Coordinate Interleaved Orthogonal Designs Research Articles

Index Modulation Based Coordinate Interleaved Orthogonal Design for Secure Communications

In this paper, we propose a physical layer security scheme that exploits a novel index modulation (IM) technique for coordinate interleaved orthogonal designs (CIOD). Utilizing the diversity gain of CIOD transmission, the proposed scheme, named CIOD-IM, provides an improved spectral efficiency by means of IM. In order to provide a satisfactory secrecy rate, we design a particular artificial noise matrix, which does not affect the performance of the legitimate receiver, while deteriorating the performance of the eavesdropper. We derive expressions of the ergodic secrecy rate and the theoretical bit error rate upper bound. In addition, we analyze the case of imperfect channel estimation by taking practical concerns into consideration. It is shown via computer simulations that the proposed scheme outperforms the existing IM-based schemes and might be a candidate for future secure communication systems.

Physical layer security in space‐time block codes from coordinate interleaved orthogonal design

In this study, the physical layer (PHY) security performance of orthogonal space-time block coding (OSTBC) employing a coordinate interleaved orthogonal design (CIOD) is analysed and investigated using two metrics: average secrecy capacity and secrecy outage probability. It is shown that the CIOD system is superior than OSTBC in terms of secrecy outage probability. Closed-form expressions for PHY security metrics in OSTBC as well as CIOD are presented and compared. Then, an extended model of CIOD with arbitrary number of antennas is considered. Furthermore, the effects of artificial noise and imperfect channel estimation on PHY security of OSTBC and CIOD systems are investigated. The validity of theoretical expressions is verified by simulation, and it is shown that in practical cases the CIOD system has a better secrecy outage performance than that of the OSTBC system.

Analysis of secrecy outage performance of TAS–CIOD systems over wireless Rayleigh fading channels

In this paper, the physical layer (PHY) security performance for a coordinate interleaved orthogonal design (CIOD) for space–time coding system with transmit antenna selection scheme (TAS) is analyzed and evaluated. As an important performance measure for the PHY security in the wireless systems, closed-form expression is derived for the secrecy outage probability (SOP) of a CIOD space–time coding system, where transmit antennas selection is employed. Using the numerical results obtained from the derived closed-form expression, the SOP performance of the CIOD with TAS is presented and compared with that of the classical orthogonal space–time block coding (OSTBC) system, in which Alamouti coding and transmit antenna selection scheme is employed. We show that the CIOD with transmit antenna selection can provide a superior secrecy performance than the Alamouti-OSTBC system with TAS. To verify the analysis we also provide the Monte Carlo simulation results to show the accuracy of the results obtained from theoretical expressions derived in this paper.

Secrecy performance analysis of CIOD–OFDM systems over wireless fading channels

Space–time block codes from coordinate interleaved orthogonal designs (CIODs) have been attracted attention due to their capability for full-diversity and full-rate transmission along with their needs for only a single-symbol decoding. When the number of transmit antennas is more than two, the code rate of orthogonal space–time block coding (OSTBC) is mostly lower than one, whereas, the CIOD offers rate-one transmission for two, three and four transmit antennas, yielding a higher transmission rate compared to that of the OSTBC. In addition, physical layer (PHY) security performance of CIOD scheme is an important issue but has not been evaluated yet. In this paper, the PHY security performance of a combined coordinate interleaved orthogonal design and orthogonal frequency-division multiplexing (CIOD–OFDM) is evaluated and studied. Closed-form expressions for two performance evaluation metrics of PHY security such as the average secrecy capacity and the secrecy outage probability are derived and presented for the considered CIOD–OFDM system and compared with the secrecy performance of the OSTBC–OFDM system. Mathematical expressions are derived for the general case, where multiple antennas are used at the transmitter and receiver sides. It is shown that the CIOD–OFDM system can provide a better security performance than the OSTBC–OFDM system. Furthermore, union bound expressions for the symbol error rate performance of CIOD–OFDM system is derived. Then, an efficient method for enhancing the PHY security of the signal transmission in CIOD–OFDM is presented. The Monte-Carlo simulation results are also presented for verifying the results obtained from mathematical and theoretical expressions.

Simultaneous Uplink/Downlink Transmission Using Full-Duplex Single-RF MIMO

In this letter, we introduce a full-duplex protocol for simultaneous transmission between the uplink and the downlink of cellular networks. The protocol takes advantage of the inactive antenna(s) in multiple-input-multiple-output (MIMO) systems with a single active radio frequency (RF) front-end. More precisely, for the downlink transmissions, we make use of spatial modulation (SM), and for the uplink, we make use of the coordinate-interleaved orthogonal design (CIOD)-based space-time block code (STBC). We provide accurate mathematical expressions for evaluating the error-performances and the achievable diversity order at the base station (BS) and at the mobile terminal (MT) in the presence of self-interference. Our results demonstrate clearly the potential of SM and CIOD for full-duplex operation.

Performance Analysis of Full-Rate Coordinate Interleaved Orthogonal Designs Over Time-Selective Fading Channels

Coordinate interleaved orthogonal designs (CIOD) (Khan and Rajan in IEEE Trans Inform Theory 52(5):2062---2091, 2006) can offer desirable properties, such as full rate, full diversity and single-symbol maximum likelihood decoding for two, three and four transmit antennas under quasi-static fading channels. When fading is time-selective, zero-forcing decoder can applied to achieve good performance while still maintain low decoding complexity. In this paper, theoretical analysis of symbol error rate performance for CIOD codes over time-selective fading channels with a zero-forcing linear receiver is derived. Firstly, a closed-form expression (i.e., not in integral form) is derived for the average symbol pair-wise error probability (SPEP) in time-selective frequency-nonselective independent identically distributed (i.i.d.) Rayleigh fading channels. Then, the SPEP is used to derive a tight upper bound (UB) for the symbol-error rate (SER) of CIOD codes. Simulation results indicate that our theoretical UB often coincides (within 0.05 dB) with the true SER obtained via Monte-Carlo simulation. The UB can thus be used to accurately predict and optimize the performance of CIOD codes over time-selective fading channels.

Space–Time Coded Spatial Modulated Physical Layer Network Coding for Two-Way Relaying

Using the spatial modulation approach, where only one transmit antenna is active at a time, we propose two transmission schemes for two-way relay channel using physical layer network coding with space time coding using coordinate interleaved orthogonal designs (CIODs). It is shown that using two uncorrelated transmit antennas at the nodes, but using only one RF transmit chain and space–time coding across these antennas can give a better performance without using any extra resources and without increasing the hardware implementation cost and complexity. In the first transmission scheme, two antennas are used only at the relay, adaptive network coding (ANC) is employed at the relay and the relay transmits a CIOD space time block code (STBC). This gives a better performance compared to an existing ANC scheme for two-way relay channel which uses one antenna each at all the three nodes. It is shown that for this scheme at high SNR the average end-to-end symbol error probability (SEP) is upper bounded by twice the SEP of a point-to-point fading channel. In the second transmission scheme, two transmit antennas are used at all the three nodes, CIOD STBCs are transmitted in multiple access and broadcast phases. This scheme provides a diversity order of two for the average end-to-end SEP with an increased decoding complexity of ${\cal O}(M^{3})$ for an arbitrary signal set and ${\cal O}(M^{2}\sqrt{M})$ for square QAM signal set. Simulation results show that the proposed schemes performs better than the existing ANC schemes under perfect and imperfect channel state information.

Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

A new class of Space Time Block Codes (STBCs) known as block orthogonal STBCs (BOSTBCs) was recently presented by Ren et al., which could be exploited by a QR decomposition decoder with M paths (QRDM decoder) to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed, was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including codes formed as the sum of Clifford Unitary Weight Designs (CUWDs). We also show that, construction methods from Coordinate Interleaved Orthogonal Designs (CIODs), Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs) can lead to BOSTBCs. In addition, we show that the block orthogonal STBCs offer a reduced decoding complexity when used in tandem with a fast sphere decoder using a depth first search approach. Simulation results involving decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.

Effect of Generalized-K Fading on the Performance of Symmetric Coordinate Interleaved Orthogonal Designs

In this letter, an efficient method of evaluating the performance of space-time block codes (STBCs) from symmetrically structured coordinate interleaved orthogonal designs (CIODs) is presented over generalized-K MIMO fading channels. By effectively approximating the moment generating function (MGF), we derive approximate closed-form expressions for the symbol pairwise error rate (SPER) and corresponding tight approximate symbol error rate (SER) of STBCs from symmetric CIODs. Finally, various Monte-Carlo simulations are performed to validate our theoretical results.

No-Zero-Entry Space-Time Block Codes Over Time-Selective Fading Channels for MIMO Systems

In MIMO systems, space-time block code (STBC) is good solution for improving system performance. Among the STBCs, coordinate interleaved orthogonal designs (CIODs) combined with QR-decomposition-based decision-feedback decoding (QR-DDF) allow achieving good performance for time-selective fading channels. However, half of entries in codeword matrix of CIODs are zeros. These zero entries result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation of the code when turning off some of the transmitting antennas whenever a zero is transmitted. In this paper, we propose a new design of space-time block codes without zero entry in codeword matrix (NZE-STBCs) for time-selective fading channels. The main advantage of the proposed NZE-STBCs is that its peak-to-average ratio (PAPR) is 3 dB lower than that of CIODs, and its hardware implementation is also easier due to eliminating on-off switchers without sacrificing performance. Moreover, similar as CIODs, the proposed NZE-STBCs can use low complexity QR-DDF decoder over time-selective fading channels to enhance performance and reduce decoding complexity. Simulation results show that the proposed NZE-STBCs outperform CIODs for three transmit antennas while performing the same for two and four transmit antennas.

Trellis‐coded CIOD using conjugate symmetric rotated QAM signal set

A trellis-coded coordinate-interleaved orthogonal design (TC-CIOD) for four transmit antennas with a rotated QAM base signal set is introduced. To design a high rate pre-encoder the base signal set is expanded by conjugating the rotated QAM signals without changing the transmit signal set at each transmit antenna. The proposed TC-CIOD provides coding gain without increasing peak-to-average-power ratio.

Training-Symbol Embedded, High-Rate, Single-Symbol ML-Decodable, Distributed STBCs for Relay Networks

Distributed space-time block codes (DSTBCs) from complex orthogonal designs (CODs) (both square and nonsquare), coordinate interleaved orthogonal designs (CIODs), and Clifford unitary weight designs (CUWDs) are known to lose their single-symbol ML decodable (SSD) property when used in two-hop wireless relay networks using amplify and forward protocol. For such networks, in this paper, three new classes of high rate, training-symbol embedded (TSE) SSD DSTBCs are constructed: TSE-CODs, TSE-CIODs, and TSE-CUWDs. The proposed codes include the training symbols inside the structure of the code which is shown to be the key point to obtain the SSD property along with the channel estimation capability. TSE-CODs are shown to offer full-diversity for arbitrary complex constellations and the constellations for which TSE-CIODs and TSE-CUWDs offer full-diversity are characterized. It is shown that DSTBCs from nonsquare TSE-CODs provide better rates (in symbols per channel use) when compared to the known SSD DSTBCs for relay networks. Important from the practical point of view, the proposed DSTBCs do not contain any zeros in their codewords and as a result, antennas of the relay nodes do not undergo a sequence of switch on/off transitions within every codeword, and, thus, avoid the antenna switching problem.

New design of no-zero-entry single symbol ML decodable STBCs based on group precoding

In multiple-input multiple-output (MIMO) systems, 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, most of these codes, for transmitting antennas more than 4, have large number of zero entries in their codeword matrix. Due to the zero entries in the design, the transmitting antennas need to be switched on and off imposing severe hardware constraints. To solve this problem, we propose a method to generate a new class of no-zero-entry single symbol maximum likelihood decodable STBCs (NZESSDCs), which is based on coordinate interleaving and group precoding technique. The ability of the proposed group precoding based NZESSDCs (called G-NZESSDCs) on single symbol ML Decoding and full diversity are analyzed and derived. The performance evaluation is accomplished by numerical simulation and is compared with recently reported NZESSDCs (called C-NZESSDCs). Compared with C-NZESSDCs, the proposed G-NZESSDCs have same bit-error-rate (BER) performance and better peak-to-average ratio (PAPR) performance.

Performance Evaluation of Space-Time Block Codes from Coordinate Interleaved Orthogonal Designs in Shadowed Fading Channels

In this correspondence, we evaluate the symbol error rate (SER) and information outage probability (IOP) of space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) in the composite channel of lognormal shadowing and Rayleigh fading. By applying the Gauss-Hermite quadrature integration, we derive an accurate closed-form approximation for the symbol pairwise error rate (SPER) and corresponding tight upper and lower bounds on the SER of STBCs from CIODs. An accurate closed-form approximate formula for the IOP is also derived by formulating the composite squared lognormal/chi-square probability density function and exploiting the high-signal-to-noise-ratio (SNR) approximation technique. Furthermore, we investigate the achievability of full diversity in Rayleigh fading channels with shadowing effects. Finally, various Monte Carlo simulations are performed to validate our theoretical results.

Enhanced 2&4 Tx Matrix a Scheme Based on Coordinate Interleaved Orthogonal Designs

Space-time block codes(STBCs) based on coordinate interleaved orthogonal designs (CIOD) are put forward integrally by analyzing the theory of generalized orthogonal designs. In accordance with the principle of Alamouti’s orthogonal receiver, the received signals are firstly processed by vector orthogonal transform, imaginary part exchange and vector-weighted spin processing, then we get the complete demodulation process. Finally, simulations for the transmit diversity configuration A with 4Tx CIOD in 802.16d/e were performed over quasi-static Rayleigh flat-fading channel. The results show that the proposed transmission scheme has a low decoding complexity similar to the classical STBC based on complex orthogonal designs(COD). However, the former can get slightly better performance.

Space–Time Block Codes With Symbol-by-Symbol Maximum-Likelihood Detections

This paper presents a new set of quasi-orthogonal space-time block codes (QOSTBCs) with symbol-by-symbol maximum-likelihood (ML) detections for four Tx antennas over quasi-static Rayleigh fading channels. Each of the codes is analytically proved to achieve full transmit diversity and the same coding gains as the rate-1 coordinate-interleaved orthogonal design by individually using their optimal constellation rotations over arbitrary quadrature amplitude modulation (QAM) or 4 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -phase-shift keying (PSK) constellations. Previous designs are included in the systematic formulation as well. Combining with simulation, the coding loss paying for simplifying the optimal decoders from complex-symbol-pairwise to symbol-by-symbol ML detections is found asymptotically equal to 0.21 dB, for the QOSTBCs achieving full transmit diversity and the optimal coding gains over general QAM constellations.

The performance of space-time block codes from coordinate interleaved orthogonal designs over nakagami-m fading channels

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) offer several advantages including full-diversity and single-symbol decodability. In an effort to assess their performance in quasi-static frequency nonselective i.i.d. Nakagami-m fading channels, we analyze the error rate, outage capacity, and information outage probability. First, based on an accurate closed-form formula for the average symbol pairwise error rate (SPER), we derive tight union upper and lower bounds on the symbol-error rate (SER). Second, we apply Gaussian and Gamma approximations to provide closed form expressions for the outage capacity. Third, using high signal-to-noise ratio (SNR) and moment-matching approximation techniques, we also derive accurate closed-form approximations for the information outage probability (IOP). Finally, we show that STBCs from CIODs provide full-diversity by deriving SER based and IOP-based asymptotic and instantaneous diversity orders. Monte-Carlo simulations show that the analytical results agree with simulation experiments.

On Optimal Quasi-Orthogonal Space–Time Block Codes With Minimum Decoding Complexity

Orthogonal space-time block codes (OSTBC) from orthogonal designs have both advantages of complex symbol-wise maximum-likelihood (ML) decoding and full diversity. However, their symbol rates are upper bounded by 3/4 for more than two antennas for complex symbols. To increase the symbol rates, they have been generalized to quasi-orthogonal space-time block codes (QOSTBC) in the literature but the diversity order is reduced by half and the complex symbol-wise ML decoding is significantly increased to complex symbol pair-wise (pair of complex symbols) ML decoding. The QOSTBC has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair-wise ML decoding. The optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal-literal triangular lattices have been found by Su-Xia, where the optimality means the optimal diversity product (or product distance). QOSTBC has also been modified by Yuen-Guan-Tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair-wise ML decoding (the same complexity as complex symbol-wise decoding) and the optimal rotation angle for square and rectangular QAM constellations has been found. In this paper, we systematically study general linear transformations of information symbols for QOSTBC to have both full diversity and real symbol pair-wise ML decoding. We present the optimal transformation matrices (among all possible linear transformations not necessarily symbol rotations) of information symbols for QOSTBC with real symbol pair-wise ML decoding such that the optimal diversity product is achieved for both general square QAM and general rectangular QAM signal constellations. Furthermore, our newly proposed optimal linear transformations for QOSTBC also work for general QAM constellations in the sense that QOSTBC have full diversity with good diversity product property and real symbol pair-wise ML decoding. Interestingly, the optimal diversity products for square QAM constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. However, the optimal diversity products for (nonsquare) rectangular QAM constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. In this paper, we also present the optimal transformations for the co-ordinate interleaved orthogonal designs (CIOD) proposed by Khan-Rajan for rectangular QAM constellations.

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.

Bandwidth-Efficient Mutually Cooperative Relaying with Spatially Coordinate-Interleaved Orthogonal Design

This letter proposes a type of mutually cooperative relaying (MCR) scheme based on a spatially coordinate-interleaved orthogonal design (SCID), in which two cooperative users are spatially multiplexed without bandwidth expansion. It provides not only diversity gain (with order of two) as in the existing MCR scheme, but also additional coding gain. Our simulation results demonstrate that the proposed SCID scheme is useful for improving the uplink performance as long as one user can find another active user as a close neighbor that is simultaneously communicating with the same destination, e.g., a base station in the cellular network.