Performance Of Space-time Codes Research Articles

Improving the performance of free space optical systems: a space-time orthogonal frequency division modulation approach

Free space optical (FSO) communication systems are known for high capacity and information security. The overall system performances of FSO systems are however significantly affected by atmospheric turbulence induced fading. This paper, therefore, proposes a technique to mitigate this effect through the introduction of an additional degree of error correction capacity by exploiting the spectral dimension in the coding space. A space-time trellis coded orthogonal frequency division modulation (OFDM) scheme was developed, simulated and evaluated for optical communication through a Gamma-Gamma channel. The evaluation of the coding gain obtained from the simulation results, the mathematical analysis and the truncation error analysis shows that the proposed technique is a promising and viable technique for improving the error correction performance of space-time codes for free space optical communication links.

Performance of General STCs over Spatially Correlated MIMO Single-keyhole Channels

For multiple-input multiple-output (MIMO) Rayleigh channels, it has been shown that transmitter correlations always degrade the performance of general space-time codes (STCs) in high signal-to-noise ratio (SNR) regimes. In this correspondence, however, we show that when MIMO channels experience single-keyhole conditions, the effect of spatial correlations between transmission antennas is more sophisticated for general STCs: When M > N (i.e., the number of transmission antennas is greater than the number of receiving antennas), depending on how the correlation matrix P beamforms the codeword difference matrix Δ, the pairwise error probability performance of general STCs can be either degraded or improved in high-SNR regimes. We provide a new measure, which is based on the eigenvalues of Δ and the numbers of transmission and receiving antennas, to examine if there exist certain correlation matrices that can improve the performance of general STCs in high-SNR regimes. Previous studies on the effect of spatial correlations over single-keyhole channels only concentrated on orthogonal STCs, whereas our study here is for general STCs and can also be used to explain previous findings for orthogonal STCs. Simulations also show that the results are applicable with imperfect channel knowledge.

Performance of Space Time Block Codes and Quasi Orthogonal Space Time Codes on Fading Channel

In this paper the performance of Space Time Codes (STC) & Quasi Orthogonal Space Time Block Codes (QOSTBC) has been analyzed. Use of multiple antennas is an emerging approach for recovering fading and reducing the bit error rate. Space diversity is introduced in space time codes. In Alamouti Space Time Code (STC) two transmit antennas are used that provide relatively better results than no coding approach. Alamouti uses a code matrix at transmitter and at receiver end it uses MLD and estimates the output signals. Space time block codes are with arbitrary number of antennas. It uses a huge code matrix at encoder and decodes using MLD. QOSTBC is one of the latest variants of the STBCs. The encoded symbols are mapped in the transmission matrix which is decoded at the receiver end using pair wise maximum likelihood decoding (MLD). Pair wise MLD is the specialty of the QOSTBC. The performance of STBC is far better than Alamouti and has no match with no coding. The performance comparison of QOSTBC, Alamouti, STBC and no coding is showed using simulations in MATLAB. Space time codes works with the price of redundancy bits and extra antenna price. Simulation results for QOSTBC also shows better performance with the price of slightly increased decoding complexity.

Predicting Approximate Performance Bounds for Space–Time Codes Over Quasi-Static Fading Channels

This paper provides a useful method for predicting the approximate performance of space time codes over quasi-static fading channels. Based on evaluating the signal-to-noise ratios (SNR) of the extrinsic information in the minimum mean-square error (MMSE) detector, we obtain upper and lower bounds on SNR, which are the convergent limits of the SNR evolution of the extrinsic information between the MMSE detector and the a posteriori probability decoder. Based on the SNR bounds the upper and lower bounds of frame-error-rate and bit-error-rate can be assessed by averaging over the fading coefficients. The results of numerical simulations are found to be in excellent agreement with the semi-analytic bounds.

Indoor Off-Body Wireless Communication: Static Beamforming versus Space-Time Coding

The performance of beamforming versus space-time coding using a body-worn textile antenna array is experimentally evaluated for an indoor environment, where a walking rescue worker transmits data in the 2.45 GHz ISM band, relying on a vertical textile four-antenna array integrated into his garment. The two transmission scenarios considered are static beamforming at low-elevation angles and space-time code based transmit diversity. Signals are received by a base station equipped with a horizontal array of four dipole antennas providing spatial receive diversity through maximum-ratio combining. Signal-to-noise ratios, bit error rate characteristics, and signal correlation properties are assessed for both off-body transmission scenarios. Without receiver diversity, the performance of space-time coding is generally better. In case of fourth-order receiver diversity, beamforming is superior in line-of-sight conditions. For non-line-of-sight propagation, the space-time codes perform better as soon as bit error rates are low enough for a reliable data link.

Asymptotic Analysis of Space-Time Codes in Generalized Keyhole Fading Channels

The keyhole phenomenon, i.e., non-fully correlated but rank-deficient fading, can lead to significant performance degradations in multiple-input multiple-output (MIMO) systems and has to be carefully taken into account for system design. In this paper, we consider generalized keyhole fading including Rayleigh, Ricean, Nakagami-q, Nakagami-m, and Weibull fading. We derive simple and elegant closed-form expressions for the asymptotic pairwise error probability (PEP) of both single-antenna transmission and space-time coded transmission with two transmit antennas. The obtained PEP expressions provide significant insight into the impact of various system and channel parameters such as the types of fading at the transmitter and receiver side, the numbers of transmit and receive antennas, and the space-time code design on performance. This insight can be exploited for system design and to explain the differences in the performance of space-time codes in non-keyhole and keyhole fading channels. Furthermore, the presented asymptotic PEP expressions can be utilized to obtain tight asymptotic approximations for the bit, symbol, and frame error probabilities of arbitrary, not necessarily orthogonal, space-time codes. Simulation results confirm the accuracy and usefulness of the derived results.

Performance and distance spectrum of space-time codes in fast rayleigh fading channels

In this paper, we analyze the performance of spacetime codes and propose a distance spectrum computation method in fast Rayleigh fading channels. We first derive a new FER upper bound using the union bound and the PEP upper bound in the fast fading environment. The derived FER upper bound is very accurate, requires only the distance spectrum of the spacetime code, and takes a closed-form expression. Then we propose a distance spectrum computation method of space-time codes in fast fading channels, which exploits the symmetric property of the error state diagram in space-time trellis coded MPSK modulation to reduce the computation complexity. Numerical results illustrate that the derived FER bound is tight enough to estimate the performance of space-time codes in fast fading channels with sufficient accuracy.

Space-Time Block Codes with Limited Feedback Using Antenna Grouping

We propose an antenna grouping method that improves the error rate performance of space-time codes in a wide range of mobility environments. The idea is to group symbols to antennas based on limited feedback from the mobile station to utilize all antennas. Our approach requires only two bits of feedback information to achieve better link performance and full rate for a certain four transmit antenna system. Numerical results confirm the bit/frame error gains over the Alamouti-based space-time block code and antenna subset selection strategies.

Space–Time Code Design for Correlated Ricean MIMO Channels at Finite SNR

Space-time code (STC) designs commonly rely on the assumptions of independent and identically distributed (i.i.d.) Rayleigh channels (being either slow or fast fading) and high signal-to-noise ratio (SNR). However, it has been shown that poor scattering conditions can have detrimental effects on the performance of STCs and that the behavior of codes at high SNR is radically different from the finite SNR behavior. This calls for new design criteria that correctly predict the behavior of codes in correlated channels at finite SNR. In this paper, we investigate how spatially and temporally correlated Ricean fading affects the performance of STCs at finite SNR. We derive a code design criterion leading to robust STCs in a wide variety of propagation conditions and do not require any channel knowledge at the transmitter. Codes satisfying this criterion are shown to perform sensibly better in correlated channels than codes designed only for i.i.d. slow or fast Rayleigh-fading channels. Examples of space-time trellis codes and algebraic codes are proposed in order to illustrate the developed criterion.

Design and Performance of Space–Time Codes for Spatially Correlated MIMO Channels

Space-time code (STC) designs classically rely on the assumption of independent and identically distributed (i.i.d.) Rayleigh channels. However, poor scattering conditions may have detrimental effects on the performance of STCs. In this letter, we derive code-design criteria leading to robust STCs in a large variety of slow-fading propagation conditions. No channel knowledge is assumed at the transmitter. Codes satisfying these criteria are shown to perform much better on real-world channels than codes designed only for i.i.d. channels. As examples, the robustness of various spatial multiplexing schemes, linear dispersion codes, and space-time trellis codes is discussed based on those criteria

Performance analysis of space-time codes in realistic propagation environments: A moment generating function-based approach

In this paper, we derive analytical expressions for the exact pairwise error probability (PEP) of a space-time coded system operating over spatially correlated fast (constant over the duration of a symbol) and slow (constant over the length of a code word) fading channels using a moment-generating function-based approach. We discuss two analytical techniques that can be used to evaluate the exact-PEPs (and therefore, approximate the average bit error probability (BEP)) in closed form. These analytical expressions are more realistic than previously published PEP expressions as they fully account for antenna spacing, antenna geometries (uniform linear array, uniform grid array, uniform circular array, etc.) and scattering models (uniform, Gaussian, Laplacian, Von-mises, etc.). Inclusion of spatial information in these expressions provides valuable insights into the physical factors determining the performance of a space-time code. Using these new PEP expressions, we investigate the effect of antenna spacing, antenna geometries and azimuth power distribution parameters (angle of arrival/departure and angular spread) on the performance of a four-state QPSK space-time trellis code proposed by Tarokh et al. for two transmit antennas.

Pairwise error probability of space-time codes in frequency selective Rician channels

In this letter, we investigate the performance of space-time codes in frequency selective correlated Rician channels. An exact expression has been derived for the pairwise error probability (PEP) of space-time trellis codes over frequency selective Rician fading channel, which is in the form of a single finite range integral. We also obtain a closed form expression for the PEP when the signal matrices are drawn from some special design and the performance upper bound.

Adaptive antennas and mimo systems for wireless communications: part II

he first part of this special issue contained eight articles that presented overviews, descriptions of different methods, performance analyses, and new ideas, all from a theoretical/simulation point of view. Part II includes articles that focus more on practical and experimental issues related to the presented topic. The first article of this issue discusses the advantages of reconfigurable antennas and the requirements for radio frequency microelectromechanical systems (RF MEMS). A simplified prototype of the reconfigurable antenna is also presented along with simulation and experimental results for impedance and radiation performance. The second article discusses a classification of multiantenna testbeds for training and research purposes. The authors present the characteristics, capabilities and cost of the testbeds, highlight their role in an educational environment and provide experimental results. The following article presents a multiple-input multipleoutput orthogonal frequency-division multiplexed (MIMOOFDM) prototype for next-generation wide area wireless networks. The uplink is based on an enhanced Universal Mobile Telecommunications System (UMTS) physical layer, the downlink on shared access MIMO-OFDM with adaptive modulation and coding. Measurements for different operational scenarios demonstrate the capabilities of the system. The fourth article describes the implementation issues related to the development of a 3 × 3 OFDM Bell Labs Layered Space-Time (BLAST) testbed for wireless metropolitan area networks. It then presents initial results for the performance and complexity of three BLAST detection techniques using experimental data from an indoor environment. The fifth article first surveys the principal space-time coding/decoding technologies for MIMO wireless LAN systems. Then it describes indoor channel sounding trials and employs the results to scope the expected performance of space-time codes in realistic deployments. The next article discusses the effects of antenna mutual coupling on correlation, radiation efficiency, diversity gain, and MIMO capacity. Measurements in a reverberation chamber and simulations are also provided to support the analysis. The last article of this issue presents a discussion of the classes of distortion that affect the performance of adaptive antennas. An eight-element circular array adaptive antenna testbed is employed to illustrate the impact of temperature on performance, while design techniques for calibration are also described. I would like to thank again all the authors who submitted their articles to this feature topic and also the many reviewers who took time out of their busy schedules and did an excellent job by providing detailed reviews.

On the Performance Analysis of Space–Time Codes in Quasi-Static Rayleigh-Fading Channels

In this paper, we analyze the performance of space-time codes by deriving a new approximation of the frame error probabilities for space-time trellis-coded modulations over quasi-static Rayleigh-fading channels. We take advantage of two techniques, the modified bounding technique and the limiting-before-averaging technique, to tighten the upper bound. In addition, we establish a theorem that enables us to reduce the computation and memory needed to calculate the frame error rate (FER) approximation. The newly derived approximation is very tight, requires only the distance spectrum of the space-time code, and can be computed through single numerical integration. Numerical results exhibit that the new approximation is much closer to the simulation results than other existing bounds are, especially in the case of one receive antenna.

On the Error Performance Analysis of Space–Time Trellis Codes

We present analytical performance results for space-time trellis codes over spatially correlated Rayleigh fading channels. Bit-error-probability estimates are obtained based on the derivation of an exact pairwise error probability expression using a residue technique combined with a characteristic function approach. We investigate both quasi-static and interleaved channels and demonstrate how the spatial fading correlation affects the performance of space-time codes over these two different channel models. Simulation results are also included to confirm the accuracy of analytical estimates.

Pairwise Error Probability of Space-Time Codes in Rician–Nakagami Channels

In this letter, we investigate the shadowing effect on the performance of space-time codes, using the Rician-Nakagami channel model which has been recently introduced. Specifically, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the Rician-Nakagami channel, which is in the form of a simple single finite-range integral. We also present numerical results how the PEP expressions for the Rician-Nakagami channel can be related to those for the classical Rician-lognormal channel based on the parameter transformation between these two models.

Combining space-time turbo trellis codes and ideal beamforming

It has been shown that if perfect channel state information is available at the transmitter, the performance of a space-time coded system can be dramatically improved by weighting the transmitted signals. In this reported work, the performance of combined space-time turbo trellis codes and ideal beamforming is evaluated. Simulation results show that the proposed scheme considerably outperforms the conventional space-time turbo trellis codes without weighting and it approaches the MIMO channel capacity within about 1.5 dB with a moderate interleaver size over quasi-static fading channels.

Errata to "space-time codes for high data rate wireless communications: performance criteria in the presence of channel estimation errors, mobility, and multiple paths"

Space-time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas. Specific codes have been constructed using design criteria derived for quasi-static flat Rayleigh or Rician fading, where channel state information is available at the receiver. It is evident that the practicality of space-time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information. It is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the Doppler spread. This paper presents a theoretical study of these issues beginning with the effect of channel estimation error. Here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy, it is proved that in the absence of ideal channel state information the design criteria for space-time codes is still valid. The analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space-time codes provided that the number of transmit antennas is small. We also derive the maximum-likelihood detection metric in the presence of channel estimation errors. Next, the effect of multiple paths on the performance of space-time codes is studied for a slowly changing Rayleigh channel. It is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space-time codes. Similar results hold for rapid fading channels with or without multiple paths. The conclusion is that the diversity order promised by space-time coding is achieved under a variety of mobility conditions and environmental effects.

Space-time processing for broadband wireless access

We present an overview of research activities on space-time coding for broadband wireless transmission performed at AT&T Shannon Laboratory over the past two years. The emphasis is on physical layer modem algorithms such as channel estimation, equalization, and interference cancellation. However, we also discuss the impact of space-time coding gains at the physical layer on throughput at or above the networking layer. Furthermore, we describe a flexible graphical user interface attached to our physical layer simulation engine in order to explore the performance of space-time codes under a variety of practical transmission scenarios. Simulation results for the EDGE cellular system and the 802.11 wireless LAN environment are presented.

Performance of space-time codes for a large number of antennas

We study the asymptotic behavior of space-time codes when the number of transmit and receive antennas grows to infinity. Specifically, we determine the behavior of pairwise error probabilities with maximum-likelihood (ML) decoding and with three types of receiver interfaces: the ML interface, the linear zero-forcing (ZF) interface, and the linear minimum-mean-square-error (MMSE) interface. Two situations are studied: when the number of receiving antennas grows to infinity while the number of transmitting antennas is finite, and when both numbers grow to infinity but their ratio remains constant. We show that with ML or linear interfaces the asymptotic performance of space-time codes is determined by the Euclidean distances between codewords. Moreover, with the two linear interfaces examined here the number r of receive antennas must be much larger than the number t of transmit antennas to avoid a sizeable loss of performance; on the other hand, when r /spl Gt/ t, the performance of these linear interfaces comes close to that of ML. The dependence of error probabilities on Euclidean distance is valid for intermediate signal-to-noise ratios (SNRs) even when the number of antennas is small. Simulations validate our theoretical findings, and show how asymptotic results may be substantially valid even in a nonasymptotic regime: thus, even for few antennas, off-the-shelf codes may outperform space-time codes designed ad hoc.