Pairwise Error Event Probability Research Articles

Multiple-Trellis-Coded Unitary Space-Time Modulation in Rayleigh Flat Fading

We propose and investigate a multiple-trellis-coded unitary space-time modulation (MTC-USTM) for a Rayleigh-flat-fading channel, where k/spl ges/2 unitary space-time signal blocks are assigned to a single branch in the trellis. We have also evolved design criteria which are aimed at minimizing the pairwise error-event probability (PEP) and a partitioning scheme for the k-fold Cartesian product of the UST signal set for MTC-USTM. We demonstrate through simulations as well as theoretical analysis that MTC-USTM can produce superior bit-error probability performance over the trellis-coded USTM (single signal per branch) of the same information rate and number of states, especially in the region of high signal-to-noise ratio.

On performance analysis and design criteria for trellis coded unitary space-time modulation

In this letter, we present formulas for the pairwise error-event probability (PEP) and bit error probability (BEP) of trellis-coded unitary space-time modulation (TC-USTM) operated in a piecewise constant Rayleigh fading channel. From these analyses we discovered design criteria for the TC-USTM encoder to achieve an optimal BEP performance. We conduct simulations and verify that our analyzes are accurate, especially at high signal-to-noise ratio (SNR).

Rotated TCM systems with dual transmit and multiple receive antennas on Nakagami fading channels

This paper analyzes the bit-error rate performance of a dual transmission-multiple reception antenna system in conjunction with a rotated trellis-coded modulation scheme over Nakagami fading channels. A simple way to combine the exact calculation of the pairwise error event probability with the transfer function bounding techniques is described. This approach allows us to evaluate an extremely tight theoretical upper bound on the average bit-error probability. The parameters which dominate the performance of these transmission schemes on fading channels are extracted from this evaluation. Optimum adaptive and fixed-phase rotations have been calculated, showing that most of the power efficiency obtained by using the optimum adaptive-phase rotation can be retained by using the optimum fixed-phase rotation.

Bit Error Probability of an Interleaved Convolutional Coded BPSK Signal Over a Correlated Fading Channel

This paper analyzes the performance of an interleaved convolutional coded BPSK with perfect channel state information and coherent detection, assuming perfect synchronization. Analytical results for the pairwise error event probability using the characteristic function technique is derived. An approximate bit error probability is obtained by summing the probabilities of the dominant error events.

Performance analysis and design of pilot-symbol aided TCM for a Rayleigh fading channel

A Chernoff bound is derived on the pairwise error event probability of pilot-symbol aided TCM schemes with L-fold space diversity in a Rayleigh fading channel. In the scheme, pilot-symbols are inserted periodically to estimate the channel characteristics. The fading processes experienced by the pilot-symbols are used to estimate those suffered by the data symbols using interpolation. The estimated fading characteristics are used to compute the symbol metrics of the Viterbi decoder. With the Chernoff bound derived, the cutoff rate of 16QAM and the bit error probability (BEP) of the trellis coded 16QAM scheme are calculated as a function of the signal-to-noise ratio (SNR) and the Doppler shift. New trellis codes are constructed according to the proposed design rule and are shown to result in a performance improvement over the conventional trellis code.

Combined Space Diversity Reception and Trellis Coding for Rayleigh Fading Channels

Space diversity reception, in which several signals received at different antennas are combined, is a well known method that can be used to combat the effects of fading in wireless systems. Also, trellis coded modulation (TCM), when combined with interleaving of sufficient depth, is known to provide some form of time diversity that allows the achievement of good error performance in fading environments. In this paper we consider the analysis of the error performance of reference-based Maximal Ratio Combining (MRC) systems when used in conjunction with trellis-coded MPSK modulation techniques over a Rayleigh fading channel. We also consider the analysis of MRC trellis-coded MPSK systems with conventional differential detection. The results are obtained by using a combination of theoretical analysis and simulation. Exact and near-exact expressions for the pairwise error-event probability in Rayleigh fading are derived. Monte-Carlo simulation results, which are more indicative of the exact system performance, are also given.

Analysis of the pairwise error probability of noninterleaved codes on the Rayleigh-fading channel

The majority of previous analytical studies of signal-space coding techniques (includes trellis and block codes) on the Rayleigh-fading channel have assumed ideal interleaving. The effect of finite interleaving on the performance of different coding schemes has been studied only by simulation In this paper we first derive a maximum likelihood (ML) decoder for codewords transmitted over a noninterleaved Rayleigh flat fading channel, followed by an exact expression for the pairwise error event probability of such a decoder. It includes phase shift keying (PSK), quadrature amplitude modulation (QAM) signal sets, trellis coded modulation (TCM) and block coded modulation (BCM) schemes, as well as coherent (ideal channel state information) and partially coherent (e.g., differential, pilot tone, etc.) detection. We derive an exact expression for the pairwise event probability in the case of very slow fading-i.e., the fading experienced by all the symbols of the codeword is highly correlated. We also show that the interleaving depth required to optimize code performance for a particular minimum fading bandwidth can be approximated by the first zero of the fading channel's auto-correlation function.

Evaluation of the exact union bound for trellis-coded modulations over fading channels

An analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over Rayleigh, Rician, or shadowed Rician-fading channels. To this end, an integral expression is derived for the pairwise error event probability (PEP). Existing bounds can be obtained as special cases of this expression. It turns out that a Gauss-Chebyshev quadrature rule offers excellent accuracy for this integral. By extension, the exact union bound (i.e., the weighted sum of an exact PEPs of a code) can readily be evaluated. This method has the same complexity as the union-Chernoff bound, and a few examples are given to show its application.

Soft information transfer for sequence detection with concatenated receivers

Concatenated encoders are found in many digital communication systems. A concatenated receiver for such a system consists of a chain of independently working estimators ended with an outer detector. Each stage of the receiver chain corresponds to a certain code in the system. Maximum likelihood sequence detection with a concatenated receiver requires soft information consisting of symbol aposteriori probabilities to be transferred between the receiver stages. In this paper the optimal inner estimator is derived and further simplified into a new asymptotically optimal one by imposing a tree structure on the inner code. By mapping several suboptimal inner estimators onto the tree structure and noting which approximations they make, a theoretical performance ranking is obtained. The asymptotical performance of the optimal concatenated detector at high signal-to-noise ratios (SNRs) is investigated. The decision variables underlying the pairwise error event probability are shown to be asymptotically Gaussian and consequently a free Euclidean distance can be found for the optimal concatenated detector.

Analysis of the error performance of trellis-coded modulations in Rayleigh-fading channels

This work presents an exact expression for the pairwise error event probability of trellis-coded modulation (TCM) transmitted over Rayleigh-fading channels. It includes phase shift keying (PSK) and multilevel quadrature amplitude modulation (QAM) codes, as well as coherent and partially coherent (e.g. differential, pilot tone, etc.) detection. Due to the form of the exact pairwise error event probabilities, this calculation technique cannot be used with the transfer function technique to obtain an upper (union) bound on the overall bit error probability. For this reason, the authors estimate the bit error probability by considering only a small number of short error events. Through simulations, they found that the estimation is usually very accurate at high signal-to-noise ratios but not as accurate at lower signal-to-noise ratios. They study several coded modulation schemes this way. Among the results are the fact that TCM provides significant improvement in the error floor when detected differentially, and an asymmetry in the pairwise error event probability for 16 QAM.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Error performance of multiple-symbol differential detection of PSK signals transmitted over correlated Rayleigh fading channels

The error performance of multiple-symbol differential detection of uncoded QPSK signals transmitted over correlated Rayleigh fading channels is studied. The optimal detector is presented, along with an exact expression for the corresponding pairwise error event probability. It is shown that multiple-symbol differential detection is a very effective strategy for eliminating the irreducible error floor associated with a conventional differential detector. In all of the cases investigated, a detector with an observation interval as small as two symbols is sufficient for this purpose. It is also found that the error performance of a multiple-symbol differential detector is not sensitive to the mismatch between the decoding metric and the channel fading statistics. >

Error performance of interleaved trellis-coded PSK modulations in correlated Rayleigh fading channels

The authors derive an exact and easily computed expression for the pairwise error event probability of interleaved coded PSK modulations transmitted over channels with correlated Rayleigh flat fading and additive white Gaussian noise. Both coherent and differential detection are considered. In the case of coded DPSK, it is found that full interleaving does not necessarily provide the best error performance, especially when the fading is relatively fast and when the autocorrelation function of the channel fading process exhibits an oscillating behavior. For coherent detection or for differential detection in channels with relatively slow fading, increasing the interleaving depth always improves the error performance. In these cases, an interleaving depth equivalent to one-fifth to one-quarter the duration of a fade cycle is almost as good as full interleaving.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>