Performance of Optimum and Suboptimum Receivers for Space-Time Coded Systems in Correlated Fading

We consider a space-time coded system in a correlated Rayleigh flat fading environment with imperfect channel estimation. Two receiver structures are considered: a suboptimum receiver and the optimum maximum likelihood receiver. The system performance of both receivers is analyzed in terms of the pairwise error probability.     

Diversity combining for coherent and differential M-PSK in fading and class-A impulsive noise

In this paper, optimum and suboptimum diversity combining schemes for coherent and differential M-ary phase-shift keying (M-PSK) transmission impaired by general Ricean fading and impulsive Class-A noise are derived and analyzed. The proposed suboptimum coherent combining (SCC) and suboptimum noncoherent combining (SNC) schemes yield similar performance as the corresponding optimum combining schemes but require a lower computational complexity. In addition, the novel SCC and SNC strategies achieve large performance gains over conventional maximum ratio combining (MRC) and equal gain combining (EGC), respectively. For MRC and EGC, respectively, we also provide a performance analysis for coherent and differential M-PSK transmissions over general Ricean fading channels with Class-A noise. Furthermore, tight performance upper bounds for the proposed optimum and suboptimum combining schemes are derived.     

Performance study of suboptimum maximum-likelihood receivers for FFH/MFSK systems with multitone jamming over fading channels

We derive two suboptimum maximum-likelihood (ML) receivers for fast frequency-hopped M-ary frequency-shift-keying (FSK) spread-spectrum (SS) communication systems. These two receiver structures attempt to countermeasure the effects of the worst case multitone jamming (MTJ) and additive white Gaussian noise over Rayleigh- and Rician-fading channels, respectively. In addition, analytical bit-error-rate (BER) expressions for the two proposed suboptimum structures are derived and validated by simulation results. Performance comparisons among various receivers show that the proposed suboptimum receivers significantly outperform the other existing receivers over fading channels. The optimum diversity level of the suboptimum ML receiver for the Rayleigh-fading case is found to be higher than that of the Rician-fading case. In addition, the proposed suboptimum ML receivers with optimum diversity levels can effectively remove the effect of MTJ, even under very low signal-to-jamming ratio conditions.     

On the chip rate of CDMA systems with doubly selective fading andrake reception

The bit error probability for a direct-sequence code division multiple access (CDMA) system is determined as a function of the chip rate for communications over doubly selective fading channels. The effect the chip rate has on the performance of a CDMA system is considered for both a correlation receiver and a rake receiver. Several selective fading channels are employed as examples to illustrate that the choice of the best chip rate depends upon the characteristics of the channel and the number of taps in the rake receiver. The tradeoff between the number of taps and the bit error probability is investigated for different chip rates. Additionally, the effects of the Doppler spread on the performance of the system and the choice of chip rate are considered. The purpose of this paper is to examine some of the fundamental issues that influence performance of CDMA systems when employed for mobile cellular telephony and personal communication systems on channels with doubly selective fading     

Optimum diversity detection over fading dispersive channels withnon-Gaussian noise

We consider the problem of M-ary signal detection over a single-input-multiple-output (SIMO) channel affected by frequency-dispersive Rayleigh-distributed fading and corrupted by additive non-Gaussian noise, modeled as a spherically invariant random process. We derive both the optimum detection structure and a suboptimal, reduced-complexity receiver, based on the low-energy-coherence approach. Interestingly, both detection structures are canonical, i.e., they are independent of the actual noise statistics. We also carry out a performance analysis of both receivers, with reference to the case that the channel is affected by a frequency-selective fading and for a binary frequency-shift-keying signaling format. The results obtained through both a Chernoff-bounding technique and Monte Carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non-Gaussian noise. Interestingly, it is also shown that the suboptimal receiver incurs a limited loss with respect to the optimum (unrealizable) receiving structure     

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     

Maximuma posteriori decorrelating discrete-time rake receiver

Recently, a discrete-time version of the rake receiver has been proposed, as an alternative to the conventional continuous-time rake receiver, to overcome the need for complex path searching and tracking procedures. This discrete-time version is able to tackle diffuse multipath channels, avoiding by the way any required knowledge on the delays associated to the most significant channel paths. Unfortunately, it has been found to be very sensitive to channel estimation quality and leads to a significant degradation in performance in practice. To reduce this degradation, we propose and investigate in this paper an optimum structure of this discrete-time rake receiver, according to the maximuma posteriori criterion. Derived from an uncorrelated version of the discrete-time channel, provided by the Karhunen-Loève orthogonal expansion theorem, this structure requires for its operation more or less precise estimates of the discrete-time channel statistics. Consequently, for a precise characterization and evaluation of the enhancement in performance provided by this new structure, we propose to use both perfect and estimated statistics of the discrete-time channel. The estimated statistics, derived in conformity with the maximum likelihood criterion, are carried on a symbol-by-symbol basis. The performance of this new structure is evaluated through theoretical and simulation results and compared to that of the conventional discrete-time rake receiver with perfect and estimated discrete-time channel state information. In this evaluation, a diffuse multipath Rayleigh fading propagation channel with classical Doppler power spectrum and exponentially decaying multipath intensity profile is used.     

Transmission and Reception Concepts for WLAN IEEE 802.11b

State-of-the-art wireless local area network (WLAN) IEEE 802.11b terminals employ complementary code keying (CCK) as modulation format. In this paper, receiver concepts tailored for CCK transmission over frequency-selective fading channels are presented in a unified and systematic framework. First, optimum maximum-likelihood (ML) detection for CCK signaling is considered. Second, for complexity reduction, minimum mean-squared error block decision-feedback equalization (MMSE-DFE) is investigated and reduced-state sequence estimation (RSSE) is considered on the basis of an Ungerbock-like set partitioning of the multidimensional CCK code wordset. In order to improve the reliability of CCK transmission over fading channels, time-reversal space-time block codes (TR-STBCs) combined with receive diversity are applied. Simulation results of the considered suboptimum receivers are compared with a performance approximation for optimum detection. Our results demonstrate the excellent performance of the advocated equalization schemes and the significant gains that can be achieved with TR-STBCs and receive diversity in typical WLAN environments     

Simple Detection Based on Soft‐Limiting for Binary Transmission in a Mixture of Generalized Normal‐Laplace Distributed Noise and Gaussian Noise

In this letter, a simplified suboptimum receiver based on soft‐limiting for the detection of binary antipodal signals in non‐Gaussian noise modeled as a generalized normal‐Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman‐Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL‐plus‐Gaussian distribution.     

Joint Detection and Diversity Techniques in CDMA Mobile Radio Systems

CDMA mobile radio systems suffer from intersymbol interference (ISI) and multiple access interference (MAI) which can be combated by using joint detection (JD) techniques. Furthermore, the time variation of the radio channels leads to degradations of the receiver performance due to fading. These degradations can be reduced by applying diversity techniques. Three suboptimum detection techniques based on matched filters (MF), zero forcing (ZF) and minimum mean square-error (MMSE) equalization are considered. For further improvements, switched and equal gain diversity techniques are employed to combat fading. The performance is depicted in terms of the average bit error probability versus the average SNR per bit in a single cell environment showing an appreciable improvement over the non diversity situation. Theoretical results for the SNR at the front end of the receiver and the BER for ideal channel are obtained and compared with the simulation results.     

Iterative rake receiver with map channel estimation for ds-cdma systems

We propose an iterative rake receiver structure using an optimum semi-blind channel estimation algorithm for ds-cdma mobile communication systems. This receiver performs an iterative estimation of the channel according to the maximum a posteriori criterion, using the expectation-maximization algorithm. This estimation process requires a convenient representation of the discrete multipath fading channel based on the Karhunen-Loève orthogonal expansion theorem. The rake receiver uses pilot as well as unknown control and data symbols optimally for improving channel estimation quality. Moreover, it can take into account the coded structure of all unknown transmitted symbols when channel estimation quality is poor or unsatisfactory. The validity of the proposed method is highlighted by simulation results obtained for the FDD mode of the umts interface.     

Performance of DSWC diversity system using suboptimum adaptive switching threshold in independent and correlated nakagami‐m fading channels

The use of dual switched combining (DSWC) diversity reception scheme, for combating the detrimental effects of fading on digital transmissions, is popular due to its simpler implementation. The performance of switched diversity strategy is dependent on the selection of the switching threshold. But, for the analysis and design of the DSWC diversity system, the closed form analytical solution for optimum adaptive switching threshold is not possible for most of the modulation schemes in correlated fading environment. This letter presents an approximate, but simple and closed form, generic expression for adaptive switching threshold, called in this case as suboptimum adaptive switching threshold, in independent and correlated Nakagami‐m fading channels for a wide range of binary and M‐ary modulation schemes. It is shown that the average symbol error rate (ASER) performance obtained using this suboptimum adaptive switching threshold is almost same as obtained using optimum adaptive switching threshold. Copyright © 2005 John Wiley & Sons, Ltd.     

Detection Schemes for Weak Signals in First-Order Moving Average of Impulsive Noise

In this paper, the detection of weak signals in additive noise described by the first-order moving average (FOMA) of an impulsive process is considered. Specifically, decision regions of the maximum likelihood (ML) and suboptimum ML (S-ML) detectors are derived in the FOMA noise model, and specific examples of the ML and S-ML decision regions are obtained. The ML and S-ML detectors are employed in the antipodal signaling system and compared in terms of bit error rate in an impulsive noise environment. Numerical results show that the S-ML detector, despite its reduced complexity and simpler structure, exhibits practically the same performance as the optimum ML detector. It is also observed that the performance gap between detectors for FOMA and independent and identically distributed noise becomes larger as the degree of noise impulsiveness increases     

Binary Signaling over Channels Containing Quadratic Nonlinearities

This paper examines the transmission of binary data signals over channels which contain quadratic nonlinearities and additive Gaussian noise. We consider the case where the channel is nonlinear with memory and where the signal is passed through an input receiver filter and sampled once every signaling interval. The samples are represented by a discrete Volterra series and a special case where the received sample contains a single quadratic distortion term is examined. The optimum (maximum-likelihood) receiver (processor) is derived and upper and lower performance bounds obtained. The performance of a practical, suboptimum receiver is examined by means of computer simulation and is shown to be very close to the lower bound of the optimum receiver. Next we examine the case where the received sample contains two quadratic distortion terms. Again, upper and lower performance bounds are obtained. The performance of a suboptimum receiver which uses nonlinear decision feedback is evaluated by computer simulation. Its performance is shown to be superior to an optimum linear receiver.     

Performance Analysis of Optimum and Suboptimum Selection Diversity Schemes on Rayleigh Fading Channels With Imperfect Channel Estimates

In this paper, we present a comparative analysis on the effects of channel estimation errors on the performance of optimum and suboptimum selection diversity (SD) receivers on Rayleigh-fading channels. By modeling the estimation errors as independent complex Gaussian random variables, we derive simple closed-form expressions for the average probability of error for both optimum and suboptimum SD schemes with noisy channel estimates. With dual diversity and imperfect estimates, we establish a connection between optimum SD and maximal-ratio combining (MRC), and between suboptimum SD and equal-gain combining diversity schemes. Interestingly, we show that the optimum SD receiver structure and the resulting performance for differential binary coherent phase-shift keying (DBPSK) signaling can be obtained, in a straightforward way, as a special case of the performance of the optimum SD scheme with binary PSK signaling and channel estimation errors. For a fixed average power and bit duration, in conjunction with pilot-assisted minimum mean-square error channel estimation, we show that the optimum coherent SD scheme coincides with that of the optimum noncoherent SD scheme with binary frequency-shift keying (BFSK) signaling, whereas the coherent MRC scheme coincides with the optimum noncoherent receiver (i.e., the square-law combiner) for BFSK. The optimum number of diversity channels, under an energy-sharing mode of operation, is also studied. Finally, we formulate the problem of optimal pilot placement, consider channel estimation with a practical pilot-symbol-assisted modulation technique, and present some numerical results illustrating the comparative performances of various SD receivers     

Spread-spectrum multiple-access performance of orthogonal codes:impulsive noise

A direct-sequence spread-spectrum multiple-access (SSMA) communication system that assigned a set of M-orthogonal sequences to each user is analyzed. An accurate model is incorporated for the impulsive noise that characterizes the LF and MF bands, so that the SSMA receiver operates in a combination of multiple-access interference and impulsive (atmospheric) noise. The performance of a linear receiver operating in such an environment is analyzed, and probability-of-error curves are presented. The presence of impulsive noise motivates the derivation and analysis of a nonlinear receiver that use a variable-gain stage to suppress noise impulses. This receiver is effectively optimum when the signal amplitudes are below a certain bound and when the noise and interference samples are independent, or nearly so. However, the gain stage of this nearly optimum receiver depends on the noise model parameters including the various user delays. Consequently, a nonparametric receiver that incorporates a simple clipper is also analyzed. The asymptotic relative efficiency of both receivers is determined     

A nonparametric approach to signal detection in impulsiveinterference

Impulsive interference poses a challenge to conventional detection techniques. The α-stable distribution, while sometimes providing a good model for impulsive interference, has proven to be no exception. Some of these difficulties have motivated the investigation and development of computationally tractable, locally suboptimum correlation, and rank correlation detectors for signals embedded in impulsive interference modeled as a symmetric α-stable process. The performance of some of these detectors is evaluated and compared with that of the locally optimum (LO), locally optimum rank (LOR), matched filter, and Cauchy detectors. Simulation results show that a rank-based detector is able to approach the performance of the computationally intensive LO and LOR detectors across a range of values for for α     

A new approach to greedy multiuser detection

We propose a new suboptimum multiuser detector for synchronous and asynchronous multiuser communications. In this approach, a greedy strategy is used to maximize the cost function, the maximum-likelihood (ML) metric. The coefficients of the ML metric are utilized as weights indicating in which order bits can be estimated. The complexity of the algorithm is approximately K/sup 2/ log K per bit, where K is the number of users. We analyze the performance of the greedy multiuser detection in the additive white Gaussian noise channel as well as in the frequency-nonselective Rayleigh fading channel, and compare it with the optimum detector and several suboptimum schemes such as conventional, successive interference cancellation, decorrelator, sequential, and multistage detectors. The proposed greedy approach considerably outperforms these suboptimum schemes, especially for moderate and high loads in low and moderate signal-to-noise ratio regions. The results show that when there is a significant imbalance in the values of the coefficients of the ML metric due to moderate to high noise, fading, and asynchronous transmission, near-optimum performance is achieved by the greedy detection.     

Coding for the discretely phase ambiguous additive white Gaussianchannel

Communication over the additive white Gaussian channel, subject to a discrete phase ambiguity at the receiver, is considered. When this phase ambiguity is considered as a discretely distributed random variable, the channel is termed the acoherent additive white Gaussian (AAWG) channel. It is shown that the optimum decoder for the AAWG channel is not practically implementable and a suboptimum decoder that is asymptotically optimum at high signal-to-noise ratio is developed. The low signal-to-noise ratio performance of the suboptimum decoder is also examined. By considering the structural possibilities for this decoder, it is shown that one implementation leads to rotationally invariant codes. Other implementations, based on a rotationally disjoint property, lead to a variety of solutions that offer a general framework for communication over this channel. Some of these solutions use a parallel receiver configuration. Various solutions are compared in terms of implementation and performance     

Performance of a frequency-hopped differentially modulated spread-spectrum receiver in a Rayleigh fading channel

The performance of a spread-spectrum receiver previously described by the authors is analyzed in detail. Performance curves are given for a wide range of mobile radio channel conditions, including multipath distortion and correlated fading. The use of optimal filters to combat the former and space diversity to combat the latter are investigated. Some errors in the authors' earlier papers are corrected. The form of space diversity suggested has the unusual feature that it can be employed at the fixed station site only and provide diversity in both communication paths, i.e., to and from the mobile. Degradation due to fading and other aberrations is shown to be in the range 3-6 dB for typical mobile channel conditions. In a nonfading channel the receiver is suboptimum by about 3 dB.