Error Probablity for Optimal and Suboptimal Quadratic Receivers in Rapid Rayleigh Fading Channels

The exact performance of optimal and suboptimal quadratic receivers in a binary hypothesis test between jointly distributed zero mean complex Gaussian variates is derived. The probability of error is given as a function of the characteristic values of a generalized eigenvalue problem set up in terms of the covariance matrix of the received signal-plus-noise and in the matrix of the quadratic form of the receiver. The results include the exact performance of various types of suboptimal receivers including those previously derived for the envelope matched filter for MFSK and the noncoherent DBPSK receiver in rapid Rayleigh fading, nonfrequency-selective channels. Also, the performance of near-optimal stationary process-long observation time [SPLOT] receivers, "energy detectors," and other approximately optimal receivers may be calculated for noncoherent signaling in the same channel.     

A union bound on the error probability of binary codes over block-fading channels

Block-fading is a popular channel model that approximates the behavior of different wireless communication systems. In this paper, a union bound on the error probability of binary-coded systems over block-fading channels is proposed. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. The distribution of error bits over the fading blocks is computed. For a specific distribution pattern, the pairwise error probability is derived. Block-fading channels modeled as Rician and Nakagami distributions are studied. We consider coherent receivers with perfect and imperfect channel side information (SI) as well as noncoherent receivers employing square-law combining. Throughout the paper, imperfect SI is obtained using pilot-aided estimation. A lower bound on the performance of iterative receivers that perform joint decoding and channel estimation is obtained assuming the receiver knows the correct data and uses them as pilots. From this, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Furthermore, the optimal energy allocation for pilot signals is found for different channel memory lengths.     

一种基于MIMO-FSO的最大似然盲检测算法

在多天线自由空间无线光通信(MIMO-FSO)系统中,提出一种基于通用最大似然的序列(MLSD)盲检测算法,使用等增益合并(EGC)获得MIMO空间分集,研究了大气湍流衰落信道不同强度条件下算法的性能。此外,针对MLSD在较长序列长度下的高复杂度,提出一种次优的快速搜寻算法。蒙特卡洛仿真结果显示,所提出的接收机模型在MIMO-FSO系统中,能够获得空间分集,在不同信道条件、中等序列长度条件下,得到接近最优检测的性能。     

A new method for phase synchronization and automatic gain controlof linearly modulated signals on frequency-flat fading channels

An optimal phase synchronization and automatic gain control (AGC) scheme for coherent reception of linearly modulated signals on frequency-flat mobile fading channels is presented. The channel model and receiver performance are described. It is shown that using the technique allows the irreducible error floors (due to random FM) known from the noncoherent methods to be practically eliminated. Depending on the fastness of the fading, large power gains over the noncoherent methods are achieved. Unfavorable analog signal processing and/or the high bandwidth inefficiency of the FDM-pilot coherent methods are also avoided     

A systematic approach to the design and analysis of optimum DPSKreceivers for generalized diversity communications over Rayleigh fadingchannels

A generalized diversity channel is introduced that models a variety of wireless communication systems that use time, frequency, multipath, and/or antenna diversity with various interbranch correlations between signaling waveforms and the fading and additive noise processes. In the context of this general model, a systematic approach to the design and analysis of optimum noncoherent differential phase-shift keying (DPSK) receivers is introduced. In particular, it is shown how the minimum error probability (MEP) and the generalized likelihood ratio tests (GLRT) can be applied to obtain optimal noncoherent combining rules. A comparative error-rate analysis of the GLRT and MEP detectors and an ad hoc equal-gain combiner is provided for binary signaling, and the suitability of the three schemes is determined as a function of fading characteristics. The asymptotic bit-error-rate analysis is undertaken for the MEP detector for slow and fast fading channels. An estimator-detector decomposition of the noncoherent MEP rule is obtained which allows an insightful comparative study of the fundamental limits of binary phase-shift keying and DPSK modulation-detection methods for both slow and fast fading. The results of this paper are also applicable to postdecorrelative receivers in multiuser channels     

Exact BER analysis for M-QAM modulation with transmit beamforming under channel prediction errors

Significant throughput improvements can be obtained in multiple-inputmultiple-output (MIMO) fading channels by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. In general, accurate channel state information (CSI) is required to achieve these performance gains. In this paper, we analyze the impact of channel prediction error on the bit error rate (BER) of combined beamforming and MRC in slow Rayleigh fading channels. Exact closed-form BER expressions are obtained in terms of elementary functions. Numerical results show that imperfect CSI causes little BER degradation using channel prediction of moderate complexity.     

Noncoherent adaptive channel identification algorithms fornoncoherent sequence estimation

In this letter, two novel noncoherent adaptive algorithms for channel identification are introduced. The proposed noncoherent least-mean-square (LMS) and noncoherent recursive least squares (RLS) algorithms can be combined easily with noncoherent sequence estimation (NSE) for M-ary differential phase-shift keying signals transmitted over intersymbol interference (ISI) channels. It is shown that the resulting adaptive noncoherent receivers are very robust against carrier phase variations. For zero frequency offset, the convergence speed and the steady-state error of the noncoherent adaptive algorithms are similar to those of conventional LMS and RLS algorithms. However, the conventional algorithms diverge even for relatively small frequency offsets, whereas the proposed noncoherent algorithms converge for relatively large frequency offsets. Simulations confirm the good performance of NSE combined with noncoherent adaptive channel estimation in time-variant (fading) ISI channels     

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu’s convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.     

Achievable Performance of Orthogonal STBC Over Spatially Correlated Rician Channels

The effect of spatial correlation on the performance of orthogonal space-time block codes (OSTBCs) over multiple-input-multiple-output (MIMO) Rician fading channels is studied. Asymptotic error-rate formulas for OSTBC with high average signal-to-noise ratios (ASNRs) over arbitrarily correlated Rician MIMO channels are derived in terms of the diversity and coding gains. Our results show that, in correlated fading, the phase vector phi of the channel line-of-sight (LOS) components affects the effective Rice K-factor at the OSTBC receiver output and, hence, may result in a coding gain that is significantly higher than that for independent Rician MIMO channels. Furthermore, when the channel covariance matrix is rank deficient and under some additional mild conditions, the error and outage probabilities of OSTBC achieve those in a nonfading additive-white-Gaussian-noise channel. For both cases of full-rank and rank-deficient channel covariance matrices, analytical expressions of optimal and worst case phase vectors phi, and exact upper and lower bounds of OSTBC performance are derived. These results provide new insights into the achievable performance of OSTBC over correlated Rician MIMO channels and, if incorporated into future multiple antenna systems design, will bring about significant performance enhancement     

Outage Capacity of the Fading Relay Channel in the Low-SNR Regime

In slow-fading scenarios, cooperation between nodes can increase the amount of diversity for communication. We study the performance limit in such scenarios by analyzing the outage capacity of slow fading relay channels. Our focus is on the low signal-to-noise ratio (SNR) and low outage probability regime, where the adverse impact of fading is greatest but so are the potential gains from cooperation. We showed that while the standard Amplify-Forward protocol performs very poorly in this regime, a modified version we called the Bursty Amplify-Forward protocol is optimal and achieves the outage capacity of the network. Moreover, this performance can be achieved without a priori channel knowledge at the receivers. In contrast, the Decode-Forward protocol is strictly suboptimal in this regime. Our results directly yield the outage capacity per unit energy of fading relay channels     

Analysis of Differential Orthogonal Space–Time Block Codes Over Semi-Identical MIMO Fading Channels

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

On the Ergodic Capacity and Energy Efficiency for Fading MIMO NOMA Systems

Non-orthogonal multiple access (NOMA) is expected to be a promising multiple access techniques for 5G networks due to its superior spectral efficiency (SE). Previous research mainly focus on the design to improve the SE performance with instantaneous channel state information (CSI). In this paper, we consider the fading MIMO channels with only statistical CSI at the transmitter, and explore the potential gains of MIMO NOMA scheme in terms of both ergodic capacity and energy efficiency (EE). The ergodic capacity maximization problem is first studied for the fading multiple-input multiple-output (MIMO) NOMA systems. We derive the optimal input covariance structure and propose both optimal and low complexity suboptimal power allocation schemes to maximize the ergodic capacity of MIMO NOMA system. For the EE maximization, the optimization problem is formulated to maximize the system EE (defined by ergodic capacity under unit power consumption) under the total transmit power constraint and the minimum rate constraint of the weak user. By transforming the EE maximization problem into an equivalent one-dimensional optimization problem, the optimal power allocation for EE design is proposed. To further reduce the computation complexity, a near-optimal solution based on golden section search and suboptimal closed form solution are proposed as well. Numerical results show that the proposed NOMA schemes significantly outperform the traditional orthogonal multiple access scheme with traditional orthogonal multiple access transmission in terms of both SE and EE.     

On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel Estimation Error

By employing spatial multiplexing, multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. Zero-forcing (ZF) detection is a simple and effective technique for retrieving multiple transmitted data streams at the receiver. However the detection requires knowledge of the channel state information (CSI) and in practice accurate CSI may not be available. In this letter, we investigate the effect of channel estimation error on the performance of MIMO ZF receivers in uncorrelated Rayleigh flat fading channels. By modeling the estimation error as independent complex Gaussian random variables, tight approximations for both the post-processing SNR distribution and bit error rate (BER) for MIMO ZF receivers with M-QAM and M-PSK modulated signals are derived in closed-form. Numerical results demonstrate the tightness of our analysis     

Detection techniques for fading multipath channels with unresolvedcomponents

In this paper we consider noncoherent detection structures for multipath Ricean/Rayleigh fading channels. The multipath components are assumed to be unresolved, with known delays. These delays could have been estimated, for example, by using super-resolution techniques or sounding the channel with a wide-band pulse. We show that the Rayleigh channel optimum receiver (R OPT) consists of an “orthogonalization” (or decorrelation) stage and then it implements an optimum decision rule for a resolved multipath channel. Since the optimum decision rule over Ricean channels is in general too complex for implementation, we propose several suboptimum structures such as the quadratic decorrelation receiver (QDR) and the quadratic receiver (QR). The QDR scheme exploits the decorrelation performed on the input samples. The nonlinear term due to the Ricean specular term is replaced by a quadratic form that is more suitable for implementation. Single-pulse performance of these schemes are studied for commonly used binary modulation formats such as FSK and DPSK. This paper shows that it is possible to have diversity-like gains over Ricean/Rayleigh multipath fading channels with unresolved components even if the channel is not fully tracked. Furthermore, this paper demonstrates the importance of using generalizations of RAKE receivers designed to handle the unresolvability condition. For two-path mixed-mode Ricean/Rayleigh channels, it is shown that improved performance can be obtained by using receivers that know the strength of the Ricean specular term     

Semi-blind maximum-likelihood joint channel/data estimation for correlated channels in multiuser MIMO networks

The aim of this paper is to investigate receiver techniques for maximum likelihood (ML) joint channel/data estimation in flat fading multiple-input multiple-output (MIMO) channels, that are both (i) data efficient and (ii) computationally attractive. The performance of iterative least squares (LS) for channel estimation combined with sphere decoding (SD) for data detection is examined for block fading channels, demonstrating the data efficiency provided by the semi-blind approach. The case of continuous fading channels is addressed with the aid of recursive least squares (RLS). The observed relative robustness of the ML solution to channel variations is exploited in deriving a block QR-based RLS-SD scheme, which allows significant complexity savings with little or no performance loss. The effects on the algorithms’ performance of the existence of spatially correlated fading and line-of-sight paths are also studied. For the multi-user MIMO scenario, the gains from exploiting temporal/spatial interference color are assessed. The optimal training sequence for ML channel estimation in the presence of co-channel interference (CCI) is also derived and shown to result in better channel estimation/faster convergence. The reported simulation results demonstrate the effectiveness, in terms of both data efficiency and performance gain, of the investigated schemes under realistic fading conditions.     

Suboptimal particle filtering for MIMO flat fading channel estimation

Particle filters have been successfully employed to track MIMO flat fading channels for wireless communications. However, an optimal importance density cannot be always found to optimize the performance of a particle filter. A suboptimal importance density such as the prior distribution can be used to reduce the complexity of the particle filtering; however, it has a problem of ignoring the current observations. A class of suboptimal particle filters uses the prior distribution as the important density and moves the predicted particles to the low‐error region. In addition, particle filters require knowledge of noise processes to estimate the posterior distribution. This paper presents a suboptimal particle filter that overcomes the drawbacks of the prior importance density and the noise uncertainty by utilizing the swarm behavior in the particle propagation. The presented method will be applied to estimate the channel state information and detect the transmitted symbols of a MIMO wireless communication system under Rayleigh flat fading channel. Computer simulation of a 2 ×2 MIMO system is presented to illustrate the performance of the proposed suboptimal particle filter technique. Copyright © 2011 John Wiley & Sons, Ltd.     

Robustness of Weighting Receive Antenna Selection Algorithm

The conventional antenna selection schemes suffer from severe performance degradations in most fading channels. This paper proposes a new receive antenna selection algorithm based on the theory of convex optimization that improve the system performance over Rayleigh fading multiple-input multiple-output (MIMO) channels. With this method, each Radio Frequency chain is not allocated to a single antenna element, but instead to the complex-weighted and combined response of a group array of elements. In this paper, we firstly get optimal solution under no constraints. Then, suboptimal algorithms are introduced based on minimised the squared error and convex optimization technique. The Monte-Carlo simulations show that the algorithm proposed can provide the performance very close to that of the optimal selection based on exhaustive search.     

Specular coherent and noncoherent optimal detection for unresolvedmultipath Ricean fading channels

This paper considers specular coherent and noncoherent optimal detection for unresolved multipath Ricean fading channels with known delays. The focus is on receiver structures and performance. Specular coherent detection employs the carrier phase of the Ricean specular component, while noncoherent detection does not. Therefore, a specular coherent detector must be augmented with a carrier phase estimator for the specular component. The structures considered are generalization of the well-known RAKE receiver to the unresolved multipath case. It is shown that both optimal structures perform a decorrelation operation before combining, which is essential to eliminating error floors under multipath unresolvability conditions. Furthermore, the noncoherent optimal receiver includes an inherent estimator for the specular component phasor. It is shown that the specular coherent and noncoherent structures converge at high SNR. This result is confirmed through analytical and numerical performance evaluation. Little performance gains can be obtained by the use of specular coherent detection for orthogonal frequency-shift keying and to a lesser extent for differential phase-shift keying over mixed mode Ricean/Rayleigh fading channels, making noncoherent demodulation attractive in these cases     

Antijam performance of FFH/BFSK with noise-normalization combining in a Nakagami-m fading channel with partial-band interference

The bit error rate (BER) performance of a noncoherent fast frequency-hopped binary orthogonal frequency-shift-keying (FFH/BFSK) spread spectrum noise-normalization combining receiver is evaluated in the presence of partial-band interference (PBI) and additive white Gaussian noise (AWGN) over independent frequency-nonselective slowly Nakagami-m fading channels. It is shown from the analytical results, and verified by simulation, that a higher diversity level greatly improves the worst-case performance of the noise-normalization receivers over Rayleigh or more severe fading channels, while a lower diversity level is preferred for less severe fading channels. In the former case, a full band strategy is optimal for the interferer and a partial-band strategy is more disruptive in the latter case.     

Stochastic gradient algorithms for design of minimum error-rate linear dispersion codes in MIMO wireless systems

Linear dispersion (LD) codes are a good candidate for high-data-rate multiple-input multiple-ouput (MIMO) signaling. Traditionally LD codes were designed by maximizing the average mutual information, which cannot guarantee good error performance. This paper presents a new design scheme for LD codes that directly minimizes the block error rate (BLER) in MIMO channels with arbitrary fading statistics and various detection algorithms. For MIMO systems employing LD codes, the error rate does not admit an explicit form. Therefore, we cannot use deterministic optimization methods to design the minimum-error-rate LD codes. In this paper, we propose a simulation-based optimization methodology for the design of LD codes through stochastic approximation and simulation-based gradient estimation. The gradient estimation is done using the score function method originally developed in the discrete-event-system community. The proposed method can be applied to design the minimum-error-rate LD codes for a variety of detector structures including the maximum-likelihood (ML) detector and several suboptimal detectors. It can also design optimal codes under arbitrary fading channel statistics; in particular, it can take into account the knowledge of spatial fading correlation at the transmitter and receiver ends. Simulation results show that codes generated by the proposed new design paradigm generally outperform the codes designed based on algebraic number theory.