Space-time Modulation Research Articles

Non-Coherent Open-Loop MIMO Communications Over Temporally-Correlated Channels

This paper investigates the use of non-coherent communication techniques for open-loop transmission over temporally-correlated Rayleigh-fading MIMO channels. These techniques perform data detection without knowing the instantaneous channel coefficients. Three non-coherent Multiple Input Multiple Output (MIMO) schemes, namely, differential unitary space-time modulation, differential space-time block code, and Grassmannian signaling, are compared with several state-of-the-art training-based coherent schemes. This paper shows that the non-coherent schemes are meaningful alternatives to training-based communication, specially as the number of transmit antennas increases. In particular, for more than two transmit antennas, non-coherent communication provides a clear advantage in medium to high mobility scenarios.

Differential Modulation Exploiting the Spatial–Temporal Correlation of Wireless Channels With Moving Antenna Array

Provisioning reliable wireless services for railway passengers is becoming an increasingly critical problem to be addressed with the fast development of high speed trains (HST). In this paper, exploiting the linear mobility inherent to the HST communication scenario, we discover a new type of spatial-temporal correlation between the base station and moving antenna array on the roof top of the train. Capitalizing on the new spatial-temporal correlation structure and properties, an improved differential space-time modulation (DSTM) scheme is proposed. Analytical expressions are obtained for the pairwise error probability of the system. It is demonstrated that, the proposed approach achieves superior error performance compared with the conventional DSTM scheme. In addition, an adaptive method which dynamically adjusts the transmission block length is proposed to further enhance the system performance. Numerical results are provided to verify the performance of the proposed schemes.

Finite-SNR Bounds on the Sum-Rate Capacity of Rayleigh Block-Fading Multiple-Access Channels With No A Priori CSI

We provide nonasymptotic upper and lower bounds on the sum-rate capacity of Rayleigh block-fading multiple-access channels for the set up where a priori channel state information is not available. The upper bound relies on a dual formula for channel capacity and on the assumption that the users can cooperate perfectly. The lower bound is derived assuming a noncooperative scenario where each user employs unitary space-time modulation (independently from the other users). Numerical results show that the gap between the upper and the lower bound is small already at moderate SNR values. This suggests that the sum-rate capacity gains obtainable through user cooperation are minimal for the scenarios considered in the paper.

Raptor-Coded Noncoherent Cooperative Schemes Based on Distributed Unitary Space–Time Modulation

In this paper, we investigate Raptor-coded distributed unitary space–time modulation (USTM) schemes, where both the amplify-and-forward (AF) and decode-and-forward (DF) relaying scenarios are considered, under a wireless relay network with arbitrary path gains for the channel fading coefficients. First, the AF and DF relaying procedures are investigated based on the use of an inner USTM signal and an outer Raptor code, and the related noncoherent detectors are also derived. The constellation search for the USTM signal, as well as the optimization for the Raptor code, is then investigated in order to enhance the system performance. It is shown that the designed systems effectively approach the predicted limit in throughput performances and outperform the noncoherent distributed MIMO scheme reported in the previous literature.

Dynamic 2D-photonic structure with the negative refractive index

The conditions of the formation of a spatially ordered optical structure on the base of media with space–time modulation of refractive index by ultrasound have been considered. It has been shown that the excitation of a standing ultrasonic wave in the medium creates a structure consisting of trajectories of separate light beams, which is a superlattice of the dynamic 2D-photonic crystal. The band gaps corresponding to negative light refraction have been revealed in beam trajectories. Possible fields of application of such structures have been discussed.

Parallel and perpendicular structure of the edge turbulence in a three-dimensional magnetic field

Edge turbulence and blobs are studied in the three-dimensional magnetic topology of the RFX-mod reversed field pinch. The edge of the RFX-mod shows a three-dimensional structure dominated by a helical equilibrium with (1, −7) symmetry, which gives the same space-time modulation to all of the kinetic properties. The interaction between the edge turbulence and this magnetic topology is studied. It is shown that the edge blobs are current-carrying filaments aligned with the magnetic field, and in the perpendicular plane each blob is a positive peak of electron density and a valley of temperature. The inner nature of these blobs is not affected by the presence of the O and X points of the (1, −7) island; however, the statistical properties are sensitive to them, pointing to the influence of the magnetic topology on the edge fluctuations.

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu's convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.

Low-Complexity LDPC-Coded USTM Noncohereny MIMO Receivers

This paper proposes a scheme of combining low-density parity check (LDPC) code with unitary space time modulation (USTM) for noncoherent multiple-input-multiple-output (MIMO) transmitter and receiver over Rayleigh block fading and additive white Gaussian noise (AWGN) channel. The main aim is to design the low complexity coded noncoherent MIMO receiver which is completely dependent on the structural feature of unitary space-time matrix without sending the pilot symbol at the transmitter and estimating the channel state information at the receiver. Considering soft information required by belief-propagation (BP) iterative decoder of LDPC code, we deduce a maximum a posteriori probability (MAP) demodulating algorithm using a special USTM based on the sine-cosine function. A novel dual-demodulator is conceived for decreasing the computational complexity of this MAP demodulator. Furthermore, the iterative feedback scheme between MAP demodulator and BP decoder is introduced and its modified parameter scheme is considered for further improving performance of the dual-demodulator. Comparing with uncoded USTM, our LDPC-coded USTM MIMO receiver can obtain about 17 dB coding gain at 10-6 BER.

Soft forwarding technique for unitary space‐time modulation

The authors propose two soft forwarding schemes for unitary space-time modulation, namely estimate-and-forward (EF) and mutual information-based forwarding (MIF), which are ideally suited for rapid piecewise-constant fading scenarios with no channel state information both at transmitters and receivers. In the EF scheme, the relay regenerates signal via the conditional expectation of the source unitary space-time (UST) signal given the received matrix at the relay node instead of hard decisions. The MIF scheme employs the instantaneous mutual information between the source UST signal and received matrix at the relay node as a measurement for maximum-likelihood detection. The authors provide the relay forwarding functions, the normalisation factors, and the detection methods at the destination firstly. Above all, the generalised signal-to-noise ratio (SNR) at the destination for our unitary space-time modulated relaying system is analysed and simulated firstly. Simulation results reveal that the proposed EF and MIF schemes can outperform the existing amplify-and-forward (AF) and detect-and-forward (DF) schemes in terms of bit-error-rate performances in most scenarios. For a parallel relay network with two relays, the proposed EF scheme achieves 2 and 3 dB SNR gain over AF and DF schemes, respectively. Moreover, the MIF scheme can further give about 1.5 dB SNR gain.

A New Quaternary Alphabet Signal Constellation for Differential Unitary Space-Time Modulation

In this letter, a new constellation design for differential unitary space-time modulation is proposed. We generate a set of unitary matrices from the multiplication of a simple unitary matrix with entries of ± 1 by diagonal matrices made from quaternary alphabets. Then, the constellation is formed from the product of the optimum matrix chosen from this set and the optimized diagonal matrix first used for the cyclic codes. We show that, without deteriorating the transmission rate, the proposed constellation yields a larger diversity product as well as a lower union bound for pairwise error probability with the same or a lower complexity compared to other previously proposed constellations.

On the Capacity of Large-MIMO Block-Fading Channels

We characterize the capacity of Rayleigh block-fading multiple-input multiple-output (MIMO) channels in the noncoherent setting where transmitter and receiver have no a priori knowledge of the realizations of the fading channel. We prove that unitary space-time modulation (USTM) is not capacity-achieving in the high signal-to-noise ratio (SNR) regime when the total number of antennas exceeds the coherence time of the fading channel (expressed in multiples of the symbol duration), a situation that is relevant for MIMO systems with large antenna arrays (large-MIMO systems). This result settles a conjecture by Zheng & Tse (2002) in the affirmative. The capacity-achieving input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a unitary isotropically distributed random matrix, and a diagonal matrix whose nonzero entries are distributed as the square-root of the eigenvalues of a Beta-distributed random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in large-MIMO systems yields a rate gain as large as 13% for SNR values of practical interest.

Matrix Coded Modulation: A New Non-coherent MIMO Scheme

This paper describes a new space-time coding scheme for non-coherent multi-antenna multi-input multi-output (MIMO) systems. This new MIMO scheme merges error-correcting and space-time coding functions by transmitting invertible matrices, so this scheme has been called "Matrix Coded Modulation" or "MCM". Coherent systems require channel state information (CSI) at the transmitters and/or at the receivers, and their performances strongly depend on the channel estimation. For example, in systems using Orthogonal frequency division multiplexing, the channel estimation requires the insertion of pilot-symbols in the transmitted frame which implies a spectral efficiency loss of the global system that increase with the number of transmit antennas. The existing non-coherent schemes such as the differential space-time modulation leads to performance degradation compared to coherent systems in which perfect CSI is assumed. Decoding in the MCM scheme is performed iteratively, based on a specified detection criteria. In the proposed MCM scheme, decoding can be achieved with or without CSI at the receiving antennas. As the space-time coding function is merged with the error-correcting code, the euclidean distances distribution between modulated signals based on the detection criteria is strongly linked to the Hamming weights distribution of the channel error-correcting code used in the MCM scheme. Moreover, a low-complexity decoding algorithm is described and compared to the existing differential schemes.

Further Results on Differential Encoding by a Table

Recently we proposed a novel differential encoder by a look-up table. In this paper, we present further research results on this subject. We first propose a bit-assigning algorithm and construct some new tables for various constellations that maximize the minimum noncoherent distance. Then differential encoding for multiple-symbol differential detection is proposed. After that, we indicate that differential encoding by a table is equivalent to differential encoding by a trellis, so we propose a novel differential detector which uses the Viterbi algorithm on the trellis. A theorem about the sufficient number of states for various modulations is proposed. In addition, we further enhance the error performance of the proposed differential encoder by concatenating it with trellis coding. For this noncoherent trellis coding scheme, we propose augmented-state Viterbi decoding. Finally, we extend the proposed differential encoding and detection to differential space-time modulation (DSTM). We propose a new definition of DSTM by which the set of transmitted blocks is determined first. The differential encoding is implemented by a look-up table which can be optimized. The proposed DSTM has satisfactory error performance without constellation expansion.

Multi-cell cooperative transmission based on unitary space-time modulation

As a non-coherent transmission scheme that does not require channel state information at both transmitters and receivers, unitary space-time modulation is a promising technique that can be applied in high mobility scenario where the fading coefficients are changing too fast to be tracked and estimated. This article proposes a multi-cell cooperative transmission scheme based on unitary space-time modulation. Each cooperative base-station transmits an individual unitary signal from the common constellation set to the mobile unit which is located at the cell edge and suffers from severe inter-cell interference. Compared with traditional unitary space-time modulation, cooperation among multi-cells not only eliminates the inter-cell co-channel interference but also increases the transmission rate by expanding the constellation size. Performance of error probability is analyzed for the proposed scenario with maximum-likelihood decoding, in which the exact pairwise error probability is derived. Additionally, constellation optimization for cooperative transmission is also discussed to achieve the balance between transmission efficiency and reliability. Simulation results are provided to confirm the effectiveness of the proposed scheme in both block-fading channels and fast-fading channels.

Magneto-Optic Fraunhofer Diffraction on 2D Magnetic Domain Patterns

Magneto-optical Fraunhofer diffraction on phase 2D domain patterns with Cmm6 and Pab2 symmetry in uniaxial iron garnet films was studied. Domain patterns contain more than 100 elementary cells and have high spatial homogeneity. The diffraction patterns contain up to 10 or more orders of peaks. Possibilities of space-time modulation of optical radiation and multiplication of the modulation frequency both under change of diffraction order as well as amplitude of magnetic bias field strength were shown.

Performance Analysis of Differential Space–Time Modulation

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.

Noncoherent unitary space-time modulated DSSS systems in multipath channels

In this paper, in order to effectively apply unitary space-time modulation to the direct-sequence spread-spectrum multiple-access (DSSS-MA) networks, we propose a low-rate, noncoherent, unitary, and space-time modulated DSSS system supporting any number of transmit antennas based on Walsh matrices. The proposed scheme simultaneously performs bandwidth spreading and space-time coding and outperforms those using high-rate, conventional unitary space-time constellations. Furthermore, the proposed scheme allows for a simple detector structure based on fast Walsh transforms.

실수 선부호기를 이용한 새로운 차등 시공간 변조 설계

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.

Reduced-Complexity Soft-Decision Aided Space-Time Shift Keying

In this letter, we propose to reduce the detection complexity of soft-decision aided Space-Time Shift Keying (STSK). More explicitly, we propose a vector-by-vector based STSK detector, which exhibits a lower complexity compared to the classic block-by-block based Space-Time Modulation (STM) detector. We further operate the STSK detector on a symbol-by-symbol basis, so that a near-capacity performance may be achieved with the aid of channel coding at a reduced complexity.

Research on low-complexity breadth-first detection for multiple-symbol differential unitary space–time modulation systems

The breadth-first searching algorithms, typically represented by K-best algorithm, are widely studied for multiple-symbol differential detection in multiple-input multiple-output systems due to the advantages of fixed complexity and latency which are very attractive for hardware implementation. However, it needs a large K value to achieve near maximum likelihood performance, which results in large complexity. In this study, a dynamic K-best detection with reduced average K value is proposed. It reduces the complexity on path expanding, path updating and comparing and swapping (C&S) operations by 24.24, 25 and 43.46%, respectively, with less performance degradation. After that, two low-complexity sorting architectures, Batcher's merge sort and K cycles sort, are presented and applied to the proposed dynamic K-best detection. The complexity analysis and simulation results show that, compared with the traditional Bubble sorting dynamic K-best detection, the K cycles sorting and the Batcher's merge sorting dynamic K-best detections can further save C&S operations by 59.5 and 11.2%, respectively, while performance cost capable of being ignored. Moreover, the K cycles sorting dynamic K-best detection achieves best trade-off on throughput and required memory, and the architecture of the Batcher's merge sorting dynamic K-best detection is more beneficial to parallel processing and multiple-processor structure.