Probability of error analysis of digital partial response continuous phase modulation with two bit differential detection and offset receiver diversity in fast Rayleigh fading

Summary form only given. Future mobile radio systems are expected to provide high-quality voice and high-speed data transmission and to be integrated into the digital communication networks in several countries. The performance of some digital modulation techniques that are relevant for future mobile radio systems is studied. These techniques are characterized by having a constant envelope signal to reduce the effect of nonlinearity and fading and a compact RF power spectrum to reduce adjacent channel interference. Most digital partial-response continuous-phase modulation (PRCPM) techniques such as 2 RC, 2 SRC, 2 RC, 3 SRC, GMSK, and GTFM have the above properties. Discriminator detection of these techniques is analyzed in fast Rayleigh fading characterizing land mobile radio channels. Approximate closed-form expressions for the probability of error are derived and numerical results are presented for land mobile radio systems. >

This paper considers the performance of a speech transmission scheme with application to cellular digital mobile radio systems. The source coder is embedded DPCM and modulation scheme belongs to a class of Partial Response Continuous Phase Modulation Both quantizing noise and transmission errors contribute to the overall mean squared error. The performance measure is audio signal to noise ratio. It is seen that in a fading environment space diversity is very effective in bringing down the threshold of channel signal to noise ratio to maintain the required audio signal to noise ratio. The number of channels the system can support is evaluated under various conditions.

The complexity of the multiple-symbol detection structures for partial response continuous phase modulation (CPM) signals goes exponentially with the length of the pulse shaping filter and the observation length as well. Simple no coherent trellis receivers for partial response CPM signals are proposed in this paper. Parallel to the simple coherent detectors, where CPM signals are approximately represented by a sum of Phase Amplitude Modulation waveforms, Laurent decomposition is applied to reduce the complexity. The proposed no coherent receiver is structured with only fixed K matched filters in the front-end and a processor which uses Viterbi algorithm with a 2N-1 states trellis to perform the sequence estimation. It is attractive because the structure does not involve any matrix calculations. The good error performance is confirmed by simulation results.

Coding for the fading channel: a survey

Recently, the differential detection scheme has attracted considerable attention as a demodulated scheme for digital mobile communications because of its robustness in the frequency nonselective fading channel. A problem of the differential detection scheme is that its bit error rate (BER) performance in the additive white Gaussian noise (AWGN) channel is inferior to that of the coherent detection scheme. To solve this problem, many methods to improve BER performance of the differential detection in the AWGN channel have been proposed. However, those methods require complex signal processings.This paper proposes a novel differential detection scheme as a simpler improvement method which estimates the differential phase of the transmitted signal by a sequence estimation scheme using the Viterbi algorithm. The proposed scheme is simplified in a manner such that its signal processing is composed of only additions and subtractions on the phase information of the received signal. Results of computer simulation show that BER performance of the proposed scheme is close to that of the ideal coherent detection in the AWGN channel. In addition, the trellis diagram of the Viterbi algorithm can be reduced without performance degradation introducing the signal processing similar to the Scarece State Transition (SST) type Viterbi decoding. The proposed scheme also is useful in the case of the fast Rician fading channel and the slow Rayleigh fading channel.

Multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets (MTCM/FPM) is investigated for performance on the additive white Gaussian noise (AWGN) channel and on the one-sided normal, Rayleigh and Rician fading channels. The Nakagami-m fading model is used as an alternative to the Rician fading model to calculate the error probability upper bound for trellis-coded schemes on the fading channel. The likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed. The design criteria for the one-sided normal fading channel, modeled by the Nakagami-m distribution, are observed to be the same as those for the Rayleigh-fading channel. For the MTCM/FPM schemes, it is demonstrated that the set partitioning designed to maximize symbol diversity (optimum for fading channels) is optimum for performance on the AWGN channel as well. The MTCM/FPM schemes demonstrate improved performance over MTCM/MPSK schemes and TCM/FPM schemes on the AWGN channel and the fading channel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Star 16QAM is a modulation method that transmits 4 bits per symbol and has the advantage that it may be differentially encoded and detected. It is very robust to fast multiplicative Rayleigh fading and is suitable for mobile telephone systems and personal communication networks. The main contribution of this paper is the derivation and bit error probability simulation of the maximum likelihood differential detector using phase differences and amplitude ratios from L diversity branches for bit decisions. As a comparison, much simpler previously known post detection combining techniques are generalized for star 16QAM and optimized. The bit error probability is simulated for both diversity detectors on a multiplicative Rayleigh fading channel with additive white Gaussian noise. It is found that the bit error probability of the ML detector may also be obtained by the simple combining detector. This is also true for the error floor due to the maximum Doppler frequency. The diversity gain is almost 8 dB, measured in signal to noise ratio per diversity branch, at a bit error probability of 1 percent. The diversity detector can sustain an almost 3 times larger Doppler frequency again at a bit error probability of 1 percent. We also show that star 16QAM offers, at most, 3 subchannels with different bit error probabilities. >

A differentially coherent receiver which uses the Viterbi algorithm is presented. This receiver compensates for intersymbol interference (ISI) and avoids noise enhancement. A phase estimate which takes into account the presence of inherent ISI in the signal is derived. This phase estimate is then used in the decision metric of a coherent receiver. The resulting decision rule can be implemented using the Viterbi algorithm. The complexity of the resulting receiver increases with the duration of observation used by the implicit phases estimator. A simple four-state Viterbi receiver with good performance is obtained when the phase estimate is based on one observable. Simulation results are given. >

This paper presents asymptotic multiuser efficiency (AME) performance analysis of the decorrelator based successive interference cancellation (DBSIC) DS-CDMA multiuser receiver DBSIC is similar to the conventional SIC receiver except that a decorrelator is used at each detection stage prior to cancellation. AMEs of DBSIC are compared with those of single-user matched filter, optimum, decorrelating and conventional SIC receivers over both additive white Gaussian noise (AWGN) and Rayleigh fading channels. It is shown that over AWGN channels, DBSIC AME is lower than the optimum receiver AME when the interfering user is weaker than the user of interest but approaches the unity optimum receiver AME as the interferer becomes stronger than the user of interest. For all spreading codes cross-correlation considered, DBSIC has a similar AME curve shape as the conventional SIC receiver but has a higher AME which remains positive for all user energy ratios, illustrating its near-far resistance over AWGN channels. The AME of DBSIC is better than that of the decorrelating detector when the interferer is much weaker or slightly stronger than the user of interest and has worse performance when the interferer is not much weaker. It is shown that DBSIC is completely near-far resistant over Rayleigh fading channels with the same AME as the decorrelating scheme for user 1 and as the optimum scheme for user 2, both AMEs being independent of the user energy ratio. This shows that DBSIC is preferable compared to the decorrelating detector, while still being less complex than the optimum scheme over Rayleigh fading channels

This correspondence analyzes the performance of concatenated coding systems and modulation schemes operating over the additive white Gaussian noise (AWGN) channel by examining the loss of capacity resulting from each of the processing steps. The techniques described in this correspondence allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. Knowledge of this capacity loss is very useful for the overall design of a communications system, e.g., for evaluating the benefits of inner decoders that produce information beyond the maximum-likelihood (ML) estimate. The first two sections of this correspondence provide a general technique for calculating the composite capacity of an orthogonal or a bi-orthogonal code and the AWGN channel in isolation. The later sections examine the composite capacities of an orthogonal or a bi-orthogonal code, the AWGN channel, and various inner decoders including the decoder estimating the bit-by-bit probability of a one, as is used in turbo codes. The calculations in these examples show that the ML decoder introduces a large loss in capacity. Much of this capacity loss can be regained by using only slightly more complex inner decoders, e.g., a detector for M-ary frequency-shift keying (MFSK) that puts out the two most likely frequencies and the probability the ML estimate is correct produces significantly less degradation than one that puts out only the most likely frequency.

Modulo lattice additive noise (MLAN) channels appear in the analysis of structured lattice codes with lattice decoding for Costa's dirty-paper channel and the additive white Gaussian noise (AWGN) channel. Building on the recent result on the optimal density of an infinite constellation over an AWGN channel, in this paper, it is shown that with a proper choice of the shaping lattice and the scaling parameter, the dispersion of the MLAN channel is asymptotically the same as that of the (zero-interference) AWGN channel at the same signal-to-noise ratio.

The joint optimization of partial response continuous phase modulation (CPM) parameters is addressed. For fixed modulation order and memory length, the modulation index, the symbol rate and the phase pulse shape are considered as degrees of freedom. In particular, we drop the restriction of “classical” phase pulses and we allow for custom shapes, which are parametrized through Bezier curves. In order to deal with the many variables involved, an evolutionary algorithm is employed for numerical optimization. The optimization metric is related to the extrinsic information transfer (EXIT), under the assumption that CPM is serially concatenated with an outer convolutional encoder, as it is the case for several practical systems. The presence of high adjacent channel interference (ACI) is explicitly accounted for in the optimization process. We show that the proposed optimization strategy can effectively exploit the power-bandwidth trade-off. Nevertheless, only moderate improvements are achievable in comparison to state-of-the-art serially concatenated systems.

In the previous two chapters, we studied specific techniques for communication over wireless channels. In particular, Chapter 3 is centered on the point-to-point communication scenario and there the focus is on diversity as a way to mitigate the adverse effect of fading. Chapter 4 looks at cellular wireless networks as a whole and introduces several multiple access and interference management techniques. The present chapter takes a more fundamental look at the problem of communication over wireless fading channels. We ask: what is the optimal performance achievable on a given channel and what are the techniques to achieve such optimal performance? We focus on the point-to-point scenario in this chapter and defer the multiuser case until Chapter 6. The material covered in this chapter lays down the theoretical basis of the modern development in wireless communication to be covered in the rest of the book. The framework for studying performance limits in communication is information theory . The basic measure of performance is the capacity of a channel: the maximum rate of communication for which arbitrarily small error probability can be achieved. Section 5.1 starts with the important example of the AWGN (additive white Gaussian noise) channel and introduces the notion of capacity through a heuristic argument. The AWGN channel is then used as a building block to study the capacity of wireless fading channels. Unlike the AWGN channel, there is no single definition of capacity for fading channels that is applicable in all scenarios.

Two three‐dimensional (3D) 16‐ary signal constellations having extended lattice structures are presented in this paper. The theoretical symbol error probabilities (SEPs) of the new constellations in additive white Gaussian noise (AWGN) and Rayleigh fading channel are derived. Computer simulation confirms that the closed‐form expressions for average SEPs of the constellations in the AWGN channel are very accurate. The theoretical SEP upper bounds in the Rayleigh fading channel are very tight. Since the presented constellations have larger minimum Euclidean distance (MED) than the conventional one, error performance can be improved up to 0.9 dB in an AWGN environment. Hence, the proposed constellations and their theoretical analysis can be used as a reference for the development of a wireless communication system with 3D signal constellations.

Evaluation of error rate of a digital communication system is usually done using the Monte Carlo simulation method. The main drawback of the Monte Carlo method is the need of a huge sample size for estimating low error rates. This paper introduces a novel quasi-analytical technique for estimating the error rate of a communication link over an Additive White Gaussian Noise (AWGN) channel, which greatly outperforms the Monte Carlo method. This technique is demonstrated for a simple spherical code.