Error bounds for trellis-coded MPSK on a fading mobile satellitechannel

Analytical performance bounds are presented for trellis-coded MPSK, transmitted over a satellite-based land mobile channel. Upper bounds are evaluated using the well-known transfer function bounding technique, and lower bounds are achieved through knowledge of exact pairwise error probabilities. In order to analyze practical trellis-codes (four or more states), the uniform properties displayed by a certain class of trellis-codes are exploited, enabling the encoder transfer function to be obtained from a modified state transition diagram, having no more states than the encoder itself. Monte Carlo simulation results are presented in confirmation of all performance bounds and indicate a general weakness in the transfer function upper bounds. A new asymptotically tight upper bound is derived based on a simple modification to the standard transfer function bound, and results are presented for the four- and eight-state trellis-codes in Rician and Rayleigh 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     

Error performance of MPSK trellis-coded modulation overnonindependent Rician fading channels

This paper presents new upper bounds on the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over nonindependent Rician fading channels. Cases considered are coherent and pilot-tone-aided detection and differential detection of trellis-coded multilevel phase-shift keying (TC-MPSK) systems. The average bit-error probability P_b can be approximated by truncating the union bound. This method does not necessarily lead to an upper bound on P_b, and, hence, the approximation must be used with simulation results. In addition, for Rayleigh fading channels with an exponential autocovariance function, bounds resembling those for memoryless channels have been derived. The bounds are substantially more accurate than Chernoff bounds and hence allow for accurate estimation of system performance when the assumption of ideal interleaving is relaxed     

Analysis of multidimensional trellis-coded MPSK in Rice-lognormalfading channels

The paper addresses the analysis of multidimensional trellis-coded M-ary phase shift keying (MPSK) modulation over a Rice-lognormal fading channel model, applicable to a variety of environments and to both terrestrial and satellite mobile communications. Bounds to the bit error probability are derived and applied to the analysis of a few selected trellis-coded modulation (TCM) schemes. The results, confirmed by simulation, show that on the Rice channel there exists a threshold in bit energy-to-noise density ratio above which the effective code length is the dominant parameter, while the free distance is dominating below. However, the influence of both parameters is mitigated when shadowing is present     

Noncoherent detection for trellis-coded MPSK

This letter shows several methods for improving the decoding of noncoherent trellis-coded M-ary phase-shift keying. We propose two new metrics for the basic decision-feedback algorithm. These metrics are derived based on the idea of reducing the effect of incorrect amplitude of the reference signal. We also propose a new decoding algorithm that uses a simple way to estimate the metric of the future sequence     

Sequential sequence estimation for trellis-coded modulation onmultipath fading ISI channels

A new receiver structure is proposed for trellis-coded modulation on multipath fading intersymbol interference (ISI) channels that permits the use of large-state trellis codes. The receiver uses a sequential sequence estimator with the Fano algorithm, and a channel estimator consisting of a fast nonrecursive start-up algorithm for training and the LMS algorithm for tracking. During the tracking mode, the channel estimates are updated dynamically by using recent tentative decisions produced by the sequential sequence estimator. This approach results in good tracking even on rapidly varying channels, and reduces the degradation in performance of the sequential sequence estimator due to channel estimation error. The effect of fading is mitigated using both implicit time diversity in the form of interleaved trellis-coded modulation and explicit antenna diversity     

A trellis-coded DS-CDMA system in correlated Rayleigh fading channels

We present the trellis-coded code-division multiple-access (TC-CDMA) system based on a multisequence signaling, called orthogonal plane sequence modulation (OPSM), in correlated Rayleigh fading channels and derive its pairwise error probability with different degrees of channel state information. Numerical results show that the OPSM-based TC-CDMA system outperforms conventional convolutionally coded CDMA or TC-CDMA systems.     

Adaptive reception of MPSK on fading channels

An adaptive estimator of the complex gain of a fading channel is proposed. Tracking of the fading process is achieved without knowledge of the fading spectrum. This enables coherent detection of MPSK to be performed. Simulations show good error rate performance. The receiver finds applications in mobile radio communications     

Bit-error probability analysis of linear receivers for CDMA systemsin frequency-selective fading channels

The bit-error probability of a linear receiver for code-division multiple-access communications is analyzed. The analysis is presented for the additive white Gaussian noise and fading multipath channels also with data-aided channel estimation. Two ways to approximate the averaging over the interfering data symbol combinations are considered and compared. Numerical examples are presented to demonstrate the usefulness of the analysis methods     

Iterative MMSE receivers for space-time trellis-coded CDMA systems in multipath fading channels

We explore code-division multiple-access (CDMA) systems with multiple transmit and receive antennas combined with space-time trellis codes over a frequency-selective channel. The conventional noniterative multiuser minimum mean square error (NIMU-mmse) detector is generalized to accommodate multiple antennas and multiple paths and then extended to include the turbo principle in an iterative fashion, allowing interference regeneration and cancellation at the receiver. Iterative multiuser mmse (IMU-mmse) receivers employing chip- and symbol-level detectors are derived and their equivalence is demonstrated. Computer simulations show that the proposed iterative mmse equalizers completely remove the interference of the other users in a multiantenna environment; they provide a significant improvement over the NIMU-mmse detector and they effectively achieve the single-user performance, even in a fully loaded system. Two suboptimal iterative mmse detectors, which allow a computational complexity reduction of up to three orders of magnitude compared to the IMU-mmse and still outperform the NIMU-mmse detector, are introduced. The proposed iterative mmse equalizers are analyzed and supported by extensive computer simulations.     

Suboptimum Viterbi algorithm for trellis-coded QAM scheme inmultipath Rayleigh fading channels

A new suboptimum Viterbi algorithm for trellis-coded quadrature amplitude modulation based on the channel state information of the multipath Rayleigh fading channel is proposed. Simulation results show that the proposed algorithm has merits for applications that require low bit energy-to-noise ratio     

Evaluation of the exact union bound for trellis-coded modulationsover 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     

Bit-error rate of binary digital modulation schemes in generalized gamma fading channels

We derive a closed-form expression for the bit-error rate of binary digital modulation schemes in a generalized fading channel that is modeled by the three-parameter generalized gamma distribution. This distribution is very versatile and generalizes or accurately approximates many of the commonly used channel models for multipath, shadow, and composite fading. The result is expressed in terms of Meijer's G-function, which can be easily evaluated numerically.     

A performance analysis of trellis-coded modulation schemes overRician fading channels

This paper presents a saddle point approximation (SAP) method to compute the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over Rician fading channels. The approximation is applicable under several conditions, such as finite and ideal interleaving, ideal coherent and pilot-tone aided detection, and differential detection. The accuracy of this approximation is demonstrated by comparison to the results of numerical integration. When ideal interleaving is assumed, an asymptotic approximation for the PEP of ideal coherent, pilot-tone aided or differentially detected TCM is derived. This asymptotic approximation of the PEP is in a product form and much tighter than the ordinary Chernoff bound on the PEP. Also, based on the SAP, the effect of finite interleaving depth on the error performance of TCM schemes over Rician and shadowed Rician channels is studied     

A noncoherent receiver for interleaved trellis-coded CPFSK signalstransmitted over frequency-flat fading channels

We propose a novel two-stage noncoherent receiver for interleaved trellis-coded CPFSK signals transmitted over time-selective channels. The first stage of the receiver computes reliability information about the transmitted symbols and delivers it to the second stage which operates as a trellis decoder. Simulation results show that the proposed detection strategy outperforms previous noncoherent receivers with a moderate increase in complexity     

The design of trellis coded MPSK for fading channels: performancecriteria

It has been well established that the appropriate criterion for optimum trellis-coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. It is shown that when the trellis-coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code of optimum performance is guided by other factors, in particular, the length of the shortest error-event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along the path. Although maximum free distance (d_free) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing d_free      

Performance of interleaved trellis-coded differential 8-PSKmodulation over fading channels

The performance of trellis-coded differential octal phase-shift keying (coded 8-DPSK) with differentially coherent detection and soft-decision Viterbi decoding is investigated. A suitable receiver is presented whose signal processing is based on Nyquist signaling, requiring only one complex sample per modulation interval. Symbol synchronization and automatic frequency control are performed in a decision-directed way. Bit-error-rate (BER) performance over Gaussian, Rayleigh, and Rician channels is determined by means of computer simulations. The performance of coded 8-DPSK on the Gaussian channel is shown for a four-state convolutional trellis code. The unquantized outputs of up to three symbol detectors with delays of 1, 2, and 3 symbol periods are used for metric computation. The coding gain which includes losses due to timing and frequency synchronization errors is found to be 2.5 dB at BER=10^-5 with respect to uncoded 4-DPSK. Much larger gains are achieved for fading channels if interleaving is applied. Using an eight-state trellis code the performance is determined on Rayleigh and Rician channels for various Doppler spreads and interleaver sizes     

Error performance of interleaved trellis-coded PSK modulations incorrelated 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     

Error probability of coherent detection for trellis-coded partialresponse CPM on Rician fading channels

Trellis-coded continuous phase modulation (TC-CPM) schemes are attractive for bandwidth and power limited communication systems such as mobile satellite communications and land mobile radio communications. A coherent receiver for interleaved partial response TC-CPM is derived. A true upper bound on the bit error probability for flat fading channels is derived by showing that TC-CPM is equivalent to a trellis-coded modulation scheme. The upper bound is evaluated by defining an error-state diagram along with a set of characteristic distances and then applying transfer function bounding techniques. Comparison with simulation results shows the upper bound tight to within 1.5-2 dB     

Adaptive reception of MPSK signals in fast fading and AWGN channels

The author describes the adaptive Viterbi coherent detection (AVCD) of MPSK signals. The adaptive LMS channel estimation used requires no knowledge of channel statistical properties. The simulated BER performances in fast Rayleigh fading and AWGN channels are reported