Further Results on Differential Encoding by a Table

기존 Zhu가 제안한 준직교 기반의 차등시공간변조(Differential Space-Time Modulation, DSTM)는 복소 선부호기와 준직교 시공간블럭부호를 연접하여 차등변조기법으로 전송함으로써 수신단에서 채널 정보 추정 없이 2개의 복소 신호들에 대한 독립적인 복조, 즉 준직교 차등복조가 가능하다는 장점을 갖는다. 본 논문에서는 이와 같은 준직교 기반 Zhu-DSTM를 기반으로 복소 선부호기 대신 실수 선부호기를 사용함으로써 수신단에서 2개의 실수 신호들에 대한 독립적인 차등복조가 가능하게 하여 수신 복잡도를 더욱 줄일 수 있는 새로운 DSTM를 제안한다. 전산 실험 결과 제안된 기법은 기존의 준직교 기반 DSTM들과 거의 같거나 향상된 성능을 가짐을 확인할 수 있으며 따라서 수신 복잡도 및 수신 성능 측면에서 큰 장점을 가지게 된다. The conventional Zhu's differential space-time modulation(DSTM) based on quasi-orthogonal design adopted a complex precoder in order to allow an independent joint detection of two complex symbols without any channel informations at a receiver. In this paper, by simply replacing the complex precoder used in Zhu's DSTM with a real precoder, a new DSTM is presented for four transmit antennas. The real precoder enables the receiver to decode two real symbols pair separately, and thus the new DSTM has greatly reduced decoding complexity compared to the Zhu's DSTM. By computer simulation results, the proposed scheme is shown to exhibit almost identical or improved error performance compared to the existing DSTMs.

Existing work on decision feedback detection (DFD) of differential space-time modulation (DTSM) were largely confined to diagonal constellations. In other works considering nondiagonal constellations, the temporal variation of fading in the DTSM supersymbol duration was ignored. In this paper, we take a close look at the DFD receiver structure for nondiagonal DSTM in temporally correlated fading. We identify the constellations of which the error performance is not influenced by ignorance of fading variation. In addition, by analyzing the error performance, we demonstrate that existing DFD, is however, fundamentally mismatched to other constellations in fast fading. A major conclusion is that diagonal design still plays an important role for the efficacy of DFD for nondiagonal constellation in fast fading.

In this paper, we analyze the performance of the differential space-time modulation (DSTM) in Rayleigh fading channels. By using the moment-generating function (MGF)-based approach, we derive a number of closed-form expressions for the pairwise error probability (PEP) of the DSTM in various fading environments. For spatially independent channels, we derive a closed-form expression for the exact PEP of the DSTM for both slow- and fast-fading cases. In the case of fast-fading channels, we show that an irreducible error floor exists in the PEP and in the block error rate of the DSTM, and derive a closed-form expression for the PEP error floor in terms of the fading rate. For spatially correlated channels, we derive a new closed-form expression for the PEP at asymptotically high signal-to-noise ratios and show that an existing asymptotic PEP expression derived by the residue method can also be obtained by using the MGF-based approach. Finally, we use computer simulations to verify the theoretical results.

In this paper, joint differential space-time modulation (DSTM) and eigen-beamforming for correlated multiple-input multiple-output (MIMO) fading channels. While DSTM does not require knowledge of each channel realization, the channel's spatial correlation can be easily estimated without training at the receiver and exploited by the transmitter to enhance the error probability performance. A transmission scheme is developed here that combines beamforming with differential multiantenna modulation based on orthogonal space-time block coding. Error probability is analyzed for both spatially correlated and independent Rayleigh fading channels. Based on the error probability analysis, power loading coefficients are derived to improve performance. The analytical and simulation results presented here corroborate that the proposed scheme can achieve considerable performance gain in correlated channels relative to DSTM without beamforming.

In this paper, noncoherent receivers for differential space-time modulation (DSTM) are investigated. It is shown that the performance of the previously proposed conventional differential detection (DD) receiver is satisfactory only for very slow flat fading channels. However, conventional DD suffers from a considerable loss in performance even for moderately fast fading, especially if more than one transmit antenna is used. In order to overcome this problem, two improved noncoherent receivers are considered. The first one is the multiple-symbol detection (MSD) receiver. Because of the high computational complexity of MSD, also a low-complexity decision-feedback differential detection (DF-DD) receiver is derived. Analytical and simulation results confirm that both receivers perform equally well and can take full advantage of the enhanced diversity provided by multiple transmit antennas even for fast fading.

Space-time coding has been receiving much research attention recently due to the potential offered by fully exploiting spatial and temporal diversity. A differential space-time modulation (DSTM) scheme was recently proposed to perform demodulation without channel state information, which is attractive in fast fading channels where accurate channel estimates are difficult to obtain. More recently, a differential space-code modulation (DSCM) scheme, which is an improvement of DSTM for combating interference (including intentional and unintentional jamming) signals, was proposed. DSCM significantly outperforms DSTM when interference is present. This advantage, however, is achieved at the cost of a lower transmission rate, a wider bandwidth, or a combination of both. To alleviate this problem, we extend DSCM to a so-called high-rate DSCM (HR-DSCM) scheme, which increases the data rate considerably at the cost of a slightly higher bit error rate, while still maintaining the interference suppression capability.

In this paper, differential modulation diversity (DMD) is introduced. This diversity scheme is based on diagonal signal constellations which have been previously proposed for differential space-time modulation (DSTM). DMD can exploit both space and time diversity and DSTM, which is a pure space diversity scheme, results as a special case. A low-complexity noncoherent receiver originally designed for DSTM is adapted to DMD and the power efficiency of DMD for spatially correlated Rayleigh fading and imperfect interleaving is investigated.

Reconfigurable Intelligent Surfaces (RIS) hold the promise of significantly improving coverage, as well as spectral and energy efficiency in wireless communication systems. Techniques based on RIS form a key technology for 6G systems, attracting a significant research interest. An important issue in RIS technology is Channel State Information (CSI), which is much more difficult to acquire in such systems. This work considers a Differential Space-Time Modulation (DSTM) technique integrated with Differential Reflecting Modulation (DRM) termed DRM-DSTM. Such a scheme does not require CSI, while providing error rate gains. The DSTM scheme is based on unitary group codes. We first consider uncoded DRM for RIS to serve as a reference point. Next we provide an overview of DSTM and outline the procedures for its integration with DRM. We consider the issue of reflecting patter selection in such systems, and explore the extension of both the original DRM and the coded DRM-DSTM scheme to a larger number of RIS reflecting patterns <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i>. Furthermore we provide tables of cyclic and dicyclic codes for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i>' = 2, 3, 4 suitable for DRM-DSTM. Encoding and decoding complexities are studied as well. Extensives Monte-Carlo simulation results over quasi-static Rayleigh fading channels confirm the effectiveness of the DRM-DSTM coded scheme, illustrating its advantages over uncoded DRM with proper system parameters.

It is well known that the performance of the wireless communication systems can be enhanced by using multiple transmit and receive antennas, which is generally referred to as the MIMO technique, and has been incorporated into the IEEE 802.11n standard, i.e. one of the Wi-Fi systems. The MIMO technique has also been adopted by the 3GPP Long Term Evolution (LTE) and the 3GPP2 Ultra Mobile Broadband (UMB) standards. The space-time coding is a promising way to realize the gain in the wireless communications system using MIMO. The space time block code, and the orthogonal space time block code in particular have been proposed in research and implemented in practical wireless communication systems due to their low computational complexity in maximum likelihood decoding implementation. However, the code rates of the orthogonal space time block codes are usually lower than $3/4$ when the number of transmit antennas is greater than two, which limit their throughput. To increase the code rate and the throughput of the orthogonal space time block code for more than two transmit antennas, a family of new space-time block codes (STBC) for 3 and 4 transmit antennas in a MIMO wireless communication system have been proposed in this Ph.D. research. These new codes are orthogonal and achieve full diversity, full rate using Triple QPSK'' modulation, which is proposed in this research. We investigated the performance of these STBCs when the channel state information (CSI) is perfectly known at the receiver. The CSI is not known to the transmitter in all of the studies in this dissertation. An analytical bound of the probability of bit error is developed and the Monte Carlo simulation is used when investigating these new STBC codes. In practical wireless communication system, the CSI is generally not available at the receiver and it is usually estimated by the receiver through the pilot signals or training signals known to the receiver. No matter what channel estimation method is used, the estimate of CSI will not match the CSI exactly and is noisy. The performance of these new STBCs using theTriple QPSK'' modulation when the estimate of the CSI is employed to detect the symbol is investigated in this dissertation. An upper bound of the bit error probability is developed when the noisy CSI is used to detect the symbols. The performance of the new STBCs using the Triple QPSK'' modulation is also evaluated using Monte Carlo simulation. When the CSI is not available to either the receiver or the transmitter, the differential encoding and decoding algorithm is applied to these new STBCs, which use theTriple QPSK'' modulation. The results showed that these orthogonal STBCs achieve full diversity full rate using ""Triple-QPSK"" modulation with differential detection. This provides a means of achieving space diversity and multiplexing gain without the CSI. A new differential encoding and decoding algorithm is proposed and analyzed for STBCs with 3 transmit antennas, whose transmission matrix is not square matrix, as part of this Ph.D. research. The STBCs using this algorithm achieve full diversity the MIMO system can possibly provide.

We consider the design of codes for differential space-time modulation in the presence of large numbers of transmit and/or receive antennas. Based on the novel upper bound on the pairwise-error probability of differential space-time modulation for large numbers of antennas, we show that Euclidean distance is an appropriate code performance indicator in the large-array regime. For two transmit antennas, we use the new design criterion to obtain new differential codes with large minimum Euclidean distance. Simulations of bit-error-rate confirms that the new codes has improved the performance of differential codes for large numbers of receive antennas.

Differential unitary space-time modulation is an attractive space-time technique because it does not require channel estimation. In this paper, we propose a new differential space-time code with rate 2.5 bit/s/Hz for two transmit antennas. In contrast to the original unitary space-time codes with one level of amplitude, the powers of the matrices in this new differential space-time code are different. We design a decoding algorithm based on the Viterbi algorithm to differentially detect the transmitted data. Simulation results show that the new two amplitude level differential space-time code outperforms the original unitary space-time code with rate 2.5 bit/s/Hz.

Differential spatial modulation (DSM) can transmit additional data bits by selecting indexes of antennas without the pilot overhead and increasing radio frequency circuits and power consumption. DSM is extended to generalized DSM (GDSM) where more than one transmit antennas are activated each time. However, the transmission rate of the existing GDSM scheme is low. In this paper, we propose a new GDSM scheme that uses symbol interleaving on differential space-time modulation. The number of interleaving patterns is derived, and interleaving patterns with transmit diversity two are created as well. By selecting the interleaving patterns, the proposed scheme has higher data rates than the existing GDSM scheme. We also propose low-complexity detectors for both schemes. Theoretical analysis and computer simulation both show that the proposed scheme has satisfactory error performance.

A new constellation which is the multiplication of the rotation matrix and the diagonal matrix according to the number of transmitters is proposed to increase the diversity product, the key property to the performance of the differential unitary space-time modulation. Analyses and the simulation results show that the proposed constellation performs better and 2dB or more coding gain can be achieved over the traditional cyclic constellation.

The performance of two demodulation schemes for the differential unitary space-time modulation (DUSTM), the standard differential demodulation and decision-feedback demodulation, are analyzed in a unified approach under Rayleigh time-varying channels. We derive compact expressions for the pairwise error probability (PEP) and its upper and lower bound. Our analysis justifies the conventional design criteria on DUSTM constellations for more general channel models and demodulation schemes. We formulate a simple expression of the effective SNR that captures the time correlation of fading, the length of the observation window, and the noise variance. Based on the derived results for general DUSTM, we further obtain an explicit closed- form expression of the PEP for the specific constellation proposed by Tarokh and Jafarkhani (12). We also show that this specific DUSTM allow efficient decision-feedback detection.

Studies on differential unitary space-time modulation are mostly focused on Rayleigh fading channels. In this paper we present new analytic results for the maximum-likelihood demodulator (MLD) and the standard differential demodulator (SDD). The resulting expressions and bounds on the pairwise error probability shed light on the impact of various system parameters and are helpful towards a deeper understanding of the DUSTM in Rician channels. Additional analytic results are also derived for the constellation in the work of Tarokh and Jafarkhani (2000). Unlike in Rayleigh fading, the exact MLD can only be implemented approximately (Cui and Tellambura, 2006). The performance loss of practical demodulator such as the SDD and a prediction-based demodulator relative to the MLD are studied under different Rician fading environments.