Space-time Trellis Codes Research Articles

Space–Time Trellis Codes With Linear Transformation for Fast Fading Channels

A space-time trellis code with linear transformation (STTC-LT) is presented. The upper bound on the pairwise error probability (PEP) is derived and a new design criterion is proposed. It is shown that the performance of STTC-LT over fast Rayleigh fading channels depends on the weighted square product distance (WSPD). Simulation results are provided for QPSK signal sets. They show that the proposed scheme is superior by about 8 dB and 10 dB to the conventional beamforming and Tarokh-Seshadri-Calderbank codes (TSC) at the bit error rate (BER) of 1.0e-4 over fast fading channels.

Genetic algorithms with applications in wireless communications

Genetic algorithms (GAs) are known to locate the global optimal solution provided sufficient population and/or generation is used. Practically, a near-optimal satisfactory result can be found by Gas with a limited number of generations. In wireless communications, the exhaustive searching approach is widely applied to many techniques, such as maximum likelihood decoding (MLD) and distance spectrum (DS) techniques. The complexity of the exhaustive searching approach in the MLD or the DS technique is exponential in the number of transmit antennas and the size of the signal constellation for the multiple-input multiple-output (MIMO) communication systems. If a large number of antennas and a large size of signal constellations, e.g. PSK and QAM, are employed in the MIMO systems, the exhaustive searching approach becomes impractical and time consuming. In this paper, the GAs are applied to the MLD and DS techniques to provide a near-optimal performance with a reduced computational complexity for the MIMO systems. Two different GA-based efficient searching approaches are proposed for the MLD and DS techniques, respectively. The first proposed approach is based on a GA with sharing function method, which is employed to locate the multiple solutions of the distance spectrum for the Space-time Trellis Coded Orthogonal Frequency Division Multiplexing (STTC-OFDM) systems. The second approach is the GA-based MLD that attempts to find the closest point to the transmitted signal. The proposed approach can return a satisfactory result with a good initial signal vector provided to the GA. Through simulation results, it is shown that the proposed GA-based efficient searching approaches can achieve near-optimal performance, but with a lower searching complexity comparing with the original MLD and DS techniques for the MIMO systems.

On Performance Bounds for Space–Time Codes on Fading Channels

We evaluate truncated union bounds on the frame-error rate (FER) performance of space-time (ST) codes operating over the quasi-static fading channel and compare them with computer simulation results. We consider both ST trellis and block codes. We make the following contributions. For the case of ST trellis codes, we develop a general method, which we denote as measure spectrum analysis, that characterizes ST codeword differences and accommodates the combined influences of the ST code and channel scenario. We propose a numerical bounding method that converges in the measure spectrum to within a very small fraction of a decibel to the simulated FER over the full range of signal-to-noise ratio. In addition, we demonstrate the existence of dominant quasi-static fading error events and detail a method for predicting them. Using only this set of dominant measure spectrum elements, very rapid and tight numerical estimation of FER performance is attained.

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.

Rotationally invariant space-time trellis codes with 4-D rectangular constellations for high data rate wireless communications

We demonstrate rotationally invariant space-time (ST) trellis codes with a 4-D rectangular signal constellation for data transmission over fading channels using two transmit antennas. The rotational invariance is a good property to have that may alleviate the task of the carrier phase tracking circuit in the receiver. The transmitted data stream is segmented into eight bit blocks and quadrature amplitude modulated using a 256 point 4-D signal constellation whose 2-D constituent constellation is a 16 point square constellation doubly partitioned. The 4-D signal constellation is simply the Cartesian product of the 2-D signal constellation with itself and has 32 subsets. The partition is performed on one side into four subsets A, B, C, and D with increased minimum-squared Euclidian distance, and on the other side into four rings, where each ring includes four points of equal energy. We propose both linear and nonlinear ST trellis codes and perform simulations using an appropriate multiple-input multiple-output (MIMO) channel model. The 4-D ST codes constructed here demonstrate about the same frame error rate (FER) performance as their 2-D counterparts, having however the added value of rotational invariance.

Distance Spectra and Performance Bounds of Space-Time Trellis Codes Over Quasi-Static Fading Channels

This correspondence presents a general approach to upper bounding coded system performance over quasistatic fading channels (QSFC). This approach has the advantage of yielding a closed-form upper bound that converge for all signal-to-noise ratios (SNRs). The proposed approach is used to upper-bound the performance of space-time trellis codes (STTC) over QSFCs. The resulting upper bounds for STTCs are better adapted to the QSFC and present an improvement over worst case pairwise error probability (PEP) analysis used so far. In its second part, this correspondence investigates several ways to reduce the complexity of computing the distance spectrum of STTCs. The combined result obtained from using the new upper bounds and the computed distance spectra are shown to be close to simulated performance for all SNRs.

Reduced Complexity I/Q Turbo Detection for Space–Time Trellis-Coded Systems

A reduced-complexity turbo-detection scheme, referred to here as the R-TD arrangement, is proposed for employment in space-time trellis-coded (STTC) systems using the inphase/quadrature-phase (I/Q) cancellation technique that was previously developed for single-transmitter and single-receiver systems. The R-TD scheme decomposes the received signal into its constituent I and Q signal components and detects these components separately; hence, reducing the number of possible signal combinations to be tested by the detector. The R-TD scheme is capable of approaching the performance of the conventional turbo detector (F-TD), while achieving a complexity reduction factor of 3 and 862 for a four-phase-shift-keying 32-state STTC system, denoted as STTC(4,32), communicating over two- and five-path Rayleigh-fading channels, respectively, exhibiting a symbol-spaced and equal-tap-weight channel-impulse response. In order to investigate the benefits of employing channel coding in conjunction with STTC schemes, the R-TD principle was also invoked in convolutional-coding-aided STTC schemes. It was observed that, at a given throughput, the turbo-detected nonchannel-coded STTC(4,32) system required a similar signal-to-noise ratio to that of the R=1/2 and constraint length K=7 convolutional-coded STTC(16,16) scheme for achieving the bit error rate (BER) of 10/sup -5/. At a higher target, BER of 10/sup -3/, the nonchannel-coded STTC(4,16) and STTC(4,32) schemes outperformed the channel-coded STTC(16,16) system by 0.8 and 2.3 dB, despite having a factor of 19 or 11 lower complexity, respectively.

Diagonal Block Space-Time Code Design for Diversity and Coding Advantage Over Flat Fading Channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.

Properties of Space-Time Codes for Frequency-Selective Channels

Some important properties are derived for the diversity gain and the coding gain of space-time codes (STCs) for frequency-selective channels. It is proven that the diversity gain of a STC that provides maximum diversity gain for channels with a given number of taps is robust to a decrease in the number of taps. For coding gain analysis, we categorize the possible types of correlation matrices into several classes based on the type of power delay profile, spatial correlation, and tap correlation. It is proven that optimum STCs found for spatially independent and frequency-selective channels with uncorrelated taps and uniform power delay profile have coding gains that are robust against a mismatch in correlation structure if the number of taps is fixed. Thereafter, a systematic design procedure is applied to search for the best space-time trellis codes (STTCs) for frequency-selective channels. At a frame error rate (FER) of 0.01, our example 16-state binary phase-shift keying (BPSK) STTC outperforms the delay diversity code by 3.4 dB for a channel with three uncorrelated uniform taps. Further, the example STC designed for a channel with a given number of taps is shown to provide good performance for channels with fewer taps.

An orthogonal space-time coded CPM system with fast decoding for two transmit antennas

Trellis-coded space-time (TC-ST) coding for continuous-phase modulation (TC-ST-CPM) was recently proposed by Zhang and Fitz. In this paper, we propose an orthogonal space-time coding for CPM (OST-CPM) systems and two transmit antennas. In the proposed OST-CPM, signals from two transmit antennas at any time t are orthogonal while both of them have continuous phases. Similar to Alamouti's OST coding for phase-shift keying (PSK) and quadrature amplitude modulation (QAM) systems, the newly proposed OST-CPM has a fast decoding algorithm.

Weighted space-time trellis codes

In existing space-time trellis codes (STTCs), the transmit power is equally distributed across all transmit antennas. However, this power allocation strategy is not optimum regarding the error performance. A new scheme is proposed, referred to as the weighted space-time trellis codes with dynamic transmit power allocation (WSTTCs/DTPA). Compared with the general open-loop STTCs, WSTTCs/DTPA have better performance and achieve a full diversity order regardless of STTCs adopted at the transmitter.

Search for space – time trellis codes: novel codes for Rayleigh fading channels

The authors address the problematic issues in generating space–time trellis codes, and propose novel methods for reducing the exponentially growing full code search. It is proved that by exploiting the symmetry in QAM and PSK constellations, together with the modulo operation in the encoder, the number of possible combinations in the generator matrix can be halved when performing a full search to obtain optimal codes. It is also shown that for a fixed set of columns in the generator matrix, interchanging columns yields identical results, hence reducing the full code search by the factorial of the number of transmit antennas. Furthermore, the existing sub-optimal (but fast) method for obtaining codes is investigated and results from this method are compared with those obtained from the two proposed methods. Using the suggested methods, novel space–time codes for both slow and fast fading environments are generated and their performance is evaluated through frame error probabilities obtained by simulation.

Space-time MSK Codes for Quasi-Static Fading Channels

In this paper, 4-state and 8-state space-time trellis codes with full rate, full diversity and high coding gain are proposed for MSK modulation, based on a technique similar to the super-orthogonal space-time trellis code (SOSTTC) design. Since the phase continuity requirement of MSK is the main constraint in space-time MSK code design not all the signal matrices corresponding to the trellis branches are orthogonal. The paper shows that the SOSTTC design technique can be extended to nonorthogonal coding structures. The new space-time MSK codes have frame error performances very close to those of their space-time QPSK counterparts given in [1]

Space-time trellis codes for keyhole channels: performance criterion and code design

A code design criterion for the design of space-time trellis codes in keyhole channels is provided. The code designed according to this criterion is shown to have a better performance compared with previously designed codes for Rayleigh fading channels.

Space-time trellis codes for 2P4PSK OPSM systems with large number of receiver antennas

The space-time (ST) trellis code for 2P4PSK orthogonal plane sequence modulation (OPSM) signals is presented when the number of receiver antennas is large. The simulation results shows that the ST codes obtained from the maximising minimum squared Euclidean distance criterion search algorithm achieve a recognisable coding gain (i.e. 1–2 dB) over the codes of Choe , where the coding gain increases for the case of two or more receiver antennas.

LDPC-based space –time coded OFDM systems with channel estimation

The authors consider a space–time coded (STC) orthogonal frequency-division multiplexing (OFDM) system with multiple transmitter and receiver antennas over correlated frequency- and time-selective fading channels. They propose first a maximum-likelihood (ML) receiver for space–time block code OFDM systems based on the expectation–maximisation (EM) algorithm. They then propose a low-density parity-check (LDPC)-code-based STC-OFDM system to interface with the EM algorithm. When comparing the proposed scheme with the conventional space–time trellis code, the LDPC-based STC significantly improves the system performance by exploiting both spatial and selective-fading diversity in wireless channels. Compared with the recently proposed turbo-code-based STC scheme, LDPC-based STC exhibits a lower complexity and more flexible scalability.

Constructing Space-Time Trellis Codes Using Orthogonal Designs

In this paper we consider the design of space-time trellis codes using orthogonal designs. We derive a condition on the codewords to obtain the maximum received signal energy and show that the codes based on orthogonal designs satisfy this condition. We consider in detail the design of a trellis code for two transmit antennas. The new code we develop has a higher diversity in fast fading and a higher coding gain in quasi-static fading when compared to other existing space-time codes. We also consider a turbo implementation of the new trellis code which results in very high diversity gains in fast fading channels.

Distance spectrum analysis of space-time trellis-coded modulations in quasi-static rayleigh-fading channels

In this correspondence, we propose an algorithm for computing the distance spectrum of a space-time trellis code achieving maximal diversity gain in quasi-static fading channels. We further present a state reduction technique for trellis codes that can reduce the complexity of the distance spectrum computation. We provide numerical results supporting the empirical evidence that a truncated union bound obtained from the distance spectrum provides an accurate characterization of the relative performance ordering of different space-time trellis codes and, therefore, it offers a tool for better space-time trellis code design.

Performance evaluation of super-orthogonal space-time trellis codes using a moment generating function-based approach

A new class of space-time codes called super-orthogonal trellis codes was introduced that combine set-partitioning with a super set of orthogonal space-time block codes in such a way as to provide full diversity with increased rate and improved coding gain over previous space-time trellis code (STTC) constructions. Here, we extend the moment generating function-based method, which was previously applied to analyzing the performance of space-time block orthogonal and trellis codes, to the above-mentioned super-orthogonal codes. It is shown that the maximum-likelihood metric and expressions for the pairwise error probability previously developed for the Alamouti (1998) space-time block code combined with multidimensional trellis-coded modulation can be readily extended to the super-orthogonal case. As such, the evaluation of the pairwise error probability for the latter can be performed in a similar manner to that previously described with the specific results depending on the particular trellis code design.

Universal space~time trellis codes

This article gives practical examples of space-time trellis codes performing as predicted by Root and Varaiya's (1968) compound channel theorem. Specifically, 32-state and 64-state 2/spl times/2 space-time trellis codes are presented that provide a bit-error rate (BER) of 10/sup -5/ on all 2/spl times/2 matrix channels with an excess mutual information (MI) within 8% of the excess MI required by standard trellis codes of the same complexity operating only in additive white Gaussian noise (AWGN). Not surprisingly, the universal space-time trellis-coded modulations (ST-TCMs) provide average bit- and frame-error rates in quasi-static Rayleigh fading (QRF) that are comparable to those achieved by ST-TCMs designed specifically for QRF as well as standard TCMs followed by the Alamouti (1998) space-time block code. However, all of these other schemes require more excess MI in the worst case, and some have a significantly wider variation in the required excess MI. The article also compares the universal and quasi-static Rayleigh fading design approaches analytically and bounds the worst case distance of a trellis code on a 2/spl times/2 channel using the distances of the code on singular and unitary channels. This bound is extended to the more general n/sub T//spl times/n/sub R/ scenario.