detectors, we study the subcarrier allocation among users and power allocation over subcarriers and antennas. The optimal algorithm is investigated and a suboptimal scheme with low complexity is proposed for each detector. For the LR based ZF and SIC detectors, we propose suboptimal schemes with allocating power equally over antennas. Simulation results confirm that the proposed scheme improves the BER performance for each detector.

Radio resource allocation for multiuser multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) systems is an important issue to improve overall system performance. Although the achievable rate has been adopted for a performance indicator in most resource allocation schemes, it may not be practical if a nonideal receiver including a suboptimal detector is used instead of optimal one. Under this practical circumstance, we study the subcarrier and power allocation to minimize the average bit error rate (BER) subject to a total power constraint. Different allocation algorithms are proposed for various MIMO detectors such as the maximum likelihood (ML) detector, linear detectors and the successive interference cancellation (SIC) detector. We also propose suboptimal algorithms to reduce the complexity. Based on the simulation results, we can confirm that the proposed suboptimal algorithm for each detector can achieve a comparable performance with the optimal allocation with a much lower complexity.

Information iteratively updating between the detection and the decoding in multiple-input multiple-output (MIMO) systems is a promising method to access the channel capacity. However, the complexity of detection algorithms is very high even if no iteration is considered. Single tree search is a very powerful detection algorithm in the iterative detection of MIMO, which combines tree searches of all byte into a single tree search (STS). But inherited from the complexity of nonlinear detection algorithm, the STS algorithm is still too complicated in many scenarios. In this article, we proposed that byte whose values of log likelihood ratio (LLR) are large enough are good enough for detecting and need no further updating. We set threshold in detection. A tree where LLR values of all byte are larger than it is free of update. As a result, a lot of calculation of search can be reduced, and the complexity can be reduced lot while the performance loss is very small. When BER=10-3, threshold=0.1 or 1, the performance loss is about 0.03dB or 0.16dB. When SNR=22dB, the complexity of the proposed algorithm is about 26.6% or 20.02% of the original algorithm.

Machine‐to‐machine (M2M) communication plays an important role in various kinds of intelligent networks. In this study, a hybrid cooperation scheme for data collection in hierarchical smart building networks (SBN) is proposed under the framework of M2M communications. The hierarchical network structure means that the data collection process is carried out via multi‐layer communications. In the first layer, smart metres organise themselves into clusters and send information to the cluster‐heads. Then all cluster‐heads forward the received information to the base station automatically in the second layer. In particular, the roles of cluster‐head can be acted by either fixed nodes or user terminals in the building, and this endow a hybrid cooperation mode to the data collection process. To construct the network structure and utilise the resources efficiently, the authors first provide some theoretical analysis on the influence of network structure and bandwidth constraints. Then a distributed scheme for joint structure formation and subband allocation is proposed based on coalitional game theory. Furthermore, for the feasibility of this scheme in practical applications, some improvements of the proposed scheme have also been made at last. The advantages of the proposed scheme are verified by simulation results.

In this paper, we consider the collaborative use of amplify-and-forward relays to form a beamforming system and provide physical layer security for a wireless network with multiple eavesdroppers. In this paper, we investigate the relay transmit power minimization under a secrecy rate constraint via secure beamforming. To minimize the relay transmit power, we design an approximate relay power minimization (RPM) beam-forming scheme, in which an iterative algorithm combining the semidefinite relaxation (SDR) technology and the gradient-based method is devised by studying the convexity of the RPM problem. By relaxing the constraints of the RPM problem, we propose a virtual eavesdropper based RPM (VE-RPM) beamforming scheme, which transforms the multivariate RPM problem into a problem of a single variable, and thus obtain an analytical solution. Our proposed beamforming designs can work well even if the number of eavesdroppers is larger than that of relays, while the existing schemes, e.g., the null-space beamforming approaches, can not work under this condition. Simulation results are presented to demonstrate the performance improvement with the RPM beamforming schemes. It is also showed that the virtual eavesdropper approaches significantly reduce the complexity with acceptable performance degradation.

In this study, a two‐stage decode‐and‐forward cooperative network is investigated consisting of a source, a corresponding destination, an eavesdropper and several intermediate nodes. In this study, the authors present an analysis of overall secrecy rate considering both distributed relay selection and secure beamforming problems. The achievable rate constraint is newly included into the system model. This modelling framework offers a more reliable approximation of the practical wireless channel. The relay selection is formulated as a coalitional game with transferable utility, which decreases the computation complexity in solving the distributed relay selection problem. A new ‘Max–Pareto order’ is constructed, which not only considers the player value, but also reflects the dominated weight of coalition value. Moreover, a distributed merge‐and‐split coalition formation algorithm is presented in this study. This algorithm achieves the system performance close to the theoretical upper limit, but it requires much less computation consumption.

This article focuses on reducing the complexity of K-best sphere decoding (K-best SD) algorithm for the detection of multiple-input multiple-output (MIMO) systems. One common reduction method is that one or more selected thresholds are set to cut excess nodes with partial Euclidean Distance (PED) larger than them. For a long time, statistical characteristic of noise has been well explored to generate thresholds. But the known noise in a certain specific transmission process is always overlooked. In this article, not only the statistical characteristic of noise is calculated, but also the known value of noise is considered. By adding a parameter determined by both noise and quality of service (QoS) to the smallest PED in each searching layer, a tighter and more suitable threshold can be calculated for this layer. Simulation results show that the proposed algorithm makes an efficient complexity reduction while the performance drops little. Specially, the proposed algorithm reduces the computational complexity about 90\% while the bit error ratio (BER) performance drops around 10\% in 4-by-4 MIMO systems employing 16-QAM or 64-QAM modulation. A new parameter, half complexity point, is proposed to evaluate the reduction effect, and half complexity points of the proposed algorithm are better than one selected original algorithm.

The Dijkstra algorithm (DA) is a kind of tree search algorithm. The biggest advantage is that it has the smallest number of visited nodes among all optimal tree search algorithms. But stack sizes required by the DA are always too large to achieve. By partitioning the searching tree into blocks, two modified algorithms are proposed in this article to shrink stack sizes. One, serial block partitioned DA, searches blocks one by one. Another, parallel block partitioned DA, searches blocks at the same time. Radii, which are updated when one block search is finished, are set to cut nodes with metrics larger than them in both algorithms. Simulation results show that the visited nodes number of serial block partitioned DA increase is very limited while the stack size is reduced exponentially. It also shows that stack sizes of the parallel block partitioned DA are reduced exponentially and the processing time is reduced efficiently. The performance of proposed algorithms is kept optimal in both proposed algorithms.

Massive multiple-input multiple-output (MIMO) is an attractive solution to achieve high data rate and tackle interference. In this paper, we study the downlink of a two-cell massive MIMO system employing coordinated zero-forcing beamforming with limited feedback, where each base station (BS) acquires both the direct link channel state information (DCSI) and the cross link CSI (CCSI) from the users through a limited feedback link. The DCSI is used to support multi-user MIMO transmission (control intra-cell interference) at each BS and the CCSI is used to control the inter- cell interference. Since the total number of feedback bits at each user is fixed, there is a tradeoff between the quantization errors of the DCSI and CCSI. We consider the allocation of the feedback bits over the DCSI and CCSI to maximize the sum-rate of the system. We obtain closed-form solution for the asymptotically optimal feedback bits allocation as the number of antennas per BS goes to infinity. The solution reveals insights on how the key system parameters such as path gains, transmit powers and the number of antennas/users affect the optimal feedback bits allocation. Numerical results validate our theoretical analysis.

ABSTRACT With the reformation of spectrum policy and the development of cognitive radio, secondary users will be allowed to access spectrums licensed to primary users. Spectrum auctions can facilitate this secondary spectrum access in a market‐driven way. To design an efficient auction framework, we first study the supply and demand pressures and the competitive equilibrium of the secondary spectrum market, considering the spectrum reusability. In well‐designed auctions, competition among participants should lead to the competitive equilibrium according to the traditional economic point of view. Then, a discriminatory price spectrum double auction framework is proposed for this market. In this framework, rational participants compete with each other by using bidding prices, and their profits are guaranteed to be non‐negative. A near‐optimal heuristic algorithm is also proposed to solve the auction clearing problem of the proposed framework efficiently. Experimental results verify the efficiency of the proposed auction clearing algorithm and demonstrate that competition among secondary users and primary users can lead to the competitive equilibrium during auction iterations using the proposed auction framework. Copyright © 2011 John Wiley & Sons, Ltd.

It is often impractical to obtain global channel knowledge and conduct centralized optimization for wireless networks. We study distributed weighted sum-rate maximization (WSRM) in general MIMO interference networks, named B-MAC interference networks. It is desirable to exploit the structure of the problem to design distributed algorithms with high performance and low signaling overhead. We recently unveiled a polite water-filling (PWF) structure satisfied by all Pareto optimal inputs of important achievable regions of the B-MAC interference networks. The PWF offers an elegant method to decompose a network into multiple equivalent single user channels and thus, facilitates the design of distributed algorithms. Based on the PWF, we design efficient distributed algorithms which only need local channel knowledge and converge to a stationary point of the WSRM problem. For TDD networks, the duality inherited in PWF and the channel reciprocity are further exploited to reduce the signaling overhead. The proposed algorithms are shown by simulations to outperform the state-of-the-art.

We propose an algorithm that reduces the complexity of the K-best sphere decoding (K-best SD) algorithm, which is a powerful parallel detection algorithm for multiple-input multiple-output systems (MIMO). By analyzing the probability of different nodes to be the final solution, the algorithm prunes some nodes during the tree search to reduce the complexity. Simulation results prove that compared with the K-best SD algorithm the proposed algorithm performance drops very little. Compared with the famous fixed-complexity sphere decoding (FSD) with the same complexity, the proposed algorithm has better performance.

A new noise variance based reduced maximum likelihood decision feedback equalization (ML-DFE) algorithm has been developed. This algorithm reduces the calculation complexity by exploring the intrinsic statistical properties layer by layer. Through setting layered thresholds, part of the nodes in the searching process will be cut by comparing with the thresholds. Simulation results show that the complexity drops lots while the performance drops small.

In this study, the superimposed training strategy is introduced into orthogonal frequency division multiplexing-modulated amplify-and-forward two-way relay network (TWRN) to perform two-hop transmission-compatible individual channel estimation. Through the superposition of an additional training vector at the relay under power allocation, the separated source–relay channel information can be directly obtained at the destination and then used to estimate the channels. The closed-form Bayesian Cramér-Rao lower bound (CRLB) is derived for the estimation of block-fading frequency-selective channels with random channel parameters, and orthogonal training vectors from the two source nodes are required to keep the Bayesian CRLB simple because of the self-interference in the TWRN. A set of optimal training vectors designed from the Bayesian CRLB are applied in an iterative linear minimum mean-square-error channel estimation algorithm, and the mean-square-error performance is provided to verify the Bayesian CRLB results.

The algorithms in this paper exploit optimal input structure in interference networks and is a major advance from the state-of-the-art. Optimization under multiple linear constraints is important for interference networks with individual power constraints, per-antenna power constraints, and/or interference constraints as in cognitive radios. While for single-user MIMO channel transmitter optimization, no one uses general purpose optimization algorithms such as steepest ascent because water-filling is optimal and much simpler, this is not true for MIMO multiaccess channels (MAC), broadcast channels (BC), and the non-convex optimization of interference networks because the traditional water-filling is far from optimal for networks. We recently found the right form of water-filling, polite water-filling, for some capacity/achievable regions of the general MIMO interference networks, named B-MAC networks, which include BC, MAC, interference channels, X networks, and most practical wireless networks as special cases. In this paper, we use weighted sum-rate maximization under multiple linear constraints in interference tree networks, a natural extension of MAC and BC, as an example to show how to design highly efficiency and low complexity algorithms. Several times faster convergence speed and orders of magnitude higher accuracy than the state-of-the-art are demonstrated by numerical examples.

We found a network version of water-filling, named polite water-filling, that is optimal for all boundary points of the capacity regions of MAC and BC and for all boundary points of a set of achievable regions of a general class of interference networks, named MIMO B-MAC networks that include BC, MAC, interference channels, X networks, and most practical networks as special cases. It is polite because it strikes an optimal balance between reducing interference to others and maximizing a link's own rate. Unlike in single-user MIMO channels, where the optimal input covariance can be solved by the water-filling, the traditional water-filling is far from optimal in networks. Thus, general purpose optimization algorithms have been used for networks but have high complexity and do not work well for non-convex cases. Together with our duality result, the polite water-filling can be used to design highly efficient low-complexity iterative centralized/distributed algorithms for the optimization of input covariance matrices, including both power and beamforming matrices, because it takes the advantage of the structure of the problems. References to the resulting algorithms that outperform the state-of-the-art by a wide margin are provided.

A reduced K-best sphere decoding (K-best SD) algorithm for Multiple-Input Multiple-Output (MIMO) detection is proposed. The algorithm reduces the complexity of the K-best SD by combining the statistics character of the signal and the requirement of the quality of service (QoS). In the reducing processing of the proposed algorithm, the chi-square distribution (CSD) property of the signal, the optimal symbol error rate (SER) property and the loss of pruning are considered together to give a theoretic error bound and then a threshold to determined which route can be pruned to reduced the calculation complexity. The algorithm reduces the complexity with a controllable cost of performance decrease. Simulation results on a 16QAM system with 4×4 antennas show that the algorithm can attain the near-optimal performance with a significant complexity reduction comparing to the original K-best SD or maximum likelihood (ML) algorithm.

It is well known that in general, the traditional water-filling is far from optimal in networks. We recently found the long-sought network version of water-filling named polite water-filling that is optimal for a large class of MIMO networks called B-MAC networks, of which interference Tree (iTree) networks is a subset whose interference graphs have no directional loop. iTree networks is a natural extension of both broadcast channel (BC) and multiaccess channel (MAC) and possesses many desirable properties for further information theoretic study. Given the optimality of the polite water-filling, general purpose optimization algorithms for networks are no longer needed because they do not exploit the structure of the problems. Here, we demonstrate it through the weighted sum-rate maximization. The significance of the results is that the algorithm can be easily modified for general B-MAC networks with interference loops. It illustrates the properties of iTree networks and for the special cases of MAC and BC, replaces the current steepest ascent algorithms for finding the capacity regions. The fast convergence and high accuracy of the proposed algorithms are verified by simulation.

This paper attempts to address the effectiveness of physical-layer network coding (PNC) on the capacity improvement for multi-hop multicast in random wireless ad hoc networks (WAHNs). While it can be shown that there is a capacity gain by PNC, we can prove that the per session throughput capacity with PNC is θ (nR(n))-1), where n is the total number of nodes, R(n) is the communication range, and each multicast session consists of a constant number of sinks. The result implies that PNC cannot improve the capacity order of multicast in random WAHNs, which is different from the intuition that PNC may improve the capacity order as it allows simultaneous signal reception and combination.

In this paper, we propose a resource allocation scheme to maximize users' minimum rate with a guaranteed outage probability for Orthogonal Frequency Division Multiple Access (OFDMA) systems with imperfect CSI. To avoid the system degradation caused by the noisy and outdated CSI, we consider the minimum mean square error (MMSE) channel prediction scheme at the base station (BS). We derive the parameter, namely, the equivalent channel gain, which is determined by the requirement of the outage probability and the channel estimates at the BS. With this parameter, we can maximizes users' minimum rates under a transmit power constraint and given outage probabilities. To reduce the complexity, we propose a two-step suboptimal approach that separately performs subcarrier and power allocation. Simulation results show that the performance of the resource allocation scheme is robust against channel estimation errors and feedback delays in OFDMA systems.

Abstract The performance of wireless networks is limited by multiple access interference (MAI) in the traditional communication approach where the interfered signals of the concurrent transmissions are treated as noise. In this paper, we treat the interfered signals from a new perspective on the basis of additive electromagnetic (EM) waves and propose a network coding based interference cancelation (NCIC) scheme. In the proposed scheme, adjacent nodes can transmit simultaneously with careful scheduling; therefore, network performance will not be limited by the MAI. Additionally we design a space segmentation method for general wireless ad hoc networks, which organizes network into clusters with regular shapes (e.g., square and hexagon) to reduce the number of relay nodes. The segmentation method works with the scheduling scheme and can help achieve better scalability and reduced complexity. We derive accurate analytic models for the probability of connectivity between two adjacent cluster heads which is important for successful information relay. We proved that with the proposed NCIC scheme, the transmission efficiency can be improved by at least 50% for general wireless networks as compared to the traditional interference avoidance schemes. Numeric results also show the space segmentation is feasible and effective. Finally we propose and discuss a method to implement the NCIC scheme in a practical orthogonal frequency division multiplexing (OFDM) communications networks. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we establish a rate duality between the forward and reverse links of MIMO interference channel, where the reverse links are obtained by exchanging the roles of transmitters and receivers in the forward links, and the corresponding channel matrices are conjugate transpose of the forward channel matrices. Since the capacity region for general interference channel is unknown, we show that the forward and reverse links have the same achievable rate region by treating interference as noise under some sum power constraint. The explicit expression of the corresponding input covariance matrix transformation is provided. We discuss the connection between the proposed transformation and the MAC-BC transformations in the previous works. As an application, a duality based iterative algorithm is proposed to maximize the sum rate of MIMO interference channel under sum power constraint. We also extend the algorithm to individual power constraint. The proposed algorithms are shown to be effective by simulation.

Based on the result of Gupta and Kumar's seminal work, it has been proven that the scheme which allows multi-packet reception (MPR) can improve the throughput capacity by Theta(logn), while the improvement of network coding (NC) scheme is only upper bounded by a constant. On the development of NC, however, the most recently proposed schemes, physical- layer network coding (PNC) and analog network coding (ANC), advanced the innovation of increasing network capacity. They embrace the interference and allow simultaneous reception. Motivated by these two new approaches, in this paper, we study their throughput order. The results of our paper are as follows. The upper bound of the throughput order with the PNC/ANC scheme is Theta(radiclog n/n) log n which is the same as the MPR scheme. The throughput lower bound of the PNC/ANC scheme is Theta(1/radicn log n ), which is the same as the traditional NC schemes. Moreover, both the upper bound and the lower bound can be achieved. The throughput varies with the locations of the nodes between these two bounds.

It is difficult to implement optimal beamforming for multi-user multiple-input multiple-output (MIMO) downlink due to the high complexity. This paper proposes a low complexity generalized beamforming (GBF) scheme combined with an efficient user selection to maximize the weighted sum-rate. For each user, the outputs of the multiple antennas are combined with a receive GBF vector to create an equivalent multiple-input single-output (MISO) effective channel. First, user selection and receive GBF vectors are jointly optimized to construct a group of preferable effective channels. Then, transmit GBF vectors are obtained by zero-forcing over these effective channels. Simulation results show significant gain over currently known suboptimal schemes in various scenarios.

In this paper, we propose a new upper bound on the error performance of binary linear codes over block-fading channels by employing Gallager's first- and second-bounding techniques. As the proposed bound is numerically intensive in its general form, we consider two special cases, namely, the spherical bound and the DS2-exponential bound, which are found to be tight in nonergodic and near-ergodic block-fading channels, respectively. The tightness of the proposed bounds is demonstrated for turbo codes. Many existing bounds for quasistatic or fully interleaved fading channels can be viewed as special cases of the proposed Gallager bound.

In this letter, we show how to compute the asymptotic growth rate of input-output weight enumerator (AGR-IOWE) for some accumulate-based codes by using the sharp tools already developed. Numerical results on the AGR-IOWE for irregular repeat-accumulate (IRA) codes, systematic regular RA (SRA) codes, and concatenated zigzag codes are reported. It is observed that the SRA code has the same AGR-IOWE as a comparable concatenated zigzag code. For both SRA and concatenated zigzag codes, if keeping the code rate fixed, the increase of the grouping factor for the component punctured accumulate code may result in better asymptotic performance under maximum-likelihood decoding, but often worse performance under iterative sum-product decoding.

We derive upper bounds on the decoding error probability of binary block codes over noncoherent block additive white Gaussian noise (AWGN) and fading channels, with applications to turbo codes. By a block AWGN (or fading) channel, we mean that the carrier phase (or fading) is assumed to be constant over each block but independently varying from one block to another. The union bounds are derived for both noncoherent block AWGN and fading channels. For the block fading channel with a small number of fading blocks, we further derive an improved bound by employing Gallager's first bounding technique. The analytical bounds are compared to the simulation results for a coded block-based differential phase shift keying (B-DPSK) system under a practical noncoherent iterative decoding scheme proposed by Chen et al. We show that the proposed Gallager bound is very tight for the block fading channel with a small number of fading blocks, and the practical noncoherent receiver performs well for a wide range of block fading channels

In this paper, the effect of unmatched despreading chip waveforms for locally generated early and late despreading codes in a coherent delay-locked loop (CDLL) for DS/SS systems is investigated. Linear and nonlinear theories are employed to evaluate the performance of the CDLL. Based on linear theory, optimum despreading chip waveforms are pursued in the sense of minimizing root mean square (RMS) tracking error with both time limited (full response) and time unlimited constraints. Nonlinear analysis shows that the use of designed chip waveforms reduces RMS tracking error and increase mean time to lose lock (MTLL). Both rectangular and sinc chip pulse-shaping waveforms are considered as two widely used examples. It is also found that the designed despreading chip waveforms are optimized for any specified early-late spacing.

Binary code-division multiple-access (CDMA) systems operating in multipath fading, noisy channels (MFNC) are studied. Interference from undesired users and multipath are analyzed; these are modeled as equivalent noise. The error probability is given as a function of channel parameters and system parameters. The maximum possible number of users is estimated as a function of the tolerable error probability.