Linear Space-time Block Codes Research Articles

Widely linear channel estimation for LD‐STBC MB‐OFDM UWB systems

SummaryThe combination of Linear Dispersion Space‐Time Block Codes (LD‐STBCs) and Multiband Orthogonal Frequency Division Multiplexing Ultra‐WideBand (MB‐OFDM UWB) technologies has been proposed in the literature to improve the error performance and data rate. Recently, it has been shown that the LD codes allow the repetitions of data symbols conjugates. They cause a transformation of the Multiple‐Input Multiple‐Output (MIMO) channel that requires a Widely Linear (WL) filtering. However, proposed LD‐STBC MB‐OFDM UWB system does not take this issue into account. In this paper, we propose a Widely Linear Minimum Mean Square Error (WLMMSE) channel estimator for LD‐STBC MB‐OFDM UWB systems. The proposed channel estimator proceeds to WL estimation instead of linear one. Via simulation results, we prove that the LD‐STBCs provide significant performance gain for MB‐OFDM UWB system compared to Single‐Input Single‐Output (SISO) configuration. We show also that the proposed WLMMSE channel estimator outperforms the LMMSE one. This performance improvement is observed for both proper and improper signal constellations. Additionally, the computational complexity of our proposal is comparable with that of LMMSE estimator. Copyright © 2016 John Wiley & Sons, Ltd.

Minimizing the Complexity of Fast Sphere Decoding of STBCs

Decoding of linear space-time block codes (STBCs) with sphere-decoding (SD) is well known. A fast-version of the SD known as fast sphere decoding (FSD) was introduced by Biglieri, Hong and Viterbo. Viewing a linear STBC as a vector space spanned by its defining weight matrices over the real number field, we define a quadratic form (QF), called the Hurwitz-Radon QF (HRQF), on this vector space and give a QF interpretation of the FSD complexity of a linear STBC. It is shown that the FSD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization) or the number of receive antennas. It is also shown that the FSD complexity is completely captured into a single matrix obtained from the HRQF. Moreover, for a given set of weight matrices, an algorithm to obtain an optimal ordering of them leading to the least FSD complexity is presented. The well known classes of low FSD complexity codes (multi-group decodable codes, fast decodable codes and fast group decodable codes) are presented in the framework of HRQF.

An Enhanced DMT-Optimality Criterion for STBC Schemes for Asymmetric MIMO Systems

For any nt transmit, nr receive antenna ( nt×nr) multiple-input multiple-output (MIMO) system in a quasi-static Rayleigh fading environment, it was shown by Elia that linear space-time block code schemes (LSTBC schemes) that have the nonvanishing determinant (NVD) property are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of nr if they have a code rate of nt complex dimensions per channel use. However, for asymmetric MIMO systems (where ), with the exception of a few LSTBC schemes, it is unknown whether general LSTBC schemes with NVD and a code rate of nr complex dimensions per channel use are DMT optimal. In this paper, an enhanced sufficient criterion for any STBC scheme to be DMT optimal is obtained, and using this criterion, it is established that any LSTBC scheme with NVD and a code rate of min{nt,nr} complex dimensions per channel use is DMT optimal. This result settles the DMT optimality of several well-known, low-ML-decoding-complexity LSTBC schemes for certain asymmetric MIMO systems.

L2-Orthogonal ST-Code Design for CPM

Non-linear modulations, like the Continuous phase modulation (CPM) with its constant envelope property, have been appealing for energy efficient communication systems. In parallel, linear orthogonal Space-Time block codes (STBC) have emerged as a simple way of achieving spectral efficiency by full diversity and simple decoupled maximum-likelihood decoding. However, linear codes rely on pointwise orthogonality which leads to a well-known degradation of data rate for more than two antennas. In this paper, we introduce the concept of L2-orthogonality for non-linear Space-Time codes (STC). Our approach generalizes code design based on pointwise orthogonality. Namely, we are able to derive new codes with the same advantages as pointwise orthogonal STBC, i.e. low decoding complexity and diversity gain. At the same time, we are no longer limited by the restrictions of pointwise orthogonal codes, i.e. the reduction in data rate. Actually, we show how to construct full rate codes for any arbitrary number of transmit antennas. More precisely, a family of codes for continuous phase modulation (CPM) is detailed. The L2-orthogonality of these codes is ensured by a bank of phase correction functions which maintains the phase continuity but also introduces frequency offsets. We prove that these codes achieve full diversity and have full rate. Moreover, these codes don't put any restriction on the CPM parameters.

나카가미 페이딩 채널하에서 MIMO-OFDM 시스템의 성능분석

In this paper, I analyzed array organization of MIMO channel antenna and effect of operation environment by evaluating average BER from linear Space-Time Block Code orthogonal design and suggests designing condition of MT antenna for improved BER and the fading index m. To analyze system performance, I used M-PSK and M-QAM modulation, and to use analysis equations I used integrated by Nakagami fading variable, non-integrated Nakagami fading variable. We can get the organization of channel array by using mathematical calculation on matrix. STBE BER performance will decrease as AOA spreading decrease and such loss can be compensated from extending antenna spacing, and changing array organization.

Diversity Analysis and Design of Space–Time Multiblock Codes for MIMO Systems Equipped With Linear MMSE Receivers

This paper addresses the problem of designing optimum full-symbol-rate linear space-time block codes (STBC) for a multi-input multi-output (MIMO) communication system with M transmitter and N ≥ M receiver antennas and a linear minimum mean square error (MMSE) receiver. By analyzing the detection error probability expression for the optimized STBC, it is shown that for QAM signaling, the maximum diversity gain for such a system is N - M + 1. The minimum probability of error STBC design is then extended to systems in which the transmission spans L independent realizations from a block fading channel model, and a (multiblock) linear MMSE receiver is employed. Necessary and sufficient conditions for the optimality of the code are obtained, and a systematic design method for generating codes that satisfy these conditions is presented. The detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed. It is proved that the error probability decreases with L, and it is shown numerically that the diversity gain increases with L. Thus, if the corresponding latency can be accommodated, for sufficiently large L an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block-fading channel and achieve higher diversity gain than that of any single-block system of the same symbol rate with a maximum likelihood (ML) receiver. The optimized multiblock linear system achieves this diversity at a substantially lower computational cost. In fact, the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver.

Blind Recognition of Linear Space–Time Block Codes: A Likelihood-Based Approach

Blind recognition of communication parameters is a research topic of high importance for both military and civilian communication systems. Numerous studies about carrier frequency estimation, modulation recognition as well as channel identification are available in literature. This paper deals with the blind recognition of the space-time block coding (STBC) scheme used in multiple-input-multiple-output (MIMO) communication systems. Assuming there is perfect synchronization at the receiver side, this paper proposes three maximum-likelihood (ML)-based approaches for STBC classification: the optimal classifier, the second-order statistic (SOS) classifier, and the code parameter (CP) classifier. While the optimal and the SOS approaches require ideal conditions, the CP classifier is well suited for the blind context where the communication parameters are unknown at the receiver side. Our simulations show that this blind classifier is more easily implemented and yields better performance than those available in literature.

Analysis of Single-Symbol Detectable Space-Time Block Codes With COD and GCIOD

In this paper, we present a simplified maximum likelihood detection metric for the newly emerging space-time block codes (STBCs) with generalized coordinate interleaved orthogonal design (GCIOD). We also derive the symbol pairwise error probability (PEP) and the union bound on symbol error rate (SER) for a space-time block coded (STBCed) system with single-symbol detection and rotated QAM scheme over flat Rayleigh fading channels. In particular, linear STBCs with complex orthogonal design (COD) and GCIOD are considered. Based on the theoretical analysis, the symbol PEP of the GCIOD codes is related to the transmit power, signal-to-noise ratio, and the rotated angle of the rotated QAM scheme. However, the symbol PEP of the COD code is irrelevant to the rotated angle. It is shown that simulation results match well with our analysis. Thus, the union bounds on SER can be applied to predict the performance of a STBCed system with adaptive code selection between the full-rate COD and GCIOD codes.

On Full Diversity Space–Time Block Codes With Partial Interference Cancellation Group Decoding

In this paper, we propose a partial interference cancellation (PIC) group decoding strategy/scheme for linear dispersive space-time block codes (STBC) and a design criterion for the codes to achieve full diversity when the PIC group decoding is used at the receiver. A PIC group decoding decodes the symbols embedded in an STBC by dividing them into several groups and decoding each group separately after a linear PIC operation is implemented. It can be viewed as an intermediate decoding between the maximum likelihood (ML) receiver that decodes all the embedded symbols together, i.e., all the embedded symbols are in a single group, and the zero-forcing (ZF) receiver that decodes all the embedded symbols separately and independently, i.e., each group has and only has one embedded symbol, after the ZF operation is implemented. The PIC group decoding provides a framework to adjust the complexity-performance tradeoff by choosing the sizes of the information symbol groups. Our proposed design criterion (group independence) for the PIC group decoding to achieve full diversity is an intermediate condition between the loosest ML full rank criterion of codewords and the strongest ZF linear independence condition of the column vectors in the equivalent channel matrix. We also propose asymptotic optimal (AO) group decoding algorithm which is an intermediate decoding between the MMSE decoding algorithm and the ML decoding algorithm. The design criterion for the PIC group decoding can be applied to the AO group decoding algorithm because of its asymptotic optimality. It is well-known that the symbol rate for a full rank linear STBC can be full, i.e., <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> , for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> transmit antennas. It has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver. The intermediate criterion proposed in this paper provides the possibility for codes of rates between <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> and 1 that achieve full diversity with the PIC group decoding. This therefore provides a complexity-performance-rate tradeoff. Some design examples are given.

A new low SNR, correlated fading-suited space-time block code based on zero-padding and unitary transforms

In recent years, extensive studies have been done to design space-time codes appropriate for communications over fading channels in multiple input-multiple output (MIMO) systems. Most of these designs have been based upon the assumption that the channel fading coefficients are uncorrelated hence independent jointly Gaussian random variables. Naturally the best strategy in such situations that the elements of the channel matrix are independent is to employ diversity techniques to combat the adverse effects of these fading media and thus the most famous space-time codes, i.e. orthogonal and trellis codes have been designed with an eye to realizing the maximum attainable diversity order in a MIMO system. In this paper, we will remove this practically difficult to meet condition and shall introduce a new linear space-time block code based on zero-padding and unitary transforms that due to having some inherent redundancy as well as diversity is better-suited to correlated fading channels. We will discuss the properties of the proposed code, derive its maximum likelihood (ML) decoder and provide simulation results which show its superiority over the highly used orthogonal space-time block codes in a wide range of signal to noise ratios in correlated fading channels.

Hierarchical Space-Time Block Code Recognition Using Correlation Matrices

The blind recognition of communication parameters is a key research issue for commercial and military communication systems. The results of numerous investigations about symbol timing estimation, modulation recognition as well as identification of the number of transmitters have been reported in the literature. But, to our knowledge, none of them have dealt with the recognition of the Space-Time Block Codes (STBC) used in multiple transmitter communications. In order to blindly recognize the STBC of a wireless communication, this paper proposes a method based on the space-time correlations of the received signals. Under perfect timing synchronization and under ideal conditions (full rank channel and a number of receivers greater or equal to the number of transmitters), it shows that the Frobenius norms of these statistics present non-null values whose positions only depend on the STBC at the transmitter side. A classifier for the space-time code recognition of 5 linear STBC (Spatial Multiplexing, Alamouti Coding, and 3 Orthogonal STBC using 3 antennas) is presented. Simulations show that the proposed method performs well even at low signal-to-noise ratios.

Maximum-Likelihood Decoding for Nonorthogonal and Orthogonal Linear Space–Time Block Codes

It is a general consensus that an orthogonal space-time block code can achieve full diversity, and due to its orthogonal nature, the multiple-input-multiple-output (MIMO) maximum-likelihood (ML) decoding metrics can be decoupled into single-input-single-output (SISO) ML metrics based on linear processing at the receiver, thus greatly reducing the decoding complexity. In fact, nonorthogonal codes also currently exist that can achieve better symbol-error-rate performance without rate reduction and complexity increase for correlated fading channels. In this paper, we show by detailed derivations that nonorthogonal linear space-time block codes can also be decoded by ML decoupling through receiver linear processing. Our derived expressions for the decoupled ML metrics automatically contain the design information for the receiver linear processors.

A New Generic Maximum-Likelihood Metric Expression for Space–Time Block Codes With Applications to Decoding

The metric expression for a generic linear space-time block code (STBC) is studied using a different approach to vectorization and a new representation of the metric. The new representation lends itself to a simple measure of reliability based on the sum of inner products, and provides a quantifiable definition for minimum distance of a STBC. This provides the framework for a new family of near-maximum-likelihood (ML) and ML decoding algorithms. It also has applications in the development of optimality test criteria for STBCs, as well as in the design of STBCs with low decoding complexity.

A NEW LINEAR SPACE-TIME BLOCK CODE FOR WIRELESS CHANNELS WITH CORRELATED FADING COEFFICIENTS

In the recent years, extensive studies have been done to design space-time codes appropriate for communications over fading channels in multiple input-multiple output (MIMO) systems. Most of these designs have been based upon the assumption that the channel fading coefficients are uncorrelated hence independent jointly Gaussian random variables. Naturally the best strategy in such situations that the elements of the channel matrix are independent is to employ diversity techniques to combat the adverse effects of these fading media and thus the most famous space-time codes, i.e., orthogonal and trellis codes have been designed with an eye to realizing the maximum attainable diversity order in a MIMO system. In this paper, we will remove this almost ever-present yet practically difficult to meet condition and shall introduce a new linear space-time block code that due to having some inherent redundancy as well as diversity is wellsuited to correlated fading channels. We will discuss the properties of the proposed code, derive its maximum likelihood (ML) decoder and provide simulation results which show its superiority to the highly used orthogonal space-time block codes in a wide range of signal to noise ratios in correlated fading channels.

MMSE optimal algebraic space-time codes

Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.

Blind Channel Identifiability for Generic Linear Space-Time Block Codes

Linear space-time block codes (STBCs) have proven their effectiveness in performance improvement of wireless multiple-input multiple-output communication systems. Their successful decoding, however, requires reliable channel knowledge at the receiver. In this paper, we present a semiblind channel estimation method for linear STBC without the usual code orthogonality condition. We provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration. We also present a simple channel estimation algorithm. Finally, we provide simulation results that illustrate the performance of the proposed scheme

On the Design of Minimum BER Linear Space-Time Block Codes for MIMO Systems Equipped With MMSE Receivers

In this paper, we consider the design of a full-rate linear space-time block code for coherent multiple-input multiple-output (MIMO) communication systems under a quasi-static Rayleigh flat-fading environment. Our design targets specifically at the use of a linear minimum mean-square error (MMSE) receiver that minimizes the asymptotic average bit error rate (BER) when the transmitted signal is selected from a 4-QAM constellation. This optimization problem is solved in two main stages: 1) a lower bound on the BER is first minimized, and 2)how this minimized lower bound can be achieved is then shown. By exploiting a rigorous convex optimization technique without any assumption on the code, we prove that individual unitary and trace-orthogonal structures are the necessary and sufficient conditions to assure the minimum asymptotic average BER with an MMSE detector. An algorithm is provided for an efficient generation of our codes, and simulation results confirm that our optimally designed codes are indeed superior in performance compared to some other commonly used codes

Automatic design of orthogonal or near-orthogonal linear dispersive space-time block codes

This paper considers a wireless multiple-input multiple-output (MIMO) communication system in a frequency-nonselective scenario with spatially uncorrelated Rayleigh fading channel coefficients and investigates the design of linear dispersive (LD) space-time block codes. Efficient LD codes are obtained by optimizing the constituent weight matrices so that an upper bound on the union bound of the codeword error probability is minimized. Interestingly, the proposed design procedure automatically generates LD codes that either correspond to, or are close to, the well-known class of orthogonal space-time block (OSTB) codes. A theoretical analysis confirms this by proving that OSTB codes are indeed optimal, when the setup under study permits their existence. Simulation results demonstrate the excellent performance of the designed codes. In particular, the importance of the codes' near-orthogonal property is illustrated by showing that low-complexity linear equalizer techniques can be used for decoding purposes while incurring a relatively moderate performance loss compared with optimal maximum-likelihood (ML) decoding

Single-symbol maximum likelihood decodable linear STBCs

Space-time block codes (STBCs) from orthogonal designs (ODs) and coordinate interleaved orthogonal designs (CIOD) have been attracting wider attention due to their amenability for fast (single-symbol) maximum-likelihood (ML) decoding, and full-rate with full-rank over quasi-static fading channels. However, these codes are instances of single-symbol decodable codes and it is natural to ask, if there exist codes other than STBCs form ODs and CIODs that allow single-symbol decoding? In this paper, the above question is answered in the affirmative by characterizing all linear STBCs, that allow single-symbol ML decoding (not necessarily full-diversity) over quasi-static fading channels-calling them single-symbol decodable designs (SDD). The class SDD includes ODs and CIODs as proper subclasses. Further, among the SDD, a class of those that offer full-diversity, called Full-rank SDD (FSDD) are characterized and classified. We then concentrate on square designs and derive the maximal rate for square FSDDs using a constructional proof. It follows that 1) except for N=2, square complex ODs are not maximal rate and 2) a rate one square FSDD exist only for two and four transmit antennas. For nonsquare designs, generalized coordinate-interleaved orthogonal designs (a superset of CIODs) are presented and analyzed. Finally, for rapid-fading channels an equivalent matrix channel representation is developed, which allows the results of quasi-static fading channels to be applied to rapid-fading channels. Using this representation we show that for rapid-fading channels the rate of single-symbol decodable STBCs are independent of the number of transmit antennas and inversely proportional to the block-length of the code. Significantly, the CIOD for two transmit antennas is the only STBC that is single-symbol decodable over both quasi-static and rapid-fading channels.

Single-carrier and multi-carrier space–time block coded transmissions over doubly selective fading channels

We propose a multi-stage successive interference cancellation (SIC) receiver for arbitrary linear space-time block codes (STBCs) over general time-frequency selective fading channels with single-carrier (SC) transmissions. The proposed receiver adopts the SIC approach to handle intersymbol interference (ISI) owing to multipath propagation. Simulation results show that the proposed receiver outperforms the OFDM system after a few iterations in the BER range 10 -3 to 10 -5 . We also propose a diversity enhancement space-time signalling scheme for four transmit antennas with an increased diversity order. Simulation results show that the proposed diversity enhancement scheme outperforms the OFDM system even at the first iteration.