Probability of error analysis of digital partial responsecontinuous phase modulation with two-bit differential detection andoffset receiver diversity in fast Rayleigh fading channels

The performance of constant envelope digital partial response continuous phase modulation (PRCPM) with two-bit differential detection and offset receiver diversity is theoretically analyzed in fast Rayleigh fading channels. A simple closed-form expression for the probability of error is derived and evaluated for cases of practical interest to researchers and designers of land mobile radio systems. It is shown that the dynamic bit error rate (BER) performance is considerably improved using the offset diversity scheme. Thus, many PRCPM signals having a compact power spectrum can be used in future digital mobile radio systems     

Iterative diversity detection for correlated continuous-time Rayleigh fading channels

An antenna array is proposed as a means of achieving a space-diversity effect that partly overcomes the severity of continuous-time Rayleigh fading channels. The investigated channel is assumed to be frequency-nonselective with correlated diversity links, where the correlation is related to the array geometry and the spatial and Doppler dispersions. Further, the error performance is improved by bit interleaving and channel coding, where the encoders/channel is viewed as a serially concatenated system: a convolutional code constitutes the outer code, whereas a differential encoder and the fading channel (having truncated memory) form a joint inner code. In order to obtain a practical detector structure it is desirable to perform iterative decoding by applying some a posteriori probability (APP) algorithms. For this purpose, we propose a novel generalization of the well-known Bahl-Cocke-Jelinek-Raviv (1974) algorithm that calculates the APPs over channels having memory. Numerical results indicate that iterative decoding becomes more powerful when the exploited channel memory depth is extended. Also, the error performance is significantly improved by introducing multiple antennas. The interleaver gain is, however, seen to be quite moderate, in contrast to additive white Gaussian noise channels.     

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     

Estimation of phase differential of signals transmitted over fading channels

The authors show that it is possible to use the Hilbert transform to estimate the absolute value of the phase differential of signals transmitted over fading channels from the envelope of the signal. This is demonstrated on a mobile radio channel and on an indoor radio channel.<>     

Post-detection diversity Nakagami fading channels with correlatedbranches

We derive a closed-form expression for the performance of the post-detection product detector combiner (PDC) operating on L correlated branches in Nakagami (1960) fading. We consider the 2-DPSK signaling scheme and nonselective slow fading. The average bit error rate (BER) obtained with this scheme is compared to the ideal predetection MRC, showing limited loss. Moreover, the post-detection PDC is shown to outperform the selection diversity combiner (SDC) under the considered case of Nakagami fading     

Multiple symbol differential detection for trellis-coded MPSK overRayleigh fading channels

This paper presents a multiple-symbol differential detection scheme for coded and interleaved transmission of MPSK data. The performance of this scheme is then evaluated for transmission of digitized voice over a Rayleigh fading channel. It is found that in terms of bit error rate, the improvement given by using multiple-symbol differential detection is minimal, but when evaluated in terms of frame-error rate, the multiple-symbol scheme gives about 1.25-dB improvement. Another 0.75-dB improvement can be obtained by also using a serial list Viterbi algorithm     

On the outage probability of optimum combining and maximal ratiocombining schemes in an interference-limited Rice fading channel

In this letter, we study the performance of optimum combining (OC) and maximal ratio combining (MRC) diversity schemes in wireless digital communication systems with Rice fading and cochannel interference. New simplified closed-form expressions are derived for the probability density function (pdf) as well as the outage probability for OC and MRC when the desired signal has a line of sight and the interferers are assumed to be scattered and further away from the receiver. It is assumed that the interferers have equal powers and their number (L) is larger than the diversity order (M), i.e., L>M     

Performance of multi-level QAM with post-detection maximal ratiocombining space diversity for digital land-mobile radio communications

A new type of post-detection maximal ratio combining for space diversity receivers in digital land-mobile communications is proposed. The combining scheme is designed for multilevel quadrature amplitude modulation (QAM) and employs a pilot-symbol-aided fading estimator. It is realized at baseband using a digital signal processing (DSP) technique to simplify the receiver hardware. Computer simulation and laboratory experiments confirm that the proposed diversity scheme achieves a performance very close to that of ideal maximal ratio combining     

Multiuser detection for continuous phase modulation over Rayleigh fading channels

We study multiuser (MU) continuous phase modulation (CPM) over Rayleigh fading channels with a receiver antenna array. An optimum symbol-by-symbol MU detector is derived and its practical implementation with reduced-complexity is considered. According to the numerical results, the MU detector performs very close to a system free of interference by other users, when each user has more than one receiving antenna. For three receiving antennas, this difference is less than 0.25 dB, 0.4 dB, and 0.6 dB for two, three and four users, respectively. Moreover, the proposed system is bandwidth efficient as CPM is a bandwidth efficient modulation scheme, and the MU system only uses the single user CPM bandwidth.     

Optimum diversity combiner based multiuser detection fortime-dispersive Rician fading CDMA channels

Multiuser detection for asynchronous code division multiple access (CDMA) data transmission over the time-dispersive two-path Rician fading channel is considered. The multiuser maximum likelihood sequence detector (MLSD) is derived, and an equivalence of the fading channel to an asynchronous Gaussian intersymbol interference (AGISI) CDMA channel is established. However, the MLSD is found to be implementationally infeasible and this motivates the derivation of the optimum linear detector with near/far resistance as the performance criterion. The optimally near/far resistant linear time-invariant K-user detector is shown to consist of a cascade of a 2 K input/K output linear multiuser diversity combining filter followed by a K input/K output decorrelator that is designed for the equivalent AGISI/CDMA channel. This detector solves the near/far problem and also supports significantly higher bandwidth efficiencies for CDMA communication over the fading channel than does the conventional near/far limited single-user diversity combiner. The performance penalties incurred by multiuser detectors designed for the Gaussian channel when used over the Rician fading channel are also analytically characterized. It is shown that these penalties can be significant, making the case for the use of multiuser detectors optimized for this fading channel, particularly the optimum linear detector due to its relative implementational simplicity     

Correlated multivariate Weibull fading channels with selection diversity

The dependent multivariate Weibull distribution is modelled for correlated fading channels, where the probability density function of a Weibull fading factor is defined with two parameters (omega, beta), and the case of equal beta is considered. The joint cumulative distribution function and probability density function of the Weibull distribution are derived, and the outage probability of selection diversity is evaluated     

Modulation diversity for frequency-selective fading channels

In this article, modulation diversity (MD) for frequency-selective fading channels is proposed. The achievable performance with MD is analyzed and a simple design criterion for MD codes for Rayleigh-fading channels is deduced from an upper bound on the pairwise error probability (PEP) for single-symbol transmission. This design rule is similar to the well-known design rule for MD codes for flat fading and does not depend on the power-delay profile of the fading channel. Several examples for MD codes with prescribed properties are given and compared. Besides the computationally costly optimum receiver, efficient low-complexity linear equalization (LE) and decision-feedback equalization (DFE) schemes for MD codes are also introduced. Simulations for the widely accepted COST fading models show that performance gains of several decibels can be achieved by MD combined with LE or DFE at bit-error rates (BERs) of practical interest. In addition, MD also enables the suppression of cochannel interference.     

Impact of diversity reception on fading channels with codedmodulation. I. Coherent detection

We address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used. Under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and is indeed verified by our analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel also will perform asymptotically well on a fading channel with diversity. This paper presents bounds on the bit-error probability of a system with coded modulation and diversity for space- and time-correlated Rician flat fading. Specifically, we derive a new method which allows evaluation of the pairwise error probability extremely easily, as well as accurately and computationally fast. The accuracy achieved improves considerably on the widely used, but rather loose Chernoff bound. Starting from this analysis, we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases, and we address the effects of diversity on coded modulation performance and design criteria, including the effect on interleaver depth (which affects the total delay of the system)     

Coded M-DPSK with built-in time diversity for fading channels

Good coded modulation for fading channels requires built-in time diversity. Under a constraint on the interleaving delay, the authors construct and compare three categories of coded M-DPSK (M-ary differential phase-shift keying) schemes with 4⩽M⩽16 for fading channels: two-dimensional trellis-coded, multidimensional trellis-coded, and block-coded. General rules for designing these schemes and their matched bit or symbol interleavers are given. A universal two-state interleaver is shown. These schemes have been extensively evaluated, using computer simulations, for a narrow-band cellular radio channel at different vehicle speeds, with and without twofold antenna diversity     

Double-filter differential detection of PSK signals transmittedover linearly time-selective Rayleigh fading channels

Linearly time-varying fading models are used to investigate differential detection of PSK signals transmitted over frequency-flat fading channels. The structure of the optimal differential PSK detector is derived and an analytical technique is developed to compute its error performance. Results obtained by computer simulation are in excellent agreement with the analytical predictions     

On diversity reception over fading channels with impulsive noise

In this paper, we analyze the performance of different diversity combining techniques over fading channels with impulsive noise. We use Middleton's Class A model for the noise distribution and adopt two noise models, which assume dependent and independent noise components on each branch. We systematically analyze the performance of maximum ratio combing (MRC), equal gain combining (EGC), selection combining (SC), and post-detection combining (PDC) under these impulsive noise models, and derive insightful lower and upper bounds. We show that even under impulsive noise, the diversity order is retained for each combining scheme. However, we also show that under both models, there is a fundamental tradeoff between diversity gain and coding gain. Under the independent noise model, PDC is shown to combat impulsive noise more effectively than MRC, EGC, and SC. Our simulation results also corroborate our analysis.     

Low complexity multisymbol differential detection of MDPSK overflat correlated Rayleigh fading channels

Low complexity algorithms for implementing multisymbol differential detection (MSDD) over flat correlated Rayleigh fading channels are proposed, which are extensions of the low complexity MSDD over additive white Gaussian noise channels also proposed by the authors. The complexities of the proposed algorithms increase roughly linearly with block length N while optimum MSDD increases exponentially with N. Simulation results show almost the same performances for practical N     

Recursive receivers for diversity channels with correlated flat fading

This paper addresses the design and performance of time-recursive receivers for diversity based communication systems with flat Rayleigh or Ricean fading. The paper introduces a general state-space model for such systems, where there is temporal correlation in the channel gain. Such an approach encompasses a wide range of diversity systems such as spatial diversity, frequency diversity, and code diversity systems which are used in practice. The paper describes a number of noncoherent receiver structures derived from both sequence and a posteriori probability-based cost functions and compares their performance using an orthogonal frequency-division multiplex example. In this example, the paper shows how a standard physical delay-Doppler scattering channel model can be approximated by the proposed state-space model. The simulations show that significant performance gains can be made by exploiting temporal, as well as diversity channel correlations. The paper argues that such time-recursive receivers offer some advantages over block processing schemes such as computational and memory requirement reductions and the easier incorporation of adaptivity in the receiver structures.     

Impact of diversity reception on fading channels with codedmodulation. II. Differential block detection

For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M⩾2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes are also shown     

Postdetection diversity using differential phase detection forM-ary DPSK

Postdetection diversity that uses L differential phase detector outputs for data decision is described for M-ary differential phase shift keying (M-ary DPSK. Data decision is based on minimising the weighted sum of the errors of L DPD detector outputs. The squared geometric mean of the two consecutively received signal envelope samples is used as the branch weight. The simulation results on average bit error rate (BER) performances due to additive white Gaussian noise (AWGN), multipath Doppler spread, and delay spread of π/4-shift 4DPSK are reported