Multiple-symbol Differential Sphere Detection Research Articles

On Multi-User Deep-Learning-Based Non-Coherent DPSK Multiple-Symbol Differential Detection in Massive MIMO Systems

In view of reducing the complexity of signal detection in massive multiple-input multiple-output (MIMO) receivers, the use of non-coherent detection is favored over usual coherent techniques that require complex channel estimation. In this paper, a deep-learning approach to implement non-coherent multiple-symbol detection for differential phase-shift keying (DPSK) multi-user massive MIMO systems is proposed. The proposed deep-learning implementation reduces the high computational complexity required in conventional DPSK detection techniques. Two deep-learning-based multiple-symbol differential detection receiver designs are proposed and compared with decision-feedback differential detection (DFDD), and conventional multiple-symbol differential detection (MSDD) for the same system parameters. Multiple-symbol differential sphere detection (MSDSD) is used to implement conventional MSDD. The results show that the proposed deep-learning-based multiple-symbol differential detection implementation outperforms decision-feedback differential detection and achieves an optimal performance compared to conventional multiple-symbol differential detection implemented by multiple-symbol differential sphere detection for single-user and multi-user scenarios.

Adaptive Coherent/Non-Coherent Single/Multiple-Antenna Aided Channel Coded Ground-to-Air Aeronautical Communication

In this treatise, first of all, we conceive a generic multiple-symbol differential sphere detection (MSDSD) solution for both single- and multiple-antenna-based noncoherent schemes in both uncoded and coded scenarios, where the high-mobility aeronautical Ricean fading features are taken into account. The bespoke design is the first MSDSD solution in the open literature that is applicable to the generic differential space-time modulation (DSTM) for transmission over Ricean fading. In the light of this development, the recently developed differential spatial modulation and its diversity counterpart of differential space-time block coding using index shift keying are specifically recommended for aeronautical applications owing to their low-complexity single-RF and finite-cardinality features. Moreover, we further devise a noncoherent decision-feedback differential detection and a channel-state information estimation aided coherent detection, which also take into account the same Ricean features. Finally, the advantages of the proposed techniques in different scenarios lead us to propose for the aeronautical systems to adaptively: 1) switch between coherent and non-coherent schemes; 2) switch between single- and multiple-antenna-based schemes as well as; and 3) switch between high-diversity and high-throughput DSTM schemes.

Multiple-Symbol Differential Sphere Detection for Dual-hop Amplify-and-Forward Relaying Based Differential Spatial Modulation

Differential Spatial Modulation (DSM) is a newly MIMO technique, which need no channel state information at the receiver. In this paper, we study the application of DSM in a dual-hop amplify-and forward (AF) relaying system. Owing to the poor performance of conventional differential detection in fast fading channels, we devise a nearly optimal multiple-symbol detector. First, we derive the ML metric, which is not a closed-form expression. Then, a modified suboptimal decision metric is derived instead. Simulation results show that the proposed multiple-symbol detection can effectively improve the performance of DSM in fast-fading channels.

Multiple-Symbol Differential Sphere Detection and Decision-Feedback Differential Detection Conceived for Differential QAM

Multiple-symbol differential sphere detection (MSDSD) relies on the knowledge of channel correlation. More explicitly, for differential phase-shift keying (DPSK), the transmitted symbols' phases form a unitary matrix, which can be separated from the channel's correlation matrix by the classic multiple-symbol differential detection (MSDD), so that a lower triangular matrix extracted from the inverted channel correlation matrix is utilized for the MSDSD's sphere decoding. However, for differential quadrature amplitude modulation (DQAM), the transmitted symbols' amplitudes cannot form a unitary matrix, which implies that the MSDD's channel correlation matrix becomes amplitude dependent and remains unknown unless all the data-carrying symbol amplitudes are detected. To tackle this open problem, in this paper, we propose to determine the MSDD's nonconstant amplitude-dependent channel correlation matrix with the aid of a sphere decoder (SD) so that the classic MSDSD algorithms that were originally conceived for DPSK may also be invoked for DQAM detection. As a result, our simulation results demonstrate that the MSDSD-aided DQAM schemes substantially outperform their DPSK counterparts. However, the price paid is that the detection complexity of MSDSD is also significantly increased. To mitigate this, we then propose a reduced-complexity MSDSD search strategy specifically conceived for DQAM constellations, which separately map bits to their ring-amplitude index and phase index. Furthermore, the classic decision-feedback differential detection (DFDD) conceived for DQAM relies on a constant channel correlation matrix, which implies that these DFDD solutions are suboptimal and that they are not equivalent to the optimum MSDD operating in decision-feedback mode. With the advent for solving the open problem of MSDSD-aided DQAM, we further propose to improve the conventional DFDD-aided DQAM solutions in this paper.

Soft-Decision Multiple-Symbol Differential Sphere Detection and Decision-Feedback Differential Detection for Differential QAM Dispensing with Channel Estimation in the Face of Rapidly Fading Channels

Turbo detection performed by exchanging extrinsic information between the soft-decision QAM detector and the channel decoder is beneficial for the sake of exploring the bit dependency imposed both by modulation and by channel coding. However, when the soft-decision coherent QAM detectors are provided with imperfect channel estimates in rapidly fading channels, they tend to produce potentially unreliable LLRs that deviate from the true probabilities, which degrades the turbo detection performance. Against this background, in this paper, we propose a range of new soft-decision multiple-symbol differential sphere detection (MSDSD) and decision-feedback differential detection (DFDD) solutions for differential QAM (DQAM), which dispense with channel estimation in the face of rapidly fading channels. Our proposed design aims for solving the two inherent problems in soft-decision DQAM detection design, which have also been the most substantial obstacle in the way of offering a solution for turbo detected MSDSD aided differential MIMO schemes using QAM: 1) how to facilitate the soft-decision detection of the DQAM’s amplitudes, which—in contrast to the DPSK phases—do not form a unitary matrix, and 2) how to separate and streamline the DQAM’s soft-decision amplitude and phase detectors. Our simulation results demonstrate that our proposed MSDSD aided DQAM solution is capable of substantially outperforming its MSDSD aided DPSK counterpart in coded systems without imposing a higher complexity . Moreover, our proposed DFDD aided DQAM solution is shown to outperform the conventional solutions in literature. Our discussions on the important subject of coherent versus noncoherent schemes suggest that compared to coherent square QAM relying on realistic imperfect channel estimation, MSDSD aided DQAM may be deemed as a better candidate for turbo detection assisted coded systems operating at high Doppler frequencies.

Reduced-Complexity Soft-Decision Multiple-Symbol Differential Sphere Detection

Unlike a generic PSK/QAM detector, which may visit a constellation diagram only once, a depth-first Sphere Decoder (SD) has to re-visit the same constellation diagram multiple times. Therefore, in order to prevent the SD from repeating the detection operations, the Schnorr-Euchner search strategy of Schnorr and Euchner may be invoked for optimizing the nodes' search-order, where the ideal case is for the SD to visit the constellation nodes in a zigzag fashion. However, when the hard-decision Multiple-Symbol Differential Sphere Detection (MSDSD) of Lampe et al. is invoked for using multiple receive antennas $N_R\ge 1$ , the Schnorr-Euchner search strategy has to visit and sort all the $M\textrm{PSK}$ constellation points. A similar situation is encountered for the soft-decision MSDSD of Pauli et al. , when the a priori LLRs gleaned from the channel decoder are taken into account. In order to tackle these open problems, in this paper, we propose a correlation process for the hard-decision MSDSD of Lampe et al. and a reduced-complexity design for the soft-decision MSDSD of Pauli et al. , so that the Schnorr-Euchner search strategy always opts for visiting the $M\textrm{PSK}$ constellation points in a zigzag fashion. Our simulation results demonstrate that a substantial complexity reduction is achieved by our reduced-complexity design without imposing any performance loss . Explicitly, up to 88.7% complexity reduction is attained for MSDSD $(N_w=4)$ aided D16PSK. This complexity reduction is quite substantial, especially when the MSDSD is invoked several times during turbo detection. Furthermore, in order to offer an improved solution and a comprehensive study for the soft-decision MSDSD, we also propose to modify the output of the SD to harmonize its operation with the near-optimum Approx-Log-MAP. Then the important subject of coherent versus noncoherent is discussed in the context of coded systems, which suggests that MSDSD aided DPSK is an eminently suitable candidate for turbo detection assisted coded systems operating at high Doppler frequencies.

Successive AF/DF Relaying in the Cooperative DS-CDMA Uplink: Capacity Analysis and Its System Architecture

A successive-relaying-aided network (SRAN) is designed for a multiuser spread-spectrum scenario conceived for noncoherent (NC) detection to convert the typical 50% half-duplex relaying induced throughput loss to a potential user-load reduction of the code-division multiple-access (CDMA) system, where the NC allows us to avoid the extra power consumption imposed by channel estimation. We commence by evaluating the NC discrete-input-continuous-output memoryless channel (DCMC) capacity of both the amplify-and-forward-based (AF) and decode-and-forward-based (DF) SRANs in the direct-sequence CDMA (DS-CDMA) uplink (UL). While NC detection has the added benefit of eliminating both the pilot overhead and the power-hungry channel estimation, it tends to form an error floor at high Doppler frequencies. We mitigate this problem using multiple-symbol detection, which increases the detection complexity upon extending the detection window. Finally, a relay-aided soft-input-soft-output multiple-symbol differential sphere detection (SISO-MSDSD) CDMA regime is proposed, which significantly reduces the system's complexity without sacrificing its performance.

Differential Interference Suppression for SDMA-OFDM Based on Joint Multiple-Symbol Filtering and Detection

This paper presents a multiple-symbol differential spatial division multiple-access (MS-DSDMA) orthogonal frequency-division multiplexing (OFDM) system conceived for low-complexity and high-bandwidth-efficiency applications operating in time-varying fading channels, where no channel estimation is required. A low-complexity adaptive multiple-symbol differential interference suppression (MS-DIS) scheme is proposed, which is based on the maximum signal-to-interference-plus-noise ratio (MSINR) criterion and facilitates the implementation of the powerful multiple-symbol differential sphere detection (MSDSD). Then, a practical three-stage turbo DIS receiver design framework is proposed for the MS-DSDMA system, which is constituted by concatenating the adaptive DIS filter bank, the MSDSD, and the channel decoder. Both the EXtrinsic Information Transfer (EXIT) chart analysis and the Monte-Carlo-based simulation results show that the proposed three-stage turbo DIS scheme is capable of achieving a substantially enhanced performance in comparison with the conventional linear minimum mean-squared error (LMMSE)-based adaptive receiver. Furthermore, two complexity reduction techniques are devised to significantly reduce the iterative detection complexity.

Multiple-Symbol Differential Sphere Detection Aided Differential Space-Time Block Codes Using QAM Constellations

We propose Multiple-Symbol Differential Detection (MSDD) aided Differential Space-Time Block Codes (DSTBCs) using QAM. Our solution eliminates the requirement of high-complexity MIMO channel estimation and its pilot overhead, while mitigating the potential performance degradation of noncoherent receivers in fast fading channels. Additionally, we develop Multiple-Symbol Differential Sphere Detection (MSDSD) for the QAM aided DSTBC schemes advocated, in order to circumvent their potentially excessive complexity.

Code-Rate-Optimized Differentially Modulated Near-Capacity Cooperation

It is widely recognized that half-duplex-relay-aided differential decode-and-forward (DDF) cooperative transmission schemes are capable of achieving a cooperative diversity gain, while circumventing the potentially excessive-complexity and yet inaccurate channel estimation, especially in mobile environments. However, when a cooperative wireless communication system is designed to approach the maximum achievable spectral efficiency by taking the cooperation-induced multiplexing loss into account, it is not obvious whether or not the relay-aided system becomes superior to its direct-transmission based counterpart, especially, when advanced channel coding techniques are employed. Furthermore, the optimization of the transmit-interval durations required by the source and relay is an open issue, which has not been well understood in the context of half-duplex relaying schemes. Hence, we first find the optimum transmission duration, which is proportional to the adaptive channel-code rate of the source and relay in the context of Code-Rate-Optimized (CRO) TDMA-based DDF-aided half-duplex systems for the sake of maximizing the achievable network throughput. Then, we investigate the benefits of introducing cooperative mechanisms into wireless networks, which may be approached in the context of the proposed CRO cooperative system both from a pure capacity perspective and from the practical perspective of approaching the Discrete-input Continuous-output Memoryless Channel (DCMC) capacity with the aid of the proposed Irregular Distributed Differential (IrDD) coding aided scheme. In order to achieve a near-capacity performance at a low-complexity, an adaptive-window-duration based Multiple-Symbol Differential Sphere Detection (MSDSD) scheme is employed in the iterative detection aided receiver. Specifically, upon using the proposed near-capacity system design, the IrDD coding scheme devised becomes capable of performing within about 1.8 dB from the corresponding single-relay-aided DDF cooperative system's DCMC capacity.

The Resource-Optimized Differentially Modulated Hybrid AF/DF Cooperative Cellular Uplink Using Multiple-Symbol Differential Sphere Detection

In multiuser cellular uplinks, cooperating mobiles may share their antennas in order to achieve transmit diversity by forming a virtual antenna array (VAA) in a distributed fashion. In this paper, based on the minimum BER criterion, we investigate cooperating-user-selection (CUS) and adaptive-power-allocation (APA) for two types of differentially modulated cooperative cellular uplinks requiring no channel state information (CSI) at the receiver, namely, for the differential-amplify-and-forward (DAF) and the selective differential-decode-and-forward (DDF) assisted systems. They both employ multiple-symbol differential sphere detection (MSDSD) to combat rapid-fading-induced performance degradation. More specifically, we investigate the cooperative-protocol-selection (CPS) of the uplink system in conjunction with a beneficial CUS as well as the APA scheme in order to further improve the achievable end-to-end performance, leading to a resource-optimized hybrid AF/DF cooperative system.