Unitary Space-time Modulation Research Articles

Constrained Riemannian Noncoherent Constellations for the MIMO Multiple Access Channel

We consider the design of multiuser constellations for a multiple access channel (MAC) with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> users, with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antennas each, that transmit simultaneously to a receiver equipped with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antennas through a Rayleigh block-fading channel when no channel state information (CSI) is available to either the transmitter or the receiver. In full-diversity scenarios where the coherence time is at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ≥ ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> + 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> , the proposed constellation design criterion is based on the asymptotic expression of the multiuser pairwise error probability (PEP) derived by Brehler and Varanasi (2001). In non-full diversity scenarios, for which the previous PEP expression is no longer valid, the proposed design criteria are based on proxies of the PEP recently proposed by Ngo and Yang (2021). Although both the PEP expression and its bounds or proxies were previously considered intractable for optimization, in this work we derive their respective unconstrained gradients. These gradients are in turn used in the optimization of the proposed cost functions in different Riemannian manifolds representing different power constraints. In particular, in addition to the standard unitary space-time modulation (USTM) leading to optimization on the Grassmann manifold, we consider a more relaxed percodeword power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">oblique manifold</i> , and an average power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trace manifold</i> . Equipped with these theoretical tools, we design multiuser constellations for the MIMO MAC in full-diversity and non-full-diversity scenarios with state-of-the-art performance in terms of symbol error rate (SER).

Unitary Space-Time Modulation Based on Coherent Codes

This paper analyzes the relationship between pilot symbol-assisted modulation (PSAM) and unitary space-time modulation (USTM). In particular, we present a map that transforms any PSAM into a USTM and vice versa. USTMs are known to be capacity-achieving. However, most of the proposed USTM construction methods in the literature are computationally expensive, and the resulting constellations do not have a known structure that could simplify their decoding. Using the relationship between PSAM and USTM, and inspired by a graphical representation of these constellations used in this paper, we propose new USTM construction methods, which ensure that the USTM has a good performance compared to the corresponding PSAM, and a feasible construction and decoding, even for high data rates.

Joint Constellation Design for Noncoherent MIMO Multiple-Access Channels

We consider the joint constellation design problem for the noncoherent multiple-input multiple-output multiple-access channel (MAC). By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to minimize the error probability. As a baseline approach, we adapt several existing design criteria for the point-to-point channel to the MAC. Furthermore, we propose new design criteria. Our first proposed design metric is the dominating term in nonasymptotic lower and upper bounds on the pairwise error probability exponent. We give a geometric interpretation of the bound using Riemannian distance in the manifold of Hermitian positive definite matrices. From an analysis of this metric at high signal-to-noise ratio, we obtain further simplified metrics. For any given set of constellation sizes, the proposed metrics can be optimized over the set of constellation symbols. Motivated by the simplified metric, we propose a simple constellation construction consisting in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">partitioning</i> a single-user constellation. We also provide a generalization of our previously proposed construction based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precoding</i> individual constellations of lower dimensions. For a fixed joint constellation, the design metrics can be further optimized over the per-user transmit power, especially when the users transmit at different rates. Considering unitary space-time modulation, we investigate the option of building each individual constellation as a set of truncated unitary matrices scaled by the respective transmit power. Numerical results show that our proposed metrics are meaningful, and can be used as objectives to generate constellations through numerical optimization that perform better, for the same transmission rate and power constraint, than a common pilot-based scheme and the constellations optimized with existing metrics.

Codebooks from generalized bent [formula omitted]-valued quadratic forms

Codebooks with small inner-product correlation have applications in unitary space–time modulations, multiple description coding over erasure channels, direct spread code division multiple access communications, compressed sensing, and coding theory. It is interesting to construct codebooks (asymptotically) achieving the Levenshtein bound. This paper presents a class of generalized bent Z4-valued quadratic forms, which contains functions proposed by Heng and Yue (2017). Using these generalized bent Z4-valued quadratic forms, we construct optimal codebooks achieving the Levenshtein bound. These codebooks have parameters (22m+2m,2m) and alphabet size 6.

Parallel soft information forwarding in non‐coherent MIMO system based on unitary space‐time modulation

Parallel relay is an effective way to extend wireless communication distance. Employing multiple-input multiple-output (MIMO) relay can improve communication quality on a large scale, but the communication efficiency is reduced due to channel estimation. In this study, a mutual information-based estimate-and-forward scheme is proposed based on unitary space-time modulation in MIMO system. An equivalent transmission model is also constructed by regarding that the source signal is affected by a multiplicative factor and an additive noise. Based on this equivalent MIMO model, the generalized signal-to-noise ratio and global mutual information of the forwarding schemes are calculated. Error rate and mutual information analysis show that the proposed soft information forwarding can improve the reliability of parallel relaying system and has a better error rate performance than all the existing memory-less forwarding schemes.

Energy Efficient Differential Cooperative MIMO Algorithm for Wireless Sensor Networks

Differential unitary space time modulation (USTM) is identified as one of the best non-coherent technique for future 5th generation mobile networks. Two or more nodes with single antennas cooperate with each other to form a cooperative multiple-input–multiple-output network. In, this paper we examine the use of differential cooperative USTM that avoids channel estimation and also prolong the lifetime of wireless sensor network. Aiming at minimizing the energy consumption per bit we form a differential cooperative energy minimization algorithm by optimally selecting the number of cooperative nodes and finding the route that consumes minimum energy.

Energy efficiency analysis of differential cooperative algorithm in wireless sensor network

Cooperative MIMO techniques deliver the speed and reliability required for future fifth generation mobile networks. However, coherent MIMO techniques demand high channel estimation complexity as well as high pilot overhead. Hence collaboration of cooperative communication and non-coherent schemes will be particularly beneficial in energy constrained wireless sensor networks (WSNs). Aiming at minimizing the energy consumption per bit, we propose an algorithm for differential cooperative communication in WSNs using unitary space time modulation technique. The algorithm computes the optimum transmission distance for the optimum number of cooperating nodes. The simulation results show that the proposed algorithm provides significant energy saving and increased network lifetime compared with the fixed distance cooperative schemes.

Grassmannian Constellation Based on Antipodal Points and Orthogonal Design and Its Simplified Detecting Algorithm

This study presents a framework of the unitary space time modulation (USTM) constellation based on antipodal points over Grassmannian manifold. The antipodal constellation enables an intrinsic simplified ML detecting algorithm. The algebraic orthogonal USTM constellation is also an antipodal constellation which, apart from being adaptive to the antipodal simplified ML detector, also has another simplified ML detector based on its self-indexing features, and the latter is simpler because of getting rid of the matrix operation. A searching orthogonal USTM constellation based on the grid search algorithm is obtained under the presented framework and its minimum Frobenius chordal distance and simulation performance are be superior to those of the algebraic orthogonal USTM constellation.

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.

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.

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.

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.

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.

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&amp;S) operations by 24.24, 25 and 43.46%, respectively, with less performance degradation. After that, two low-complexity sorting architectures, Batcher&apos;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&apos;s merge sorting dynamic K-best detections can further save C&amp;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&apos;s merge sorting dynamic K-best detection is more beneficial to parallel processing and multiple-processor structure.

Maximum-Likelihood Multiple Symbol Differential Detection for Unitary Space-Time Modulation in Continuous Fading

为酉空时调制系统设计的多符号差分球形译码(MSDSD)能以较低复杂度获得最大似然(ML)检测性能。但是，该算法基于准静态信道假设，当将它用于快衰落信道时会出现严重的误码平层现象。本文基于连续衰落信道假设，推导了一种ML度量的递推形式，并将其嵌入自动球形译码算法中，得到了的多符号差分自动球形译码(MSDASD)算法。该算法适用于一般酉空时星座，克服了MSDSD的误码平层现象，可达到ML检测的性能，其平均复杂度在大多数情况下低于相同假设下的判决反馈检测算法。

A Soft-Detector Based on Multiple Symbol Differential Detection for Unitary Space-Time Modulation

A Soft-Detector Based on Multiple Symbol Differential Detection for Unitary Space-Time Modulation