Uncoded Modulation Research Articles

Product coded modulation

This paper presents a new and powerful technique for constructing MPSK block modulation codes using product codes as the basic building blocks. Basic multilevel block modulation codes turn out to be a special case of this construction. Codes are constructed for both the AWGN and the Rayleigh fading channel and compared with the existing basic multilevel block modulation codes. Conditions on phase invariance of these codes are derived and two sub-optimal decoding schemes for these codes are proposed. Analytical performance bounds and simulation studies show that these codes perform very well and achieve significant coding gains over uncoded reference modulation systems. >

Multidimensional trellis coded phase modulation using a multilevel concatenation approach .II. Codes for the AWGN and fading channels

For pt.I see ibid., vol.45, no.1, p.64-72, 1997. We use the construction technique proposed in part I to construct multidimensional trellis coded modulation (TCM) codes for both the additive white Gaussian noise (AWGN) and the fading channels. Analytical performance bounds and simulation results show that these codes perform very well and achieve significant coding gains over uncoded reference modulation systems. In addition, the proposed technique can be used to construct codes which have a performance/decoding complexity advantage over the codes listed in literature.

A sequential soft-decision decoder for Reed-Solomon codes applied to encoded PSK in Rayleigh-fading channels

A soft-decision stack algorithm with a variable-bias-term branch metric and accurate channel state information estimate is applied to a Reed-Solomon-encoded phase-shift keying (PSK) system in the presence of memoryless Rayleigh fading. To compensate for the variable decoding delay inherent in sequential decoding algorithms, a time-out mechanism is used by the inner decoder: if a time-out occurs before complete decoding of a given block, the decoder declares an erasure. An erasures-and-errors correction decoding algorithm is implemented at the outer decoder to recover any incorrect or incompletely decoded inner code words. Simulation results show that significant improvement over uncoded modulation can be achieved with this approach with moderate cost in decoding complexity.

Symbol-aided channel estimation with nonselective Rayleigh fading channels

New algorithms are proposed to implement coherent detection of PSK signals transmitted over frequency-flat Rayleigh channels. Channel gain estimates are derived both from known symbols multiplexed with the data stream and from tentative data decisions. The performance of these algorithms is assessed by computer simulation with uncoded and trellis-coded modulation. Comparisons are also made with differentially coherent detection (DPSK) and with perfect coherent detection (corresponding to ideal knowledge of the fading process). Simulation results demonstrate that these algorithms can track adequately the severe fading fluctuations encountered on a Rayleigh channel and that their superiority over DPSK becomes impressive with fast fading.

Coding and modulation schemes for slow fading channels

Two new schemes are presented to improve the error performances of coding and modulation on slow fading channels. The first scheme consists of permuting coordinates of multidimensional modulation and trellis coded modulation (TCM) on interleaved channels. Theoretical and simulation results show that this simple permutation may provide gains of 3.8 dB on slow Rayleigh fading channels for uncoded modulation. It also improves by 5 dB the performance of fully interleaved 16-QAM TCM. The second scheme consists of using coded frequency diversity. Without bandwidth expansion, the signal is spread over different independent fading channels. For two very slow fading channels, where interleaving is impractical and coding usually does not provide any gain, coded diversity and 16-QAM TCM provides gains of 13 dB at a BER of 10/sup -4/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Per-Survivor Processing: a general approach to MLSE in uncertain environments

Per-survivor processing (PSP) provides a general framework for the approximation of maximum likelihood sequence estimation (MLSE) algorithms whenever the presence of unknown quantities prevents the precise use of the classical Viterbi algorithm. This principle stems from the idea that data-aided estimation of unknown parameters may be embedded into the structure of the Viterbi algorithm itself. Among the numerous possible applications, the authors concentrate on (a) adaptive MLSE, (b) simultaneous trellis coded modulation (TCM) decoding and phase synchronization, (c) adaptive reduced state sequence estimation (RSSE). As a matter of fact, PSP is interpretable as a generalization of decision feedback techniques of RSSE to decoding in the presence of unknown parameters. A number of algorithms for the simultaneous estimation of data sequence and unknown channel parameters are presented and compared with techniques based on the use of tentative decisions. Results for uncoded modulations over interSymbol interference (ISI) fading channels and joint TCM decoding and carrier synchronization are presented. In all cases, it is found that PSP algorithms are clearly more robust than conventional techniques both in tracking a time-varying channel and acquiring its characteristics without training. >

Power spectrum of block-coded modulation

The power density spectrum of block-coded modulated signals is computed. Sufficient conditions for this spectrum to be the same as for uncoded modulation are derived. In the special case of a PSK-based-scheme, necessary conditions are derived in order to achieve spectrum shaping. The spectral lines obtained may be used for block synchronization. >

Optimum modulation and diversity for DS-SS communication over Rayleigh fading channels subject to pulse burst interference

Results of optimum modulation and coding for MPSK and MDPSK signals transmitted over fading channels and subject to high level interference are presented. The author uses the exact expressions of the probability of error for the uncoded M-ary modulations. However, the analysis of optimum diversity (repetition code) is carried out by a Chernoff bound approximation. Simple expressions are derived to determine the optimum modulation and diversity in terms of the channel parameters. To examine the validity of approximations used throughout, exact analysis of the coded bit-error rate is found numerically, and the results are compared. It is concluded that the exact and the Chernoff bound analysis yield the same results for the optimum modulation and coding and there exist an optimum modulation and coding for each value of signal-to-noise ratio. The results are particularly useful for power and bandwidth limited channels.

A bit error probability analysis of a digital PLL based demodulator of differentially encoded BPSK and QPSK modulation

Presents a bit error probability analysis of a digital phase-locked loop based demodulator, of differentially encoded BPSK and QPSK modulations. Differential decoding is a method of resolving a phase ambiguity, typical of fully modulated signals, that uses two consecutive demodulated symbols to estimate the information symbols. The effects of a noisy phase reference on demodulator performance are well documented for uncoded modulations (single symbol demodulation). The paper investigates performance for phase reference time variations between the two symbols. The time varying reference investigated is produced by a digital phase-locked loop. The noisy phase reference has negligible additional effect on the bit error probability for differentially encoded BPSK and QPSK. >

Trellis coding of quadrature frequency/phase modulated signals

The authors explore the trellis coding of continuous-phase quadrature frequency/phase modulated (CPQFPM) signal sets and continuous-phase FPM (CPFPM) signal sets, which are embodiments of the quadrature biorthogonal modulation (QBOM) technique. Conventional TCM and multiple TCM schemes with these modulation formats are examined using both the AWGN channel and the Rician fading channel design. Asymptotic coding gains in d/sup 2/(free) are tabulated for trellis-coded rate 3/4, 5/6, and 6/7 QFPM schemes, in comparison with uncoded modulations (8AMPM, 32AMPM) and other trellis-coded modulations (TCM (2FSK/4PSK 16QAM, 64QAM), MTCM (2FSK/8PSK)) of equivalent throughput rate. Performance gains on the Rician fading channel are demonstrated by increased values of the design parameters for this channel, namely symbol diversity L/sub min/ and branch distance product P. >

Combined coding and precoding for PAM and QAM HDSL systems

A system is described for high-speed digital subscriber line (HDSL) applications. It uses trellis coding combined with Tomlinson (1971) precoding. Theoretical performance results are provided for uncoded pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) assuming an ideal decision feedback equalizer (DFE) that includes an optimum feedforward filter. The similarities and differences in behavior are explained. It is shown that combined coding and Tomlinson precoding can achieve the equalization performance of the DFE and full coding gain of the trellis code. Simulation results are given to show that about 3.4 dB additional margin is obtained by using a four-dimensional eight-state trellis code. The receiver complexity is increased by it is quite manageable. >

Phase jitter sensitivity of rotationally invariant 8 and 16 point trellis codes

Prabhu examined the sensitivity of uncoded PSK modulations to carrier phase jitter. A Gaussian phase jitter model was assumed. The same study is conducted for trellis coded PSK and QAM modulations. Rotationally invariant codes are considered and an explicit design procedure is included. Through digital computer simulation it was found that for practical values of rms phase jitter coding gains for rotationally invariant codes are either maintained or enhanced through trellis coding. Four examples are presented which represent the design procedure. The phase jitter sensitivity is given in each case. Analytic expressions are also derived for the differential encoding rules to be used in the 8 and 16 point examples presented.

Multiple trellis coded modulation (MTCM)

The authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation (MTCM) wherein more than one channel symbol per trellis branch is transmitted. They have found simple two-state trellis codes for symmetric MPSK multiple phase-shift keying and AM modulations that can achieve 3-dB gain over uncoded modulation at very high signal-to-noise ratios without bandwidth expansion or reduction in information bit rate. The gain of these codes with respect to previously reported two-state trellis codes is between 1 and 2 dB at very high signal-to-noise ratios, depending on the number of bits per Hertz transmitted. These gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram. The authors note that additional computations per branch are needed for the multiple trellis coding scheme. The concept can be extended to a higher number of states and other types of modulations. >

Coded Phase/Frequency Modulation

Channel coding combined with expanded signal sets has been shown [1] to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals. In this paper, new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented. The new schemes combine FSK and PSK modulation and make use of trellis coding and Viterbi decoding to improve error performance over uncoded modulation. The free Euclidean distance is calculated for several classes of codes, and upper bounds and simulation results are also presented for some simple codes. The spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two-dimensional modulation formats. Differential encoding and various extensions of the basic scheme are also discussed.

Efficient Modulation for Band-Limited Channels

This paper attempts to present a comprehensive tutorial survey of the development of efficient modulation techniques for bandlimited channels, such as telephone channels. After a history of advances in commercial high-speed modems and a discussion of theoretical limits, it reviews efforts to optimize two-dimensional signal constellations and presents further elaborations of uncoded modulation. Its principal emphasis, however, is on coded modulation techniques, in which there is an explosion of current interest, both for research and for practical application. Both block-coded and trellis-coded modulation are covered, in a common framework. A few new techniques are presented.