Super-orthogonal Space-time Trellis Research Articles

Super-orthogonal double space–time trellis code

This study develops a new class of super-orthogonal trellis codes for four transmit antennas based on double space–time codes. The transmit antennas are divided into two groups, each having two transmit antennas. The information bits are demultiplexed into two streams; each is encoded independently using a super-orthogonal trellis code and then is transmitted from the corresponding antenna group. The resultant parallel-trellis code structure offers a higher data rate and, at the same time, it has a smaller number of parallel branches in the trellis encoder compared to a single stream encoder. The decoding is done using the maximum likelihood (ML) decoder with an interference cancellation algorithm.It is shown that the proposed scheme reduces the required number of overall calculations by about half compared with super-orthogonal space–time trellis codes (SO-STTC) and super-orthogonal trellis coded spatial modulation (SOTC-SM).The performance of the designed codes is simulated and shows that an improvement in the frame error rate (FER) is achieved at 4 and 5 b/s.Hz compared with SO-STTC and SOTC-SM, while at 6 b/s.Hz, it achieved an improvement in the lower and medium range of signal-to-noise ratio (SNR) (<22 dB).

Modified codewords design for space–time block coded spatial modulation

Two kinds of modified codewords for space–time block coded spatial modulation (STBC-SM) are presented in this study. The first modified codeword introduces a concept of flexible coefficients into the M-ary phase shift keying STBC-SM. A method is proposed to obtain the optimal flexible coefficients. Moreover, the first modified codewords can also be applied to the systems developed from the STBC-SM. In the second provided codewords, super-orthogonal space–time trellis codes are applied in STBC-SM. Therefore, a higher spectral efficiency is obtained compared with the original STBC-SM. Finally, the simulation results and theoretical analysis demonstrate these performance advantages of the two kinds of modified codewords for STBC-SM.

Space Time State Trellis Codes for MIMO Systems Using Reconfigurable Antennas

We present a novel class of space time trellis codes based on super quasi-orthogonal space time codes for a reconfigurable antenna system. We call them space time state trellis codes (STSTCs). We design for 4 trellis states and both 2 and 4 branch trellis structures for BPSK and QPSK constellations. The proposed codes take advantage of the additional degrees of diversity offered by reconfigurable antennas and changing propagation states. They achieve full rate, full diversity and high coding gain. Simulation results demonstrate their good performance. STSTCs achieve the diversity order expected of four transmit antennas while using only two reconfigurable transmit antennas. Our code out performs the existing super orthogonal space time trellis code, which fails to achieve full diversity in a reconfigurable antenna system. The proposed 4 trellis state STSTC is designed based on the following performance criteria: minimum coding gain distance of the minimum return path (CGD MRP), performance factor (PF), rank of the partial valid path (RPVP) on top of traditional minimum coding gain distance of parallel path (CGD PP). We show through analysis and simulations that minimum CGD PP is not a sufficient criteria and that additional performance gains are provided by considering the CGD MRP.

Hybrid Concatenated Super-orthogonal Space-time Frequency Trellis Coded MIMO-OFDM Systems

In this study, we propose two hybrids concatenated Super-Orthogonal Space-Time Trellis Codes (SOSTTC) applying iterative decoding in Orthogonal Frequency Division Multiplexing (OFDM) over frequency selective fading channels. The coding scheme is based on the concatenation of convolution coding, interleaving and space-time coding along multiple-transmitter/multiple-receiver diversity systems. The Pair wise Error Probability (PEP) for the two proposed concatenated schemes is derived and their performance is evaluated using computer simulation with Maximum a Posteriori (MAP) iterative decoding algorithm. Simulation results based on the iterative decoding process show a significant improvement in the achieved error rate performance of the concatenated scheme over existing concatenated designs.

SUPER ORTHOGONAL SPACE TIME TRELLIS CODES OVER NAKAGAMI FADING MODEL

Performance evaluation of super orthogonal space-time trellis codes for non-frequency selective fading channels &amp; frequency selective fading channels. The analysis is done in presence of fast fading, block fading and quasi-static fading in Rayleigh, and Nakhagami fast fading channels along with comparison. While providing full diversity and full rate, the structure of our new codes allows an increase in the coding gain. Not only does our new SOSTTC outperform the space-time trellis codes in the literature, but it also provides a systematic method for designing space time trellis codes at different rates and for different trellises. Since we have used orthogonal designs as the building blocks in our new SOSTTCs, the complexity of the decoding remains low while full diversity is guaranteed. Codes operating at different rates, up to the highest theoretically possible rate, for different number of states, can be designed by using our optimal set partitioning. In general, new SOSTTCs can provide a tradeoff between rate and coding gain while achieving full diversity.

Super-orthogonal trellis-coded spatial modulation

Spatial modulation (SM), which employs the indices of multiple transmit antennas to transmit information in addition to the conventional M-ary signal constellations, is a novel transmission technique that has been proposed for multiple-input multiple-output systems. In this study, a new class of space-time trellis codes, called ‘super-orthogonal trellis-coded SM’ (SOTC-SM), is proposed. These codes combine set partitioning and a super set of space-time block coded SM (STBC-SM) codewords to achieve maximal diversity and coding gains by exploiting both SM and space-time block codes. Unlike super-orthogonal space-time trellis codes (SOSTTCs), which parametrise the orthogonal STBCs, these new codes expand the antenna constellation using the principle of SM. Systematic construction methods are presented for the SOTC-SM scheme and design examples are given for 2, 4 and 8 trellis states, at 2, 3 and 4 bits/s/Hz spectral efficiencies. The approximate bit-error probability performance of SOTC-SM is derived and shown to match computer simulation results. A simplified maximum likelihood detection method for the proposed scheme is given. It is shown through computer simulations that the proposed SOTC-SM schemes achieve significantly better error performance than SOSTTCs with comparable complexity.

SISO APP Searches in Lattices With Tanner Graphs

An efficient, low-complexity, soft-output detector for general lattices is presented, based on their Tanner graph (TG) representations. Closest-point searches in lattices can be performed as non-binary belief propagation on associated TGs; soft-information output is naturally generated in the process; the algorithm requires no backtrack (cf. classic sphere decoding), and extracts extrinsic information. A lattice's coding gain enables equivalence relations between lattice points, which can be thereby partitioned in cosets. Total and extrinsic a posteriori probabilities at the detector's output further enable the use of soft detection information in iterative schemes. The algorithm is illustrated via two scenarios that transmit a 32-point, uncoded super-orthogonal (SO) constellation for multiple-input multiple-output (MIMO) channels, carved from an 8-dimensional non-orthogonal lattice (a direct sum of two 4-dimensional checkerboard lattice): it achieves maximum likelihood performance in quasistatic fading; and, performs close to interference-free transmission, and identically to list sphere decoding, in independent fading with coordinate interleaving and iterative equalization and detection. Latter scenario outperforms former despite the absence of forward error correction coding---because the inherent lattice coding gain allows for the refining of extrinsic information. The lattice constellation is the same as the one employed in the SO space-time trellis codes first introduced for 2-by-2 MIMO by Ionescu et al., then independently by Jafarkhani and Seshadri. Complexity is log-linear in lattice dimensionality, vs. cubic in sphere decoders.

New super-orthogonal space-time trellis codes using differential M-PSK for noncoherent mobile communication systems with two transmit antennas

In this paper, we develop super-orthogonal space-time trellis codes (SOSTTCs) using differential binary phase-shift keying, quadriphase-shift keying and eight-phase shift keying for noncoherent communication systems with two transmit antennas without channel state information at the receiver. Based on a differential encoding scheme proposed by Tarokh and Jafarkhani, we propose a new decoding algorithm with reduced decoding complexity. To evaluate the performance of the SOSTTCs by way of computer simulations, a geometric two-ring channel model is employed throughout. The simulation results show that the new decoding algorithm has the same decoding performance compared with the traditional decoding strategy, while it reduces significantly the overall computing complexity. As expected the system performance depends greatly on the antenna spacing and on the angular spread of the incoming waves. For fair comparison, we also design SOSTTCs for coherent detection of the same complexity as those demonstrated for the noncoherent case. As in the case of classical single antenna transmission systems, the coherent scheme outperforms the differential one by approximately 3 dB for SOSTTCs as well.

Super-Orthogonal Block Codes with Multichannel Equalisation and OFDM in Frequency Selective Fading

Super-orthogonal block codes in space-time domain (i.e., Super-orthogonal space-time trellis codes (SOSTTCs)) were initially designed for frequency nonselective (FNS) channels but in frequency selective (FS) channels these super-orthogonal block codes suffer performance degradation due to signal interference. To combat the effects of signal interference caused by the frequency selectivity of the fading channel, the authors employ two methods in this paper, namely, multichannel equalization (ME) and orthogonal frequency division multiplexing (OFDM). In spite of the increase complexity of the SOSTTC-ME optimum receiver design scheme, the SOSTTC-ME scheme maintains the same diversity advantage as compared to the SOSTTC scheme in FNS channel. In OFDM environments, the authors consider two forms of the super-orthogonal block codes, namely, super-orthogonal space-time trellis-coded OFDM and super-orthogonal space-frequency trellis-coded OFDM. The simulation results reveal that super-orthogonal space-frequency trellis-coded OFDM outperforms super-orthogonal space-time trellis-coded OFDM under various channel delay spreads.

Performance of super-orthogonal space–time trellis codes with transmit antenna selection

Super-orthogonal space-time trellis (SOSTT) codes provide a significant coding gain with respect to the conventional space-time trellis (STT) codes without increasing the decoding complexity at the receiver. Transmit antenna selection (TAS) is an important technique to solve the implementation complexity problems of multiple-antenna systems that arise from employing a separate RF chain for each antenna. This study treats a scheme combining SOSTT coding with TAS in order to exploit performance improvements provided by SOSTT codes while realising the promises made by the TAS technique. In the proposed scheme, transmit antennas that maximise the signal-to-noise ratio at the receiver are chosen and activated out of all available transmit antennas for transmission of the baseline SOSTT code, whereas all other transmit antennas are silent. The error performance of the proposed structure is investigated by deriving moment generating function (MGF)-based upper bound expressions on the pairwise error probability in quasi-static flat Rayleigh fading channels for both perfect and imperfect antenna subset selection. The performance analysis demonstrates that the proposed scheme provides full diversity order as if all transmit antennas were used when antennas are perfectly selected. Moreover, it is shown that this structure provides better error performance almost at the same decoding complexity compared to the previous STT coding structures with TAS in the literature.

New Layered Space-Time Schemes Based on Group of Three Transmit Antenna

We present a new architecture of layered space-time codes as a combination of Bell Laboratory Layered Space-Time (BLAST) architecture and of special Space Time Trellis (STTC) Codes which are variations about the Super Orthogonal Space-Time Trellis Codes (SOSTTC) first introduced by Ionescu et al in [1] [2] and further improved by Jafarkhani et al. in [3]. The system we propose is named Super Quasi Orthogonal Horizontal Layered Space Time Trellis Code (SQOHLSTTC). It consists in a powerful Space-Time Block Code (STBC) based STTC originally derived for a three transmit antenna system, together with an original block based decoding algorithm. The decoding algorithm of SQOHLSTTC combines group interference suppression and group interference cancellation techniques. To implement the system, we propose a low complexity hard decision iterative decoding method. System performances confirm the great interest of the proposed transmission scheme.

Improved super-orthogonal space-time trellis codes for fast Rayleigh fading channels

For fast Rayleigh fading channels, the performance of super-orthogonal space-time trellis codes (SOSTTCs) is analysed and a new code design process is developed. A binary phase shift keying design example is presented. Simulation results and transfer function upper bounds show that the proposed SOSTTC is superior to the previous work.

Punctured super-orthogonal space-time trellis codes

In this paper, we propose punctured super-orthogonal space-time trellis codes. First, considering a system with two transmit antennas, we present the basic design criteria for the punctured super-orthogonal codes. Then, staged decoding, a sub-optimal decoding technique used in single-input single-output systems, is extended to the proposed punctured codes. To reduce the complexity of staged decoding, we propose two complementary design rules of the punctured super-orthogonal codes. After that, we discuss the constraints under which the punctured codes can be designed without metric distortion. Compared with the conventional codes, the punctured super-orthogonal codes can provide lower decoding complexity. Also, they allow an easy implementation of various spectral efficiencies with a single encoder/decoder. Furthermore, the puncturing scheme can be generalized to the case of more than two transmit antennas. In addition, we implement differential modulation schemes based on the punctured codes. Such implementations do not require channel estimation at the transmitter and the receiver. Simulation results demonstrate that the performance of the punctured super-orthogonal space-time trellis codes is close to that of the corresponding conventional codes in the literature.

STBC-Based (Turbo) STTC Codes Built by Set Partitioning for Three Transmit Antennas: Construction and Performances

This paper introduces new studies on the codes named Super Orthogonal Space Time Trellis Codes (SOSTTC). Using set partitioning rules combined with a set of orthogonal designs, SOSTTC's are able to combine the coding gain of STTC's together with diversity advantage of orthogonal STBC's. We propose new application fields of these codes in the particular context of three transmit antenna systems. We introduce new STTC's built on STBC designs that outperform some STTC's schemes based on the determinant and rank criteria. Further- more, we demonstrate by simulation that the use of these codes in a turbo parallel concatenated scheme permits working very close to the channel outage probability.

Super-orthogonal space-time trellis codes with eight dimensional phase-shift keying signal constellations

We propose a new method of designing super-orthogonal space-time trellis codes (SOSTTCS) by labeling each state transition of the trellis diagram with an ordered pair of 2×2 orthogonal matrices instead of only a single 2×2 orthogonal matrix. An 8D instead of a 4D signal constellation is thus used for modulation and the delay elements of the trellis encoder are 4T instead of 2T, where T is the 2D symbol duration. Therefore, at the receiver, the sequence decoding using Viterbi algorithm requires two times less frequent updating of the branch metrics. We investigate by computer simulation the performance of the new sosttcs compared to sosttcs designed by the known method. The frame error rate (fer) and the bit error rate (ber) simulation results show that the performance of the new sosttcs is practically as good as that of the sosttcs of similar complexity designed along classical lines, with the advantage that the number of arithmetic and logic operations performed by the decoder per time unit is smaller, which is crucial in high data-rate applications.

Computer design of super-orthogonal space-time trellis codes

Super-orthogonal space-time trellis codes (SOSTTCs) designed by hand can significantly improve the performance of space-time trellis codes. This paper introduces a new representation of SOSTTCs based on a generator matrix that allows a systematic and exhaustive search of all possible codes. This will verify that some of the known codes are optimal, and provides a means to easily implement encoders and decoders with a large number of states without relying on a graphical representation. New codes with up to 256 states that outperform previously known codes are presented

Super-orthogonal space-time-frequency trellis coded OFDM

Super-orthogonal space-time trellis codes (SOSTTCs) given in the literature are full rate and provide full spatial diversity with high coding gain in narrowband quasistatic fading channels. The high number of parallel transitions in their trellis structure restricts their performance in wideband channels where the code performance suffers from multipath. Code design criteria are derived and a computer search based method is proposed to design full-rate optimised SOSTTCs exploiting full spatial and multipath diversity for multiple-input multiple-output orthogonal frequency division multiplexing systems. The proposed codes have codewords defined in space, time, and frequency. We evaluate the codeword error rates of the new 16, 32 and 64-state super-orthogonal space-time-frequency trellis codes for quadrature phase shift keying by computer simulation and show that they provide significant error performance improvement compared to their counterparts with equivalent delay length.

Space–Time Trellis Code Design Based on QAM-MTCM With Trellis Shaping

In this letter, super-orthogonal space-time trellis codes (SOSTTCs) are extended for quadrature amplitude modulation (QAM) constellations. A systematic set-partitioning method for QAM constellations is given. Furthermore, trellis shaping based on set partitioning is incorporated in SOSTTCs with QAM symbols to achieve extra shaping gain. Peak constraints can be used to limit the constellation expansion ratio and peak-to-average power ratio

Differential Super-Orthogonal Space-Time Trellis Codes

In this paper, we present two differential trellis coded space-time modulation schemes when the channel state information is not available at the transmitter and at the receiver. First, we extend the design of super-orthogonal space-time trellis codes to improve their performance. Then, based on these extended super-orthogonal codes, we propose the first differential scheme. Compared with the trellis coded differential unitary space-time modulation scheme, not only does the proposed differential scheme achieve full diversity, but also it provides identical or higher coding gain and much lower decoding complexity. In order to achieve further improved coding gain in addition to full diversity for more than two transmit antennas, we propose a second differential scheme which is based on super-quasi-orthogonal codes. Such a differential scheme outperforms the differential modulation scheme based on super-orthogonal codes with simpler decoding. Simulation results demonstrate the good performance of our schemes

Super-orthogonal space-time codes with rectangular constellations and two transmit antennas for high data rate wireless communications

We demonstrate super-orthogonal space-time (ST) trellis codes with rectangular signal constellations for wireless communications with a spectral efficiency of 4 bits/s/Hz. Considering a mobile wireless communications system with two transmit antennas, we form a 4D signal constellation as Cartesian product of two 2D rectangular signal sets, a 4D point being transmitted by the first antenna as two concatenated 2D points in two consecutive channel uses. The 2D symbols transmitted by the second antenna are not independent, but so chosen as to form, together with the symbols transmitted by the first antenna, the entries of a 2 times 2 orthogonal matrix. This can be done in four different ways, resulting in four sets of 2 times 2 orthogonal matrices. To obtain a higher data rate, the union of two of them forms a super-orthogonal signal set. With 2 times 2 orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. We perform simulations using a model that takes into account the Doppler effect as well as the effect of spatial antenna correlation at both the base station (BS) and at the mobile station (MS). The frame error rate (FER) and the bit error rate (BER) performance results show an excellent behaviour of our proposed super-orthogonal ST trellis code, which clearly outperforms all known simple ST trellis codes of same spectral efficiency using 16QAM or 16PSK