Multiple-symbol Differential Detection Research Articles

Revisiting Non-Coherent Detection of Differential PSK: A Factor Graph Perspective

For non-coherent differential modulated communications, the multiple-symbol differential detection (MSDD) may approach the coherent detection performance by jointly detecting a block of symbols. However, MSDD cannot support large-size block detection due to its complexity exponentially increasing with the block size. Moreover, MSDD assumes that the channel phase is constant over the symbols in a block, which is not realistic. In this letter, we propose to formulate the signal model of non-coherent differential modulated communications by means of a factor graph. Based on the factor graph, we develop a sum-product message-passing algorithm to enable the maximum a posteriori probability detection. Compared with MSDD, the detection complexity of our proposed scheme is linearly proportional to the block size. Simulation results show that the proposed scheme can not only achieve the performance of MSDD over the constant-phase channel, but also outperform it over the random-walk phase channel.

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.

Energy efficient decision fusion for differential space-time block codes in wireless sensor networks

The non-coherent techniques that do not require the channel state information have gained significant interest especially when multiple transmitter and receiver nodes are involved in communication. In this paper, we analyze the energy efficiency of differential and coherent cooperative Multiple-input Multiple-output (MIMO) method using space-time block codes (STBC). We exploit the benefits of the extension of the observation interval of differential STBC to three blocks in Wireless sensor networks (WSNs). We propose an energy efficient decision fusion (EEDF) algorithm in WSNs which utilizes the benefits of Multiple symbol differential detection (MSDD) decision fusion by optimally selecting the ring amplitude of the differential amplitude phase shift keying (DAPSK) constellation. The simulation results show that processing differential multiple symbols provides significant energy saving compared to the conventional two-symbol processing. Furthermore, significant performance gain is achieved for the proposed algorithm compared to 16 DPSK MSDD decision fusions.

Lattice-reduction aided multiple-symbol differential detection in two-way relay transmission

Multiple-symbol differential detection MSDD algorithms are proposed in two-way relay transmission TWRT . Firstly, generalized likelihood ratio test based MSDD GLRT-MSDD is proposed in TWRT. Unfortunately, as the number of observation windows increases, the computational complexity of GLRT-MSDD increases exponentially. Hence, this detection in TWRT constitutes a challenging problem. Moreover, we find a way to reformulate the GLRTMSDD model and additionally propose a lattice-reduction aided MSDD LR-MSDD model. Performance analysis and simulations show that the proposed LR-MSDD provides bit-error rate performance close to that of GLRT-MSDD with lower complexity in TWRT.

A New Multiple-Symbol Differential Detection Strategy for Error-Floor Elimination of IEEE 802.15.4 BPSK Receivers Impaired by Carrier Frequency Offset

In this paper, we pay our attention towards the noncoherent demodulation aspect of binary phase shift keying (BPSK) receivers for IEEE 802.15.4 wireless sensor networks (WSNs), and a carrier frequency offset invariant as well as error-floor free multiple-symbol differential detection (MSDD) strategy is proposed over the flat fading channel. This detector is an alternative to the multiple-symbol detector that has been considered almost exclusively in the past. In this new configuration, the receivers do not perform chip-level precompensation as in conventional scheme but bit-level postcompensation. That is, the bit-level autocorrelation operation is first implemented with the “raw” chip sample, and then the carrier frequency offset effect (CFOE) embedded in the achieved statistic is compensated. Correspondingly, the cumulative error in the detection metric is decreased so much that the pervasive error floor for the conventional MSDD scheme is suppressed. Also, complexity efficient estimators for the MSDD scheme are reinvestigated, analyzed, and summarized. Simulation results demonstrate that this new detection strategy may achieve rather more encouraging gain from differential and spread spectrum coding than the conventional single differential coherent detection (SDCD) scheme. The pervasive error floor is also eliminated as compared with conventional MSDD scheme even if the most simple estimator is configured under large bit observation length. Then, much transmitting energy may be saved for each chip symbol, which is practically desired for transmit-only nodes in WSNs.

Semidefinite relaxation aided noncoherent detection in two-way relay transmission

A high-performance noncoherent transmission scheme is proposed in the broadcasting phase of a two-way relay transmission (TWRT), where multiple-symbol differential detection (MSDD) is performed because of its excellent detection performance with no channel estimation. Specifically, the generalized likelihood ratio test aided MSDD (GLRT-MSDD) is developed for the down-link. Furthermore, GLRT-MSDD is reformulated and a semidefinite relaxation aided MSDD (SDR-MSDD) is proposed. The reformulation of GLRT-MSDD to SDR-MSDD is desirable owing to its reduced complexity. Performance analysis and the simulations validate that the proposed SDR-MSDD provides the bit-error-rate performance close to that of GLRT-MSDD with reasonable complexity in TWRT.

Decision-Feedback Aided Multiple-Symbol Differential Detection in Two-Way Relay Transmission

In this paper, noncoherent transmission algorithms are proposed in a two-way relay transmission (TWRT), where differential space-time block codes based multiple-symbol differential detection (MSDD) is performed. Specifically, generalized likelihood ratio test aided MSDD (GLRT-MSDD) is developed with the exhaustive search in the TWRT. In order to solve the challenging problem of high complexity, the GLRT-MSDD model is reformulated and a decision-feedback aided MSDD (DF-MSDD) model is derived. Furthermore, performance analysis and the simulations confirm that the proposed DF-MSDD provides solid bit error-rate performance with a lower complexity than GLRT-MSDD in the TWRT.

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 Detection Scheme for IEEE 802.15.4 BPSK Receivers

Multiple Symbol Differential Detection Scheme for IEEE 802.15.4 BPSK Receivers

Multiple Symbol Differential Detection for Noncoherent Communications With Large-Scale Antenna Arrays

For communications over large-scale antennas, noncoherent differential detection is an attractive option for avoiding expensive channel estimation, but it cannot maximally collect the performance benefits as the antenna number increases. For a desired performance-complexity tradeoff, this letter develops multiple symbol differential detection (MSDD) with simple implementation for single-input multiple-output (SIMO) systems, which jointly detects a block of symbols within the channel coherence time. The generalized likelihood ratio test criterion is adopted that maximizes the likelihood function over both the information symbols and the unknown channels. Simple formulas of the MSDD-SIMO detector are derived, whose performance is competitive to training-based coherent detection.

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.

Factor Graph Aided Multiple-Symbol Differential Detection in the Broadcasting Phase of a Network Coding Based UWB Relay System

A factor-graph-aided multiple-symbol differential detection (FG-MSDD) is proposed and its performance is analyzed and evaluated in the broadcasting phase (i.e., the downlink phase) of an ultra-wideband (UWB) two-way relay system (TWRS). In the downlink of the TWRS, the relay is transmitting network-coded information to the sources, and each source node aims to calculate a posteriori probabilities (APPs) of the information symbols from the relay node. A sampling method based on the modified autocorrelation receiver is proposed for FG-MSDD, which has a trellis structure. The trellis can be decomposed into multiple subtrellises depending on the FG factorization. Then, a methodology for APPs is derived when the forward-and-backward message passing is performed on the subtrellises. The main advantage of FG-MSDD is that it exploits soft information accurately with the aid of the bidirectional message passing. In addition, the proposed FG-MSDD, in conjunction with any soft-input soft-output (SISO) decoding scheme, is capable of obtaining an iterative detection algorithm. Various performance evaluation results obtained by means of computer simulations have verified that the proposed algorithm improves detection performance for the noncoherent UWB TWRS.

Joint Multiple Symbol Differential Detection and Channel Decoding for Noncoherent UWB Impulse Radio by Belief Propagation

This paper proposes a belief propagation (BP) message passing algorithm-based joint multiple symbol differential detection (MSDD) and channel decoding scheme for noncoherent differential ultra-wideband impulse radio (UWB-IR) systems. MSDD is an effective means to improving the performance of noncoherent differential UWB-IR systems. To optimize the overall detection and decoding performance, this paper proposes a novel soft-in soft-out (SISO) MSDD scheme for noncoherent differential UWB-IR. We first propose a new sampling mechanism for the noncoherent auto-correlation receiver to sample the received UWB-IR signal. The proposed sampling mechanism can exploit the dependences (imposed by the differential modulation) among data symbols throughout the whole packet. The signal probabilistic model has a hidden Markov chain structure. We use a factor graph to represent this hidden Markov chain. Then, we apply BP message passing algorithm on the factor graph to develop an SISO MSDD scheme, which is easy to integrate with SISO channel decoding to form a joint MSDD and channel decoding scheme. Performance results of bit error rate simulations and EXIT chart analyses indicate the performance advantages of our scheme over the previous MSDD scheme.

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.

A Belief Propagation-Based Framework for Soft Multiple-Symbol Differential Detection

Soft noncoherent detection, which relies on calculating the \textit{a posteriori} probabilities (APPs) of the bits transmitted with no channel estimation, is imperative for achieving excellent detection performance in high-dimensional wireless communications. In this paper, a high-performance belief propagation (BP)-based soft multiple-symbol differential detection (MSDD) framework, dubbed BP-MSDD, is proposed with its illustrative application in differential space-time block-code (DSTBC)-aided ultra-wideband impulse radio (UWB-IR) systems. Firstly, we revisit the signal sampling with the aid of a trellis structure and decompose the trellis into multiple subtrellises. Furthermore, we derive an APP calculation algorithm, in which the forward-and-backward message passing mechanism of BP operates on the subtrellises. The proposed BP-MSDD is capable of significantly outperforming the conventional hard-decision MSDDs. However, the computational complexity of the BP-MSDD increases exponentially with the number of MSDD trellis states. To circumvent this excessive complexity for practical implementations, we reformulate the BP-MSDD, and additionally propose a Viterbi algorithm (VA)-based hard-decision MSDD (VA-HMSDD) and a VA-based soft-decision MSDD (VA-SMSDD). Moreover, both the proposed BP-MSDD and VA-SMSDD can be exploited in conjunction with soft channel decoding to obtain powerful iterative detection and decoding based receivers. Simulation results demonstrate the effectiveness of the proposed algorithms in DSTBC-aided UWB-IR systems.

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.

A Random Channel Sounding Decision Feedback Receiver for Two-Way Relay Communication With Pilotless Orthogonal Signaling and Physical-Layer Network Coding

We propose a decision feedback (DFB) receiver at the relay of a two-phase (2P) two-way relay (TWR) communication system that employs pilotless orthogonal modulation (such as frequency-shift keying) in the uplink and physical-layer network coding over finite field in the downlink. The proposed relay receiver is able to attain a performance very close to that of an ideal coherent detector in the presence of time-selective Rayleigh fading and additive white Gaussian noise in the uplinks. It exploits the fact that when the uplink symbols from the users are different, then the fading gains affecting these symbols can be separated and individually tracked at the relay. In essence, the proposed receiver performs random channel sounding although no actual pilots are transmitted. The channel estimates obtained this way can then be subsequently used in a coherent detector to improve the reliability of the relay detected data. To ensure fast convergence, we propose to kick start the DFB receiver using a partial-coherent detector developed earlier by the authors. We compare the performance of the proposed system against a similar 2P-TWR system that employs differential phase-shift keying (DPSK) in the uplink and DFB multiple-symbol differential detection at the relay. We found that the proposed pilotless orthogonal modulation system can actually attain a significantly lower bit error rate (BER) than its DPSK counterpart. For static fading and a BER of $\mbox{10}^{-3}$ , the signal-to-noise ratio (SNR) gap between the two approaches is 1 dB in the binary case and 8 dB in the quaternary case. These gaps increase further with time-selective fading.

Multiple-Symbol Differential Detection for Spatial Modulation

Approximately 3 dB Signal-to-Noise Ratio (SNR) loss is always paid with conventional Differential Spatial Modulation (DSM) as compared to coherent Spatial Modulation (SM). In this paper, a Multiple-Symbol Differential Detection (MSDD) technique is proposed for DSM systems to mitigate the loss due to differential detection. 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 the conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit error probability (BEP) are derived for multiple-symbol differential spatial modulation. Results show that the theoretical BEP matches well the simulated one. 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.

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.

Multiple-Symbol combined differential detection for satellite-based AIS Signals

In this paper, a multiple-symbol combined differential Viterbi decoding algorithm which is insensitive to frequency offset is proposed. According to the theories of multiple-symbol differential detection and maximum-likelihood detection, we combine the multiple-order differential information with the Viterbi algorithm. The phase shift caused by the frequency offset is estimated and compensated from the above information in the process of decoding. The simulation results show that the bit error rate (BER) of 2 bits combined differential Viterbi algorithm is below 10−3 when the normalized signal-to-noise ratio (NSNR) is 11 dB, and the decoding performances approach those of the coherent detection as the length of the combined differential symbols increases. The proposed method is simple and its performance remains stable under different frequency offsets.