Differential modulation based on quasi-orthogonal codes

A general and simple differential modulation scheme that can be applied to both partial-diversity quasi-orthogonal space–time block codes and full-diversity quasi-orthogonal space–time block codes is reported. A new class of quasi-orthogonal coding structures is presented for various number of transmit antennas. Differential encoding and decoding can be simplified to differential Alamouti codes by grouping the signals in the transmitted matrix and decoupling the detection of data symbols, respectively. For the codes with partial transmit diversity, the new scheme can achieve constant amplitude of transmitted signals, and avoid signal constellation expansion; in addition, it has a linear signal detector with very low complexity. Simulation results show that these partial-diversity codes can provide very useful results at low signal-to-nose ratio for current communication systems. For codes with full transmit diversity achieved by constellation rotation, the proposed scheme has performance equal to the best full-rate quasi-orthogonal schemes previously described in the literature with the benefit of a simpler detector. Moreover, a simple linear detector is also presented for the case when two orthogonal ASK constellations are used. Extension to more than four transmit antennas is also considered.

In this paper, we present a method to improve the performance of the four transmit antenna quasi-orthogonal space-time block code (STBC) in the coded system. For the four transmit antenna case, the quasi-orthogonal STBC consists of two symbol groups which are orthogonal to each other, but intra group symbols are not. In an uncoded system with matched filter detection, constellation rotation can improve the performance. However, in coded systems, its gain is absorbed by the coding gain, especially for lower rate codes. We propose an iterative decoding method to improve the performance of quasi-orthogonal codes in coded systems. With conventional quasi-orthogonal STBC detection, the joint ML detection can be improved by iterative processing between the demapper and the decoder. Simulation results shows that the performance improvement is about 2 dB at 1% frame error rate.

An enhanced transmission is presented in a multiple‐input‐multiple‐output (MIMO) dense‐wavelength division multiplexed (DWDM) free‐space‐optical (FSO) communication link using diversity coding techniques under the effect of turbulent weather phenomenon. The findings show good performance with an (8 channels × 2.5 Gbps data rate/channel) 20 Gbps 1500 m transmission distance. The bit‐error‐rate (BER), outage probability (OP), and signal‐to‐noise ratio (SNR) of the diversity combining techniques using maximum‐ratio combining (MRC), selection combining (SC), and equal‐gain combining (EGC) technique are evaluated in this work. The obtained results illustrate that Alamouti, space‐time coding (STC), space‐time block coding (STBC), space‐time trellis code (STTC), orthogonal STBC (O‐STBC), and quasi‐orthogonal STBC ( QO‐STBC ) on the minimum mean‐square‐error, and MRC are worth implementing on the DWDM‐FSO wireless communication systems. The mitigation of atmospheric turbulence is achieved using MIMO diversity combining techniques coding. The simulation results for diversity coding techniques using QO‐STBC/STTC and SC/MRC in the MIMO‐DWDM FSO communication system can improve BER performance, OP, and SNR. The MRC exhibits the lowest OP and BER when compared with the SC and EGC. The numerical results demonstrate that the FSO communication link using DWDM QO‐STBC/STTC improves the power penalty at both BER values under varying atmospheric turbulence conditions for ST, MT, and WT, in comparison to FSO systems without DWDM QO‐STBC/STTC diversity coding techniques.

Massive multiple-input multiple-output (MIMO) using a large number of antennas at both transmitter and receiver sides based on quasi-orthogonal space time block code (QOSTBC) is presented. Space-time block code (STBC) is a MIMO transmit strategy that applies transmit diversity and high reliability. QOSTBC is attractive because it achieves higher code rate than orthogonal STBC and lower decoding complexity than non-orthogonal STBC. We present the performance of massive MIMO systems using the QOSTBC with multiple antennas up to the 16 × 16 configuration. The performances of 2 × 2, 4 × 4, 8 × 8 and 16 × 16 massive MIMO systems have been presented. Simulation results show that the massive MIMO systems with QOSTBC give significant performance improvement with full rate and full diversity, compared with previously considered massive MIMO systems.

Differential modulation schemes are very relevant in receivers having power and processing limitations, as these schemes dispense with the need for knowledge of channel coefficients for symbol detection. Spatial modulation (SM) is a scheme used in multi-antenna transmission scenarios where the data is transmitted in the amplitude, phase and spatial domains through selected antennas. In the coherent domain, generalized SM (GSM) employs multiple antennas in combination during every time slot to enhance the spectral efficiency (SE). In this paper, we propose two differential schemes which activate two or more antennas at a time to transmit the modulated symbol. These schemes achieve higher SE using a lesser number of antennas and lower order modulation schemes instead of the higher number of antennas required for conventional SM schemes based on differential modulation. Simulation studies reveal that the proposed schemes have better bit error rate performance than traditional differential SM schemes. We also derive the analytical union bound for the proposed schemes and is satisfied from medium to high signal-to-noise ratio (SNR) ranges.

In this paper, we propose a novel distributed space-time block coding (STBC) scheme for multi-relay system. We consider the full-duplex cooperation which is more spectrally efficient than the half-duplex cooperation. In full-duplex mode, the new scheme requires relay nodes to stack only every two successive symbols for swapping. Thus, the end-to-end delay may be lower than that induced by orthogonal STBC and conventional quasi-orthogonal STBC (QOSTBC) schemes. We show the new distributed STBC is capable of achieving cooperative diversity by using multi-dimensional rotated signal constellation. Besides, due to the simpler maximum-likelihood metric compared to that of conventional QOSTBC, the code achieves a lower decoding complexity without any performance degradation. To furthermore reduce complexity, the fast sphere decoder is adopted for the proposed code. The proposed transmission scheme is evaluated and compared in terms of performance by simulation.

We present a novel differential space-time modulation (DSTM) scheme that is single-symbol decodable and can provide full transmit diversity. It is the first known singlesymbol- decodable DSTM scheme not based on Orthogonal STBC (O-STBC), and it is constructed based on the recently proposed Minimum-Decoding-Complexity Quasi-Orthogonal Space-Time Block Code (MDC-QOSTBC). We derive the code design criteria and present systematic methodology to find the solution sets. The proposed DSTM scheme can provide higher code rate than DSTM schemes based on O-STBC. Its decoding complexity is also considerably lower than DSTM schemes based on Sp(2) and double-symbol-decodable QOSTBC, with negligible or slight trade-off in decoding error probability performance.

Approximately 3 dB signal-to-noise ratio (SNR) loss is always paid with conventional differential space-time block codes (STBCs), compared with coherent STBCs. In this paper, a multiple-symbol differential detection (MSDD) technique is proposed for M-ary phase-shift keying (PSK) STBCs. The new scheme can greatly narrow the 3-dB performance gap by extending the observation interval for differential decoding. The technique uses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric is derived for an observation interval of arbitrary length. It is shown that for a moderate number of symbols, MSDD provides approximately 1.5 dB performance improvement over conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit-error probability (BEP) are derived for multiple-symbol differential binary PSK STBC. Results show that the theoretical BEP matches simulation results well. The BEP is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection.

We show that certain signal constellations invoked for classic differential encoding result in a phenomenon we term as the {\\em unbounded differential constellation size} (UDCS). Various existing differential transmission schemes that suffer from this issue are identified. Then, we propose an enhanced algebraic field extension based differential spatial modulation scheme (AFE-DSM) and its enhanced counterpart that strikes a diversity-rate trade-off (AFE-DSM-DR), both of which overcome the UDCS issue without compromising its full transmit diversity advantage. Furthermore, the proposed schemes are extended to incorporate amplitude and phase shift keying (APSK) in order to exploit all the available degrees of freedom. Additionally, we propose a pair of detection schemes specially designed for APSK aided differential transmission schemes. Explicitly, we conceive the buffered minimum mean squared error (B-MMSE) detector and buffered maximum likelihood (B-ML) detector, which exploit the knowledge of previously detected symbols in order to further improve the detection performance. Our simulation results have shown that the proposed detectors are capable of bridging the performance gap between the conventional differential detector (CDD) and the coherent detector that has full channel state information. Specifically, when employing the proposed APSK aided AFE-DSM scheme operating at a rate of 2 bits per channel use (bpcu), the B-MMSE and B-ML detectors are observed to give about 3 dB and 3.5 dB signal-to-noise ratio gain with respect to their CDD counterpart at a bit error ratio of $10^{-5}$.

In this paper, in allusion to the problems that space-time block code with complex signals cannot achieve full transmitting rate when the transmit antennas are more than two, based on the quasi-orthogonal space-time block coding scheme with beamforming, we present a novel method of quasi-orthogonal space-time block code with feedback information, which is designed by aiming at the maximum instantaneous signal-to-noise ratio gain for compensating the performance degradation, to overcome the multi-user access interference of the previous quasi-orthogonal space-time block coding and obtain full diversity gain and maximum coding rate at the same time. The simulation results demonstrate that the proposed closed-loop beamforming scheme can obviously improve the performance of the system without increasing the decoding complexity in the meantime.

We consider an asynchronous two-way relay network in which a few distributed relays assist in the communication between two single-antenna terminals through analog network coding. The asynchronous transmission between relays and terminals causes symbol misalignments and results in diversity loss in space–time codes (STCs). We propose a family of zero-padded time-reversal STC that can achieve full diversity with low-complexity maximum likelihood (ML) decoding, given a bound for the path delay difference. With ML decoding, the proposed code is decomposed into several independent parts, which greatly facilitate the decoding process. For two-relay scenarios, three code designs based on Alamouti code, quasi-orthogonal space–time block code, and multigroup decodable STC are provided for each relay with one, two, and four antennas, respectively. For three-relay scenarios, one code design based on quasi-orthogonal space-time block code is provided for each relay with one antenna. Proof of full diversity is established, and the decoding complexity order is analyzed for all four designs. Simulations confirm the full diversity gain of all designs. The bit-error-rate performance in asynchronous scenarios is almost similar to that in synchronous scenarios.

This paper considers the problem of massive multiple-input-multiple-output (MIMO) wireless communication systems with quasi-orthogonal space-time block code (QOSTBC) transmission in the presence of spatial correlation effect (SCE) and mutual coupling effect (MCE). Conventional MIMO channels with QOSTBC transmission suffer from several drawbacks. The number of transmit antennas is restricted to a few in order to achieve full transmission rate. Therefore, it is difficult to make a quasi-orthogonal space time block coded massive MIMO system to achieve full transmission rate. Moreover, MIMO channel with QOSTBC transmission is usually considered for the case where the number of user equipments (UEs) is one. We present a joint beamforming and spatial precoding method to deal with the above drawbacks. The proposed method incorporates a beamforming scheme and spatial precoding to formulate an appropriate optimization process to effectively alleviate the considered problems. The resulting optimization problem will be solved by using a cooperative coevolutionary particle swarm optimization algorithm under two proposed fitness functions. During the optimization process, the proposed method finds the optimal beamforming coefficients of the precoding matrix, the optimal normalized positions of transmit and receive antenna elements for the case of using linear antenna arrays, and the optimal angle differences of transmit and receive antenna elements for the case of using circular arrays. Based on the proposed method, we are able to cure the performance degradation of a quasi-orthogonal space time block coded massive MIMO system due to the SCE and MCE. Moreover, the proposed method makes QOSTBC MIMO communications with full transmission rate for any number of transmit antennas achievable. Several simulation examples are presented to show the superior bit error rate (BER) performances of QOSTBC wireless MIMO scenarios with linear as well as circular antenna arrays by using the proposed method as compared to the existing methods.

Orthogonal space-time block coding is a transmit diversity method that has the potential to enhance forward capacity. For a communication system with a complex alphabet, full diversity and full code rate space-time codes are available only for two antennas, and for more than two antennas full diversity is achieved only when the code rate is lower than one. A quasi-orthogonal code could provide full code rate, but at the expense of loss in diversity, which results in degradation of performance. We propose a closed loop feedback scheme for quasi-orthogonal codes which provides full diversity while achieving the full code rate. We investigate, in particular, the performance of this scheme, when the feedback information is quantised and when the fading of the channel is frequency-selective.

A full-rate and full-diversity closed-loop quasi-orthogonal space time block coding scheme pioneered by Toker, Lambotharan and Chambers is proposed for application in virtual antenna arrays. The theoretical capacity and throughput gains are evaluated as a function of signal-to-noise ratio. It is shown that the scheme has particular benefits in both ergodic and non-ergodic channel environments, and outperforms virtual antenna arrays based solely upon conventional orthogonal space time block codes.

In this paper, we use a quasi-orthogonal STBC (QO-STBC) instead of the conventional O-STBC as the inner code for OFDM MIMO systems, resulting in quasi-orthogonal space-frequency block coding (QO-SFBC). Due to the effect of multi-path, the conventional signal detector in H. Jafarkhani (2001) causes an irreducible error floor in the high signal-to-noise ratio (SNR) region for these new QO-SF-OFDM systems This paper addresses this issue by employing a zero-forcing approach, which has the potential advantage of low complexity and can fully remove the error floor.