Non-orthogonal Space-time Block Codes Research Articles

Generalized designs for precoded receive spatial modulation derived from non-orthogonal space time block codes

Generalized designs for precoded receive spatial modulation derived from non-orthogonal space time block codes

СИНТЕЗ СПЕКТРАЛЬНО ТА ЕНЕРГЕТИЧНО-ЕФЕКТИВНИХ СИГНАЛЬНО-КОДОВИХ КОНСТРУКЦІЙ ДЛЯ СИСТЕМ МІМО З ПРОСТОРОВИМ КОДУВАННЯМ СИГНАЛІВ

Wireless communication systems are considered, the main task of which is to increase their spectral (SE) and energy efficiency (EE) in conditions of limited frequency and energy resources. Additional use of the spatial resource based on flexible and universal methods of signals Space-Time Coding (STC) in MIMO-systems (Multiple Input - Multiple Output) can significantly increase the SE and EE values, as well as significantly improve the capabilities and conditions for EE exchange on SE. The advantages and disadvantages of Orthogonal Space-Time Block Coding (OSTBC) and Non-Orthogonal STBC (NOSTBC) are shown. Two main methods of synthesis of spectrally and energy-efficient information transmission methods are demonstrated. The first method is implemented by creating Perfect-codes that simultaneously achieve maximum diversity and multiplexing gains. The exponential computational decoding complexity of such codes makes it impossible for their practical implementation in mobile terminals at the present stage of development of circuitry. The second method of synthesis is based on improving the simple basic STC methods in terms of increasing the SE and EE by creating Signal-Code Constructions (SCC), which have the advantages of the basic STC methods and are devoid of the disadvantages inherent in Perfect-codes. A technique for the synthesis of SCC is proposed, the essence of which is to determine the priority areas (by the value of the Signal-to-Noise Ratio (SNR)) of using the STC and corresponding signal constellations, which provide the maximum SE for a guaranteed Bit Error Rate (BER). It was found that MIMO 2x2 with Alamouti OSTBC has an advantage in terms of EE over NOSTBC type VBLAST for SE not more than 8 b/s/Hz and SNR under 35 dB, BER not exceeding 10-5. In MIMO 4x4, OSTBC codes are inferior to NOSTBC in terms of EE. VBLAST code allows to provide SE 4 - 8 b/s/Hz at SNR 10 - 20 dB, BER not exceeding 10-5. Based on the results obtained, propositions for further improvement of OSTBC and NOSTBC are formulated.

Performance of Full Rate Non-Orthogonal STBC in Spatially Correlated MIMO Systems

Spatial correlation is a crucial impairment for practical Multiple Input Multiple Output (MIMO) wireless communication systems. It is important to consider spatial correlation between antennas in actual communication scenario at both sides, i.e. transmit and receive side. Furthermore, we have considered nonorthogonal full rate STBC in MIMO systems equipped with four transmit antennas and four receive antennas in a quasi-static Rayleigh fading channel. In this paper, Bit Error Rate (BER) performance of full rate non-orthogonal Space Time Block code (STBC) is obtained using simulations in MIMO wireless communication systems. Spatial correlation is assumed between antennas at both the transmitter and the receiver sides. For this analysis, we have considered various transmit antenna spacing values of d t = 0.1π, 0.2π, and 0.4π keeping fixed d r = 0.1π and various receive antenna spacing values of d r = 0.1π, 0.2π, and 0.4π keeping fixed d t = 0.1π. The obtained results show that the transmitting diversity is more serious than the receiving diversity in the spatially correlated antenna environment for the specified signal-to-noise ratio. This study will be useful for actual wireless communication implementation where spatial correlation antennas are present in the practical environment of the MIMO wireless communication system.

Spatially Modulated Non Orthogonal Space Time Block Code: Construction and design from cyclic codes over Galois Field

A new class of non-binary Spatially Modulated Non-orthogonal Space Time Block Code designs (SM-NSTBC) has been proposed. These designs employ full rank, length n,(n|qm−1,m≤n) cyclic codes defined over GF(qm). The underlying cyclic code constructions have the property that the codewords when viewed as m×n matrices over GF(q) have rank equal to m (Full rank). These codes are punctured to yield m×m full rank matrices over GF(q). Rank preserving transformations are used to map the codewords of full rank codes over a finite field to full rank Space Time Block Codes. The proposed scheme can be generalized to handle any number of transmit antenna greater than two. Due to the characteristics of Full rank cyclic codes employed, a coding gain of approximately 1.5 dB to 5 dB is obtained over conventional STBC-SM and SM-OSTBC schemes. This is demonstrated for spectral efficiencies of 4, 5, 7 and 8 bpcu. Analytical as well as Monte-Carlo simulations show that proposed SM-NSTBC outperforms STBC-SM and its variants. The upper bound on average bit error rate has been derived and the computation complexity for ML detection has been estimated.

Discreteness-Aware Decoding for Overloaded Non-Orthogonal STBCs via Convex Optimization

This letter proposes a decoding scheme for non-orthogonal space-time block codes (NO-STBCs) in overloaded multiple-input multiple-output systems, where the number of different transmitted streams is greater than that of receive antennas. For the underdetermined decoding problem, we iteratively solve a convex optimization problem with the update of the parameters in the objective function, which utilizes the discreteness of the transmitted symbols. For the NO-STBC based on cyclic division algebra, we can reduce the order of computational complexity of the algorithm by taking advantage of the structure of the code. Simulation results show that the proposed algorithm outperforms conventional schemes in the decoding of large-scale overloaded NO-STBCs.

Near Optimal Receive Antenna Selection Scheme for MIMO System under Spatially Correlated Channel

Spatial correlation is a critical impairment for practical Multiple Input Multiple Output (MIMO) wireless communication systems. To overcome from this issue, one of the solutions is receive antenna selection. Receive antenna selection is a low-cost, low-complexity and no requirement of feedback bit alternative option to capture many of the advantages of MIMO systems. In this paper, symbol error rate (SER) versus signal to noise ratio (SNR) performance comparasion of proposed receive antenna selection scheme for full rate non-orthogonal Space Time Block Code (STBC) is obtained using simulations in MIMO systems under spatially correlated channel at transmit and receive antenna compare with several existing receive antenna selection schemes. The performance of proposed receive antenna selection scheme is same as conventional scheme and beat all other existing schemes.

Performance Comparison of STBC-OFDM with Maximum Likelihood Detection for Rayleigh Fading Channel

The combined system STBC-OFDM has considered an important association to integrate into actual and next wireless system. Such as the Wifi standard, WiMAX standard, the LTE fourth generation of mobile. Which combat the effect of multipath fading channel that limited the performance in wireless communications. In recent years, this association has been a large study to achieve a better performance of BER and designed for the different situation of the wireless channel from slow to fast fading channel, with various parameters of OFDM modulation and under different condition of STBC code. To contribute in this axis of research, we present a comparative study of the simulation result for STBC-OFDM. The first results are the comparison between three schemes of STBC (Alamouti code, Orthogonal STBC, Non-Orthogonal STBC) associated with OFDM. The second results are the comparison between three schemes when applied OFDM in different parameters and also when these codes used without OFDM modulation. The channel considered across simulation is Rayleigh fading channel that presented a real situation of the wireless environment, the Maximum Likelihood (ML) is used for detection the data that encoded in the first. The performance of three schemes is evaluated by BER (Bit Error Rate) versus the different values of SNR (Signal Noise Ratio).

Novel QO-STBC Scheme

In order to satisfy the huge communications demands MIMO (Multiple input and Multiple Output) systems is one of the techniques which provide high data rates under the constraints of limited bandwidth and transmit power. Space-Time Block Coding (STBC) is based on MIMO transmission strategy which exploits transmit diversity. STBCs are divided into two main classes i.e. Orthogonal Space-Time Block Codes (OSTBCs) and Non-Orthogonal Space-Time Block Codes (NO-STBCs). The Quasi-Orthogonal Space-Time Block Codes (QO-STBCs) belong to class of NO-STBCs and have been our area of interest. Full data rate and full diversity can only achieved with QSTBCs with a small loss in the diversity gain. The foremost purpose of this work is to provide a unified theory of QSTBCs for four transmit antennas and one receive antennas.

One Bit Feedback Based Diagonal Precoding for Non-Orthogonal Space-Time Block Codes

Quantized feedback about the channel state information (CSI) at the transmitter improves the error performance of MIMO systems. In literature, most of the work is done to improve the error performance of the orthogonal space time block codes (OSTBCs) using feedback of CSI from the receiver to the transmitter. In this letter, we study the performance of non-orthogonal space-time block codes (NOSTBCs) in a 2 $\!\times\!$ 1 multiple-input single-output system with diagonal weighting scheme; this scheme utilizes quantized one bit feedback with no delay from the receiver in a quasi-static Rayleigh fading channel. The considered NOSTBCs are Golden code and Silver code. Error-tolerant diagonal weighting parameter which improves the pair wise error probability (PEP) of the receiver is derived. The PEP performance of the considered set-up is studied for the complex-valued constellation like quadrature amplitude modulation. Simulation results indicate that similar to OSTBCs, the error performance of the NOSTBCs also improves with the proposed diagonal precoding scheme.

On the design of full-rate full-diversity space-time block codes for multiple-input–multiple-output systems with a turbo minimum mean square error equaliser at the receiver side

Non-orthogonal space-time block (STB) code structures used to be optimised considering a maximum-likelihood detection, but depending on the modulation order and/or the antenna number, the prohibitive complexity of such a receiver makes it infeasible in practice. Suboptimal low-complexity receiver structures like linear detectors can be applied instead, yielding degradation of performance compared with the predictions. When a forward error correction (FEC) code is used upstream of the STB code, an iterative receiver consisting of a FEC decoder and an interference canceller (IC) co-operating according to the turbo equalisation principle, can achieve near-optimal performance. This study aims to define the construction of full-rate full-diversity linear dispersion codes with reduced peak-to-average power ratio (PAPR), taking into account the serial concatenation with a FEC at the transmitter and a minimum mean square error (MMSE) turbo equaliser at the receiver. Optimisation criteria are mutual information maximisation, symbol error rate minimisation at the MMSE–IC output, full-diversity thanks to the threaded algebraic space time concept and PAPR minimisation. Explicit constructions are given and the resulting code efficiency is analysed through comparison with equivalent perfect STB codes.

Linear precoding of STBC over correlated ricean MIMO channels

A linear precoder is designed to minimize an upper bound of the pairwise error probability (PEP) when using arbitrary space-time block codes (STBC) over correlated Ricean fading channels. The proposed precoder design differs from the previously proposed precoders as follows: 1) Existing precoders are applicable when there exists only transmit correlation and no receive correlations, however, the proposed precoder is applicable to correlated Ricean MIMO channels with an invertible correlation matrix. 2) We minimize the upper bound of the PEP of non-orthogonal STBC for obtaining a precoder over correlated Ricean channels, whereas, one existing precoder minimizes an upper bound of PEP for orthogonal STBC (OSTBC). The proposed precoder outperforms two existing precoders for non-orthogonal STBC especially for highly correlated channels.

Differential coding for non-orthogonal space-time block codes with non-unitary constellations over arbitrarily correlated rayleigh channels

In this paper, we propose a maximum likelihood (ML) decoder for differentially encoded full-rank square nonorthogonal space-time block codes (STBCs) using unitary or non-unitary signal constellations, which is also applicable to full-ranked orthogonal STBC (OSTBC). As the receiver is jointly optimized with respect to the channel and the unknown data, it does not require any knowledge of channel power, signal power, or noise power to decode the signal, and the decision is purely based on two consecutively received data blocks. We analyze the effect of channel correlation on the performance of the proposed system in Rayleigh fading channels. Assuming a general correlation model, an upper bound of the pair-wise error probability (PEP) of the differential OSTBCs is derived. An approximate bound of the PEP for the differential nonorthogonal STBCs is also derived. We propose a precoder designing criterion for differential STBC over arbitrarily correlated Rayleigh channels. Precoding improves the system performance over the correlated Rayleigh MIMO channels. Our precoded differential codes differ from the previously proposed precoder designs for differential OSTBC in the following ways: 1) We propose a precoder design for arbitrarily correlated Rayleigh channels, whereas the previous work considers only for transmit correlation. 2) The previous work is only applicable to the OSTBCs with PSK constellations, whereas our precoder is applicable to any type of full-rank square STBCs with unitary and non-unitary signal constellations.

Frequency-Domain Receivers for Rate-1 Space-Time Block Codes

This paper considers iterative frequency-domain receivers for block transmission techniques with rate-1 Space Time Block Coding (STBC) for two and four transmit antennas using both Orthogonal Frequency Division Multiplexing (OFDM) and Single-Carrier (SC) schemes. The proposed receiver includes an interference canceller which enhances the performance of the non-orthogonal STBC scheme with 4 transmit antennas, allowing performances close to those of orthogonal codes. Our performance results show that combining STBC with block transmission techniques allows excellent performances.

High-rate full-diversity space-time block codes for three and four transmit antennas

The authors deal with the design of high-rate, full-diversity, low-maximum likelihood (ML) decoding complexity space-time block codes (STBCs) with code rates of 2 and 1.5 complex symbols per channel use for multiple-input multiple output (MIMO) systems employing three and four transmit antennas. The authors fill the empty slots of the existing STBCs from coordinate interleaved orthogonal designs (CIODs) in their transmission matrices by additional symbols and use the conditional ML decoding technique, which significantly reduces the ML decoding complexity of non-orthogonal STBCs while ensuring full-diversity and high coding gain. First, two new schemes with code rates of 2 and 1.5 are proposed for MIMO systems with four transmit antennas. The authors show that our low-complexity rate-2 STBC outperforms the corresponding best STBC recently proposed by Biglieri et al. (2008) for quadrature phase shift keying (QPSK), due to its superior coding gain while our rate-1.5 STBC outperforms the full-diversity quasi-orthogonal STBC (QOSTBC). Then, two STBCs with code rates of 2 and 1.5 are proposed for three transmit antennas, which are shown to outperform the corresponding full-diversity QOSTBC. The authors prove by an information-theoretic analysis that the capacities of new rate-2 STBCs for three and four transmit antennas are much closer to the actual MIMO channel capacity than the capacities of classical OSTBCs and CIODs.

Full-Diversity Codes for MISO Systems Equipped With Linear or ML Detectors

In this paper, a general criterion for space time block codes (STBC) to achieve full-diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas (MISO). Particularly, the STBC with Toeplitz structure satisfies this criterion and therefore, enables full-diversity. Further examination of this Toeplitz STBC reveals the following important properties: a) The symbol transmission rate can be made to approach unity. b) Applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a non-vanishing determinant. In addition, if QAM is used as the signalling scheme, then for independent MISO flat fading channels, the Toeplitz codes is proved to approach the optimal diversity-vs-multiplexing tradeoff with a ZF receiver when the number of channel uses is large. This is, so far, the first non-orthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when ML detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pair-wise error probability.

A Low-Complexity Detector for Large MIMO Systems and Multicarrier CDMA Systems

We consider large MIMO systems, where by 'large' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just O(N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ), where N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> denote the number of transmit and receive antennas, respectively. With an outer turbo code, the proposed detector achieves good coded bit error performance as well. For example, in a 600 transmit and 600 receive antennas V-BLAST system with a high spectral efficiency of 450 bps/Hz (using BPSK and rate-3/4 turbo code), our simulation results show that the proposed detector performs to within about 7 dB from capacity. This practical feasibility of the proposed high-performance, low-complexity detector could potentially trigger wide interest in the theory and implementation of large MIMO systems. We also illustrate the applicability of the proposed detector in the low-complexity detection of high-rate, non-orthogonal space-time block codes and large multicarrier CDMA (MC-CDMA) systems. In large MC-CDMA systems with hundreds of users, the proposed detector is shown to achieve near single-user performance at an average per-bit complexity linear in number of users, which is quite appealing for its use in practical CDMA systems.

New Design for Linear Precoding over STBC in the Presence of Channel Correlation

In order to account for spatial correlation in a multiple input multiple output (MIMO) channel using precoding over space-time block codes (STBC), an approach was proposed for the design of a linear precoder (H. Sampath and A. Paulraj, 2002). This approach works well for orthogonal STBC but fails in the case of non-orthogonal STBC. Based on a min-max problem formulation, a new design of the linear precoder is proposed in this paper. Simulation results in the case of quasi-orthogonal STBC (ABBA) are presented in order to show the gain over the conventional design approach and the non-precoded system

Extended Techniques for Transmit Antenna Selection With STBCs

In this paper, we consider transmit antenna selection (TAS) with space-time block codes (STBCs). We consider a general framework for TAS which, besides antenna subset selection, includes the possibility of having more than one STBC to choose from as well as non-uniform power allocation. Also, to limit the number of transmit RF chains, we require that the maximum (row) rank of the STBC matrices have an upper limit. Simple analysis indicate that transmitting uncoded data via the transmit antenna with the largest Frobenius norm, which can be viewed as a particular case of TAS with orthogonal STBC (OSTBC), not only provides full diversity as if all the transmit antennas were used but also has larger signal-to-noise ratio as compared to TAS with any standard OSTBC (like the Alamouti code). This suggests that TAS with non-orthogonal STBCs should be considered, in particular by means of exploiting instantaneous coherence within subsets of antennas. A few TAS schemes are proposed and computer simulations are used to demonstrate their superior error performance.

A general method to decode ABBA quasi-orthogonal space-time block codes

ABBA codes, a class of quasi-orthogonal space-time block codes (STBC) proposed by Tirkkonen et al., allow low complexity pair-wise complex-symbol decoding. A refined version of ABBA codes with special signal mapping leads to pair-wise real-symbol decoding, i.e. with minimum decoding complexity (MDC) achievable by non-orthogonal STBC. Despite these advantages, a general simple closed-form method to decode ABBA and MDC-ABBA codes for an arbitrary number of transmit/receive antennas is not available. We thus derive an equivalent channel representation to address this issue. The maximum mutual information of ABBA/MDC-ABBA codes is also derived. We found that MDC-ABBA codes perform better than ABBA codes when using two 8QAM constellations.

Design Criteria for Non-Orthogonal Space–Time Block Codes in Multipath Channels

We consider the problem of designing high rate space–time block codes in multipath fading channels. For this, both minimizing the effect of the self-interference induced by the code itself, and mitigating the inter-symbol-interference induced by the channel have to be addressed. We translate the problem into an equivalent problem of designing a constrained code in a single-path channel with more antennas, and argue that design criteria derived in single-path apply when optimizing this constrained code. Here we concentrate on an analytic measure pertinent to mutual information maximization and BER-performance optimization. The design program is successfully applied to rate one linear space–time transmissions from four transmit antennas. A family of discrete permutations of the transmitted sequences are considered. Performance is optimized within this family, and the results are seen to effect directly both mutual information and error performance.