Blind equalization of turbo trellis-coded partial-response continuous-phase modulation signaling over narrow-band Rician fading channels

In this paper, a blind maximum-likelihood channel estimation algorithm is developed for turbo trellis-coded/continuous-phase modulation (TTC/CPM) signals propagating through additive white Gaussian noise (AWGN) and Rician fading environments. We present CPM for TTC signals, since it provides low spectral occupancy and is suitable for power- and bandwidth-limited channels. Here, the Baum-Welch (BW) algorithm is modified to estimate the channel parameters. We investigate the performance of TTC/CPM for 16-CPFSK over AWGN and Rician channels for different frame sizes, in the case of ideal channel state information (CSI), no CSI, and BW estimated CSI.     

Design of unpunctured turbo trellis-coded modulation

In this paper, the design of newly introduced turbo encoding scheme called ‘Unpunctured Turbo Trellis-Coded Modulation’ (UTTCM) is exposed. The performance improvement of this encoding scheme is obtained by setting a design criterion for each of its components namely: the search rules of best constituent encoders’ generator polynomials, the constellation and the associated mapping. Simulation results show that the optimized UTTCM outperforms TTCM and PCTCM for all considered spectral efficiencies, and presents competitive error floors. As examples, for a spectral efficiency of 3 bits/symbol (bps), UTTCM with 8 decoding iterations outperforms TTCM by 0.05 dB at BER = 10^?4; and for a spectral efficiency of 4 bps and 6 decoding iterations, UTTCM outperforms Fragouli's PCTCM by 0.07 dB at BER = 10^?5.     

EXIT charts for turbo trellis-coded modulation

In this letter, we extend the previously proposed extrinsic information transfer charts (EXIT) method to the analysis of the convergence of turbo codes to turbo trellis-coded modulation (TTCM) schemes. The effectiveness of the proposed method is demonstrated through examples. The proposed method provides a convenient way to systematically compare between schemes and thus can be used as a tool in the design of TTCM.     

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     

Pilot-symbol aided coherent M-ary PSK in frequency-selective fastRayleigh fading channels

Pilot-symbol aided coherent M-ary PSK modems in digital cellular mobile radio systems are analyzed theoretically. The error-floors caused by the Doppler spread in a fast fading channel are removed in both flat and selective fading channels. However, the error-floors caused by the delay spread are lower-bounded by those that exist in the ideal coherent detection. The systems are modeled as frequency-selective fast Rayleigh fading channels, corrupted by co-channel interference (CCI) and additive white Gaussian noise (AWGN). In the proposed scheme, pilot symbols are inserted periodically to monitor the channel characteristics. The fading processes experienced by the pilot symbols are used to estimate those suffered by the data symbols using interpolation or filtering. The estimated fade characteristics are used to compensate the random phase variation caused by the Doppler spread, so that the signals can be demodulated coherently. The theoretical performances of the fade compensated coherent modems are evaluated. The results show that the fade compensated coherent demodulation with the least redundancy achieves the same performance as the ideal differential detection in a fading channel. The performance approaches that of the ideal coherent demodulation as more redundancy is allowed. The pilot-symbol-insertion (PSI) scheme is also applicable to M-ary QAM modems and Rician channels. The residual frequency offset can also be compensated by the PSI technique     

Symbol-interleaver design for turbo trellis-coded modulation

A design method for a code-matched symbol-interleaver for turbo trellis-coded modulation is proposed. The method constructs an interleaver by code matched criteria to eliminate some input error events of low symbol Hamming weight (SHW) sequences of the code which can produce low SHW codewords. Numerical results confirm that the interleaver can lower the error floor at moderate to high signal-to-noise ratio.     

Bandwidth-efficient turbo trellis-coded modulation using puncturedcomponent codes

We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used     

Space-time trellis-coded transmissions with parallel sequences over time-varying channels

In this letter, we investigate the performance of space-time trellis codes in a time-varying channel of a multiple-access wireless system where symbols of a user are transmitted using parallel sequences. Using rank and determinant criteria, it is shown that space-time trellis codes originally designed for quasi-static channels are efficient codes for this system as well. Simulation results demonstrate that the proposed transmission scheme can exploit spatial and temporal diversities to achieve performance gains at practical decoding complexity levels.     

The effects of constellation density on trellis-coded modulation infading channels

Dense constellations such as 16-QAM (quadrature amplitude modulation) have not seen much use in mobile communication because of their greater peak-to-average power ratio and their seemingly greater sensitivity to noise and channel interference. It is demonstrated that dense constellations can actually improve performance. Using a completely analytical method, three constellations are compared with the same net throughput of 2 bits/symbol: uncoded QPSK (quadrature phase-shift keying), rate 2/3 TCM (trellis-coded modulation) 8-PSK and rate 1/2 TCM 16-QAM. Comparison on the basis of average power puts TCM 16-QAM 5-dB ahead of TCM 8-PSK (phase-shift keying). Even comparison on the basis of peak power gives TCM 16-QAM a 2.44-dB advantage over TCM 8-PSK. QPSK is much poorer than either     

Optimum asymmetric constellation design for trellis-coded modulation over gaussian channels

This letter studies the optimization of asymmetric constellations for trellis-coded modulation (TCM). Unlike the conventional criterion of maximizing the free Euclidean distance, the criterion here is to minimize the bit error rate (BER) of TCM systems. The letter presents an easy way to derive the BER upper bound for any TCM codes, and proposes the method for designing optimum asymmetric constellations by minimizing the bound. The given method can be applied to TCM systems with arbitrary state numbers. Numerical results verify that all the codes designed by the proposed method achieve better BER performance than symmetric ones.     

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     

Refined channel estimation for coherent detection of turbo codesover flat-fading channels

Channel state information is required for the coherent detection and decoding of turbo codes transmitted over flat-fading channels. A channel estimation technique suitable for turbo codes is presented. The technique uses pilot symbols to obtain initial channel estimates, and refines the estimates after each iteration of the turbo decoder     

An upper bound on turbo codes performance over quasi-static fading channels

This letter proposes an upper bound on the performance of turbo-codes over quasi-static fading channels. First an upper bound is derived for the case of a single-input single-output channel. The result is then extended to the case of a serial concatenation of a turbo-code and a space-time block code. Unlike a simple extension of the union bound, the derived upper bounds are shown to converge for all signal-to-noise ratios. Additionally the closed form upper bounds obtained confirm analytically that, unlike over additive white Gaussian noise channels, turbo-code performance does not improve by increasing frame length over quasi-static fading channels.     

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     

Linear coherent distributed estimation over unknown channels

We study linear distributed estimation with coherent multiple access channel model and MMSE fusion rule. The flat fading channels are assumed unknown at the fusion center and need to be estimated. We adopt a two-phase approach, which first estimates channels and then estimates the source signal, to minimize the MSE of the estimated signal. We study optimal power allocation under a total network power constraint. We consider the optimal power allocation scheme in which training power and data power for each sensor are optimized, and the equal power allocation scheme in which training power is optimized while data power for each sensor is set equal. In both schemes, the problem is formulated as a constrained optimization problem and analytical closed-form solution is obtained. Analytic results reveal that (i) with estimated channels, the MSE approaches to a finite nonzero value as the number of sensors increases; (ii) the optimal training powers are the same in both schemes; (iii) the MSE performance compared with the case when channels are known shows the penalty caused by channel estimation becomes worse as the number of sensors increases. Simulation results verify our findings.     

M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

Bandwidth‐efficient turbo coding over Rayleigh fading channels

Introduced in 1993, turbo codes can achieve high coding gains close to the Shannon limit. In order to design power and bandwidth‐efficient coding schemes, several approaches have been introduced to combine high coding rate turbo codes with multilevel modulations. The coding systems thus obtained have been shown to display near‐capacity performance over additive white Gaussian noise (AWGN) channels. For communications over fading channels requiring large coding gain and high bandwidth efficiency, it is also interesting to study bit error rate (BER) performance of turbo codes combined with high order rectangular QAM modulations. To this end, we investigate, in this paper, error performance of several bandwidth‐efficient schemes designed using the bit‐interleaved coded modulation approach that has proven potentially very attractive when powerful codes, such as turbo codes, are employed. The structure of these coding schemes, termed ‘bit‐interleaved turbo‐coded modulations’ (BITCMs), is presented in a detailed manner and their BER performance is investigated for spectral efficiencies ranging from 2 to 7 bit/s/Hz. Computer simulation results indicate that BITCMs can achieve near‐capacity performance over Rayleigh fading channels, for all spectral efficiencies considered throughout the paper. It is also shown that the combination of turbo coding and rectangular QAM modulation with Gray mapping constitutes inherently a very powerful association, since coding and modulation functions are both optimized for operation in the same signal‐to‐noise ratio region. This means that no BER improvement is obtainable by employing any other signal constellation in place of the rectangular ones. Finally, the actual influence of the interleaving and mapping functions on error performance of BITCM schemes is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Soft-decision differential phase detection of turbo-coded M-ary CPFSK signals over Ricean channels

The performance of turbo codes is examined over the Ricean fading channel with soft-decision differential phase detection (DPD). M-ary continuous phase frequency-shift keying (CPFSK) signaling and puncturing of the coded sequence are considered to achieve bandwidth efficient communication. The effects of the number of phase decision regions, fading conditions, number of states of the constituent codes, and code rate are examined. A bit error rate upper bound is developed, which is useful at low values of bit error probability where computer simulations are lengthy. Significant gains using soft-decision DPD over hard-decision DPD and conventional noncoherent detection are reported.     

Bit-interleaved turbo equalization over static frequency-selective channels: constellation mapping impact

The purpose is to assess the performance of bit-interleaved turbo equalization (TE) over static frequency-selective channels. The asymptotic performance is therefore first pointed out, emphasizing the fundamental role played by the constellation mapping. This specific feature is then further analyzed using the extrinsic information-transfer chart technique, leading to an efficient optimization tool. This finally enables showing that bit-interleaved TE can outperform its symbol-interleaved counterpart.