Differential Space-time Coding Research Articles

A Hybrid Differential Detection Scheme for the Ultra-Wideband Orientational Beamforming System

Differential space-time coding methods have been investigated for ultra-wideband communication systems to avoid channel estimation. However, their performance in the line-of-sight (LOS) environment is worse than the recently proposed orientational beamforming (OBF) system under low signal-to-noise ratios (SNRs). On the other hand, the OBF system cannot work well in the non-LOS (NLOS) environment. To address these issues, a hybrid differential detection (HDD) scheme is proposed in this paper, which combines the OBF system with a proposed differential OBF (DOBF) system. First, the DOBF system with a fully differential detection scheme is proposed, whose performance is almost the same as the differential space-time block coding method. However, its detection complexity only linearly increases with the number of transmitting antennas. Then, the HDD scheme is proposed, with its decision statistic being a combination of a modified OBF decision statistic and the DOBF decision statistic. In the NLOS environment, the HDD scheme is reduced to the DOBF system. In the LOS environment, a combination coefficient is obtained by mapping an SNR-related factor through a sigmoid function. The optimal parameters for the sigmoid function are determined through simulations, with which the proposed HDD scheme can achieve overall better performance than the OBF and DOBF systems.

Differential Space-Time Coding Dispensing With Channel Estimation Approaches the Performance of Its Coherent Counterpart in the Open-Loop Massive MIMO-OFDM Downlink

In this paper, we propose a simple yet powerful mapping scheme that converts any conventional square-matrix-based differential space-time coding (DSTC) into a nonsquare-matrix-based DSTC. This allows DSTC schemes to be used practically in open-loop large-scale multiple-input multiple-output scenarios. Our proposed scheme may be viewed as the differential counterpart of coherent spatial modulation (SM), of the generalized SM, of Bell Laboratories layered space-time architecture, and of subcarrier-index modulation. The fundamental impediment of the existing DSTC schemes is the excessive complexity imposed by the unitary constraint. Specifically, the transmission rate of conventional DSTC schemes decays as the number of transmit antennas increases. Our proposed scheme eliminates this impediment and thus achieves a significantly higher transmission rate. We introduce four novel construction methods for the nonsquare codewords, some of which include an arbitrary number of nonzero elements in each codeword column. Our analysis shows that the proposed encoding technique reduces the complexity of both the inverse Fourier transform and the detection processes. Our proposed scheme is shown to approach the performance of its coherent counterpart for low-mobility scenarios, where the number of transmit antennas is increased up to 256.

Decision fusion in mobile wireless sensor networks using cooperative multiple symbol differential space time coding

In this article, we propose a cooperative scheme for differential space-time codes (DSTCs) to be applied for mobile wireless sensor networks (WSNs) in order to mitigate multipath fading effect. We assume that sensors make independent local decisions about the existing hypothesis and report their decisions to a fusion center, where the final decision is made. Sensors are divided into groups with two sensors each, where sensors in each pair cooperate to send their decisions as a DSTC. Differential modulation scheme, which does not require knowledge of the instantaneous fading gains, is considered to avoid the channel estimation overhead at the cooperating sensors and the fusion center. Channels between sensors and the fusion center are assumed independent identically distributed (i.i.d) Rayleigh fading channels. Moreover, Jakes-Clarkes’ channel model is considered to model the mobility of sensors and/or the fusion center. Since the complexity of the optimal fusion rule grows up exponentially with the observation interval, suboptimal fusion rules are derived and discussed. Finally, simulation results of the proposed cooperative scheme are provided and the detection capabilities of the derived decision fusion rules are compared.

Two-group decodable distributed differential space-time code for wireless relay networks based on SAST codes

Two-group decodable distributed differential space-time code for wireless relay networks based on SAST codes

Asynchronous Two-Way Relaying Networks Using Distributed Differential Space-Time Coding

A signal detection scheme is proposed for two-way relaying network (TWRN) using distributed differential space-time coding (DDSTC) under imperfect synchronization. Unlike most of existing work, which assumed perfect synchronization and channel state information (CSI) at all nodes, a more realistic scenario is investigated here by considering the signals transmitted from the two source nodes arriving at the relay not exactly at the same time due to the distributed nature of the nodes, and no CSI is available at any node. The proposed signal detection scheme is then demonstrated to remove the imperfect synchronization effect significantly through simulation results. Furthermore, pairwise error probability (PEP) of the asynchronous TWRN is analyzed and derived for both source nodes. Based on the simplified PEP expression, an optimum power allocation (OPA) scheme is then determined to further improve the whole system performance, when neither the source nor the relay has any knowledge of the CSI.

Distributed differential space-time coding for asynchronous two-way relaying networks with Nakagami-m fading

A signal detection scheme was proposed for two-way relaying networks (TWRNs) using distributed differential space-time coding (DDSTC) under imperfect synchronization. Unlike most existing work perfect with synchronization assumed, a relative delay between the signals transmitted from both sources to the relay was considered. Since perfect channel state information (CSI) is difficult to be acquired in fast fading, the scenarios and computation complexity will be increased especially when there appear multiple relays, CSI is assumed unavailable at all nodes. Therefore, the article proposes a differential signal detection scheme based on estimating and cancelling the imperfect synchronization component in the received signal at the two source nodes, followed by a least square (LS) decoder. Simulations, using the Nakagami-m fading channel due to its versatile statistical distribution property, show that the proposed scheme for both source nodes are effective in suppressing the inter-symbol interference (ISI) caused by imperfect synchronization while neither the source nodes nor the relay nodes have any knowledge of CSI.

An Inter Symbol Interference Estimation and Cancellation Scheme for Asynchronous Distributed Differential Space-Time Code

In cooperative communication systems, as poor synchronization of different relays may induce inter symbol interference (ISI) and lead to substantial performance degradation, it is necessary to cancel ISI. In this letter, a simple ISI estimation and cancellation scheme is proposed for asynchronous distributed differential space-time code, where the destination node does not need to know the channel state information (CSI) from the source node to different relays or the CSI from the relays to the destination node. Simulation results show that the proposed scheme can cancel ISI effectively and obtain good bit error rate performance.

基于Weyl交互律的分布式差分空时码

For a relay network in which receivers and relays have channel state information, or partial channel information, distributed space time block codes (DSTBC) are proposed to achieve full diversity of the system, and different DSTBC are well-designed. For a relay network in which transmitters, receivers and relays do not have any channel state information, it is proved that distributed differential space time codes (DDSTC) are an efficient way to transmit signals for transmitters and to forward signals for relays, while some basic issues for this DDSTC are still unclear. To make up these issues, in this paper, firstly, ML-decoding is derived rigorously based on calculation of density function of received signals. Secondly, by using Weyl reciprocity appearing in Representation of Finite Groups, a new designing method of DDSTC is proposed to satisfy the commuting property of codes required in the designing criteria. Thirdly, designing examples are given based on this designing method and representations of finite groups. These examples show that the proposed methods are more flexible, and easier to get codes than existing methods, especially in a case with high-dimensional unitary matrices and a large number of relays. Furthermore, simulations show that our codes have better performances than existing codes.

A Distributed Differential Space-Time Coding Scheme With Analog Network Coding in Two-Way Relay Networks

In this correspondence, we consider general two-way relay networks (TWRNs) with two source and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> relay nodes. A distributed differential space time coding with analog network coding (DDSTC-ANC) scheme is proposed. A simple blind estimation and a differential signal detector are developed to recover the desired signal at each source. The pairwise error probability (PEP) and block error rate (BLER) of the DDSTC-ANC scheme are analyzed. Exact and simplified PEP expressions are derived. To improve the system performance, the optimum power allocation (OPA) between the source and relay nodes is determined based on the simplified PEP expression. The analytical results are verified through simulations.

Performance and Design of Coherent and Differential Space-Time Coded FSO Systems

Free-space optical (FSO) communication enables high rate data transmission over the atmospheric channel. However, turbulence-induced fading poses severe challenges for operating these systems. Employing spatial diversity has been proposed as an effective measure to improve system performance. In this paper, we first develop a comprehensive model for multiple-input multiple-output (MIMO) coherent and differential FSO systems with heterodyne detection taking into account all relevant signal and noise terms. For the sake of comparison, a similar model is also developed for direct detection. An asymptotic performance analysis is presented for MIMO FSO systems employing coherent and differential space-time codes (STCs) over Gamma-Gamma fading channels. We consider the practically important case of two transmit and an arbitrary number of receive apertures and provide a simple STC design criterion for coherent and differential FSO systems. Our results reveal that, in contrast to FSO systems with intensity modulation and direct detection (IM/DD), for coherent and differential FSO systems, orthogonal space-time block codes previously introduced in the RF literature, are preferable over repetition STCs, which do not yield full diversity. We quantify the asymptotic performance gain of coherent space-time coded FSO systems compared to IM/DD systems and show that this gain is mainly caused by the superiority of heterodyne detection compared to direct detection rather than the different STC and modulation designs.

Multi-amplitude Differential Space-time Block Coding Scheme for Square/Non-Square Code Matrix in MIMO Systems

Differential space-time coding (DSTC) technique has become a good choice when channel estimations are difficult to obtain in multiple antennas system. On the basis of analyzing the existing DSTC schemes, by introducing multi - level quadrature amplitude modulation (MQAM) and matrix transform method, we develop a multi - amplitude differential space-time block coding (STBC) scheme for square or non-square code matrix in MIMO systems , and give the derivation of calculation formula e of the coding advantage in detail. The developed scheme can effectively avoid the performance loss of conventional DSTC schemes based on PSK modulation (i.e. single amplitude DSTC) in high spectrum efficiency . It can be applied to non-square code matrix case , and thus overcomes the shortcoming that existing DSTC schemes are only suit able for square code matrix. Compared with single amplitude DSTC schemes, our scheme has higher spectrum efficiency by carrying information not only on phases but also on amplitudes. Moreover, our scheme has linear decoding complexity, higher coding advantage, and higher code rate for more than two antennas. The simulations results show that the proposed scheme can provide lower BER than the existing single amplitude differential STBC schemes for both square and non-square code matri ces .

Differential Space-Time Network Coding for Multi-Source Cooperative Communications

Due to the asynchronous nature of cooperative communications, simultaneous transmissions from two or more nodes are challenging in practice. The existing cooperative communications employing successive transmission from one user node to the other can avoid the synchronization problem but results in large transmission delay. In addition, channel estimation in multi-source cooperative communications is a challenging and costly task due to the amount of training, especially when the number of cooperative users is large. Considering these practical challenges in multi-source cooperative communications, this paper proposes a differential space-time network coding (DSTNC) scheme for narrowband multi-source cooperative communications to overcome the problems of imperfect synchronization and complex channel estimation without introducing large transmission delay. Each user in the network linearly combines the correctly decoded symbols via network coding and transmits its packet in time division multiple access (TDMA) mode. The pairwise error probability is analyzed and the design criteria of the DSTNC are derived to achieve full diversity. For broadband cooperative communications, distributed differential space-time-frequency network coding (DSTFNC), which is differentially encoded within each orthogonal frequency-division multiplexing (OFDM) block, is designed through mapping from the proposed DSTNC. When the statistical channel power-delay profile is known at the corresponding user node, each node can permutate its channel independently to improve the performance of the DSTFNC scheme. Simulation results are presented to verify the performance of the proposed schemes.

Differential Space–Time Coded Switch and Stay Combining

The design and analysis of differential space-time coding is considered where the receiver, with a single radio frequency (RF) chain, uses switch and stay combining (SSC). Without channel knowledge at the receiver, a receive-power-based switching algorithm is proposed. By deriving the distribution of the received signal on the selected antenna, upper and lower bounds on the Chernoff bound on the pairwise error probability are derived. Using the upper bound, it is shown that even when the code satisfies the conditions to achieve full transmit diversity, if a fixed switching threshold with respect to the average SNR is used, receive diversity will not be attained. Following this, a switching threshold that offers full diversity is obtained and shown to be a logarithmic function of the average SNR at a high SNR. Furthermore, code design criteria for the proposed system are developed. For the special case of two transmit antennas, new codes for the proposed differentially modulated SSC scheme are designed and shown to perform better than existing codes. Simulation results are included to corroborate our analytical results.

Cooperative Differential Space–Time Spreading for the Asynchronous Relay Aided CDMA Uplink Using Interference Rejection Spreading Code

This letter proposes a differential Space-Time Coding (STC) scheme designed for asynchronous cooperative networks, where neither channel estimation nor symbol-level synchronization is required at the cooperating nodes. More specifically, our system employs differential encoding during the broadcast phase and a Space-Time Spreading (STS)-based amplify-and-forward scheme during the cooperative phase in conjunction with interference rejection direct sequence spreading codes, namely Loosely Synchronized (LS) codes. Our simulation results demonstrate that the proposed Cooperative Differential STS (CDSTS) scheme is capable of combating the effects of asynchronous uplink transmissions without any channel state information.

Differential space–time coded cooperation for decode-and-forward-based wireless relay networks

Estimating channel state information (CSI) in the fast fading conditions is very challenging. In this study, a simple structure for cooperative diversity in decode-and-forward mode is examined, in which the transmitter, the relay and the receiver do not know the CSI. In this scheme, transmission of information is done in a two-phase process. In the first phase, differential modulated signals are radiated from the source. After decoding the received signal in the relay, the source and the relay collectively send information using differential space–time codes. A closed-form optimum power allocation in the sense of minimising pairwise error probability (PEP) for high signal-to-noise ratio (SNR) scenarios has been obtained. An interesting property of the optimum point is that it is independent of the channel statistics and the position of the relay, which improves its feasibility in the future communication systems. Numerical simulations verify the analytical results.

Asymptotic analysis of coherent and differential space-time codes in non-gaussian noise and interference

In this paper, we provide a unified framework for the asymptotic performance analysis of space-time codes (STCs) in correlated Ricean fading and non-Gaussian noise and interference. In particular, we derive simple and asymptotically tight expressions for the pairwise error probability (PEP) of coherent and differential STCs which are valid for any type of noise and interference with finite moments and detection with general Mahalonobis distance (MD) metrics including Euclidean distance (ED) and noise decorrelating (ND) metrics. These PEP expressions can be combined with truncated union bounds to obtain accurate asymptotic approximations for the bit, symbol, and frame error probabilities of STCs. We show that while the diversity gain of an STC is independent of the type of noise and the type of MD metric used, the coding gain is not and depends on certain moments of the noise and interference. We provide closed-form expressions for these moments for several practically relevant types of noise and interference. We show that for correlated noise significant performance gains can be achieved with the ND metric compared to the ED metric. While noise correlations are beneficial at high signal-to-noise ratios if they can be exploited by the metric, they are harmful if this is not the case and the simple ED metric is employed. All our analytical findings are confirmed by simulations for various popular STCs and several different types of noise and interference.

New group product differential unitary space-time codes with simplified design and detection

A new differential unitary space-time code is presented that is a product of group diagonal matrices of different orders and a unitary Vandermonde matrix. Design is simplified through properties of the union bound on block error probability for the presented code. Detection is simplified via properties of the diagonal matrices which form a cyclic group. Superior performance to best known differential space-time codes is shown, particularly for 3, 5 and 6 transmit antennas.

Algebraic distributed differential space-time codes with low decoding complexity

The differential encoding/decoding setup introduced by Kiran et al, Oggier-Hassibi and Jing-Jafarkhani for wireless relay networks that use codebooks consisting of unitary matrices is extended to allow codebooks consisting of scaled unitary matrices. For such codebooks to be usable in the Jing-Hassibi protocol for cooperative diversity, the conditions involving the relay matrices and the codebook that need to be satisfied are identified. Using the algebraic framework of extended Clifford algebras, a new class of Distributed Differential Space-Time Codes satisfying these conditions for power of two number of relays and also achieving full cooperative diversity with a low complexity sub-optimal receiver is proposed. Simulation results indicate that the proposed codes outperform both the cyclic codes as well as the circulant codes. Furthermore, these codes can also be applied as Differential Space-Time codes for noncoherent communication in classical point to point multiple antenna systems.

Distributed differential space-time coding for wireless relay networks

Distributed space-time coding is a cooperative transmission scheme for wireless relay networks. With this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a space-time code at the receiver. It achieves the maximum diversity. Although the scheme needs no channel information at relays, it does require full channel information, both the channels from the transmitter to relays and the channels from relays to the receiver, at the receiver. In this paper, we propose a differential transmission scheme, which requires channel information at neither relays nor the receiver, for wireless relay networks. As distributed space-time coding can be seen as the counterpart of space-time coding in the network setting, this scheme is the counterpart of differential space-time coding. Compared to coherent distributed space-time coding, the differential scheme is 3dB worse. In addition, we show that Alamouti, square real orthogonal, and Sp(2) codes can be used differentially in networks with corresponding numbers of relays. We also propose distributed differential space-time codes that work for networks with any number of relays using circulant matrices.

A Differential Modulation Scheme for MIMO Links with Distributed Transmit Antennas

This letter proposes a differential en/decoding scheme for multiple-input multiple-output (MIMO) communication links with distributed transmit antennas, in which neither the transmitter nor the receiver knows channel knowledge. The proposed scheme is based on the layered differential space-time codes we present. Simulation results show that the bit error rate (BER) performance is nonidentical in different channel propagation delay cases. The optimum delay time for two transmit antennas system, for example, is about 0.6Ts (where Ts denotes symbol period) when the links achieve better performance.