Diversity Multiplexing Tradeoff of Asynchronous Cooperative Relay Networks

The assumption of nodes in a cooperative communication relay network operating in synchronous fashion is often unrealistic. In the present paper we consider two different models of asynchronous operation in cooperative-diversity networks experiencing slow fading and examine the corresponding diversity-multiplexing tradeoffs (DMT). For both models, we propose protocols and distributed space-time codes that asymptotically achieve the transmit diversity bound for all multiplexing gains and for number of relays N >= 2.

Reverse Channel Training For Reciprocal Mimo Systems With Spatial Multiplexing

This paper investigates the problem of designing reverse channel training sequences for a TDD-MIMO spatial-multiplexing system. Assuming perfect channel state information at the receiver and spatial multiplexing at the transmitter with equal power allocation to them dominant modes of the estimated channel, the pilot is designed to ensure an stimate of the channel which improves the forward link capacity. Using perturbation techniques, a lower bound on the forward link capacity is derived with respect to which the training sequence is optimized. Thus, the reverse channel training sequence makes use of the channel knowledge at the receiver. The performance of orthogonal training sequence with MMSE estimation at the transmitter and the proposed training sequence are compared. Simulation results show a significant improvement in performance.

Block- and strand-multiplexing for fast computation of a class of transforms

The transforms dealt with in this paper are defined in terms of the transform kernels which are Kroneeker products of the two or more component kernels. The signal flow-graph for the computation of such a transform is obtained with the flow-graphs for the component transforms as building blocks.

Multiplexing in multiple imaging through the theta modulation technique

We apply the theta modulation technique to simultaneously multiple image more than one object independently with a Fourier plane sampling type of multiple imaging system. Experimental results of multiple imaging two objects is presented.

On the improvement of diversity-multiplexing gain tradeoff in a training based TDD-simo system

This paper investigates the diversity-multiplexing gain tradeoff (DMT) of a time-division duplex (TDD) single-input multiple-output (SIMO) system with perfect channel state information (CSI) at the receiver (CSIR) and partial CSI at the transmitter (CSIT). The partial CSIT is acquired through a training sequence from the receiver to the transmitter. The training sequence is chosen in an intelligent manner based on the CSIR, to reduce the training length by a factor of r, the number of receive antennas. We show that, for the proposed training scheme and a given channel coherence time, the diversity order increases linearly with r for nonzero multiplexing gain. This is a significant improvement over conventional orthogonal training schemes.

Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP)networks and layered networks.KPP networks, can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4.For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks.For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable.Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. We also give alternative and often simpler proofs of several existing results and show that codes achieving full diversity on a MIMO Rayleigh fading channel achieve full diversity on arbitrary fading channels. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT

Maximum likelihood algorithms for joint estimation of synchronisation impairments and channel in multiple input multiple output-orthogonal frequency division multiplexing system

Maximum likelihood (ML) algorithms, for the joint estimation of synchronisation impairments and channel in multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system, are investigated in this work. A system model that takes into account the effects of carrier frequency offset, sampling frequency offset, symbol timing error and channel impulse response is formulated. Cramer-Rao lower bounds for the estimation of continuous parameters are derived, which show the coupling effect among different impairments and the significance of the joint estimation. The authors propose an ML algorithm for the estimation of synchronisation impairments and channel together, using the grid search method. To reduce the complexity of the joint grid search in the ML algorithm, a modified ML (MML) algorithm with multiple one-dimensional searches is also proposed. Further, a stage-wise ML (SML) algorithm using existing algorithms, which estimate less number of parameters, is also proposed. Performance of the estimation algorithms is studied through numerical simulations and it is found that the proposed ML and MML algorithms exhibit better performance than SML algorithm.

Power-Controlled Reverse Channel Training in a Multiuser TDD-MIMO Spatial Multiplexing System With CSIR

This paper considers the design of a power-controlled reverse channel training (RCT) scheme for spatial multiplexing (SM)-based data transmission along the dominant modes of the channel in a time-division duplex (TDD) multiple-input and multiple-output (MIMO) system, when channel knowledge is available at the receiver. A channel-dependent power-controlled RCT scheme is proposed, using which the transmitter estimates the beamforming (BF) vectors required for the forward-link SM data transmission. Tight approximate expressions for 1) the mean square error (MSE) in the estimate of the BF vectors, and 2) a capacity lower bound (CLB) for an SM system, are derived and used to optimize the parameters of the training sequence. Moreover, an extension of the channel-dependent training scheme and the data rate analysis to a multiuser scenario with M user terminals is presented. For the single-mode BF system, a closed-form expression for an upper bound on the average sum data rate is derived, which is shown to scale as ((L-c - L-B,L- tau)/L-c) log logM asymptotically in M, where L-c and L-B,L- tau are the channel coherence time and training duration, respectively. The significant performance gain offered by the proposed training sequence over the conventional constant-power orthogonal RCT sequence is demonstrated using Monte Carlo simulations.

Channel estimation at the transmitter in a reciprocal MIMO spatial multiplexing system

This paper considers the problem of channel estimation at the transmitter in a spatial multiplexing-based Time Division Duplex (TDD) Multiple Input Multiple Output (MIMO) system with perfect CSIR. A novel channel-dependent Reverse Channel Training (RCT) sequence is proposed, using which the transmitter estimates the beamforming vectors for forward link data transmission. This training sequence is designed based on the following two metrics: (i) a capacity lower bound, and (ii) the mean square error in the estimate. The performance of the proposed training scheme is analyzed and is shown to significantly outperform the conventional orthogonal RCT sequence. Also, in the case where the transmitter uses water-filling power allocation for data transmission, a novel RCT sequence is proposed and optimized with respect to the MSE in estimating the transmit covariance matrix.

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in Amplify-and-Forward (AF) relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

Space-Time Codes Achieving the DMD Tradeoff of the MIMO-ARQ Channel

For the quasi-static, Rayleigh-fading multiple-input multiple-output (MIMO) channel with n(t) transmit and n(r) receive antennas, Zheng and Tse showed that there exists a fundamental tradeoff between diversity and spatial-multiplexing gains, referred to as the diversity-multiplexing gain (D-MG) tradeoff. Subsequently, El Gamal, Caire, and Damen considered signaling across the same channel using an L-round automatic retransmission request (ARQ) protocol that assumes the presence of a noiseless feedback channel capable of conveying one bit of information per use of the feedback channel. They showed that given a fixed number L of ARQ rounds and no power control, there is a tradeoff between diversity and multiplexing gains, termed the diversity-multiplexing-delay (DMD) tradeoff. This tradeoff indicates that the diversity gain under the ARQ scheme for a particular information rate is considerably larger than that obtainable in the absence of feedback. In this paper, a set of sufficient conditions under which a space-time (ST) code will achieve the DMD tradeoff is presented. This is followed by two classes of explicit constructions of ST codes which meet these conditions. Constructions belonging to the first class achieve minimum delay and apply to a broad class of fading channels whenever n(r) >= n(t) and either L/n(t) or n(t)kslashL. The second class of constructions do not achieve minimum delay, but do achieve the DMD tradeoff of the fading channel for all statistical descriptions of the channel and for all values of the parameters n(r,) n(t,) L.

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the orthogonal and the nonorthogonal amplify-and-forward (NAF) protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Moreover our code construction for the OAF protocol incurs less delay. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. The variable-NSDF protocol is shown to improve on the DMT of the best previously known static protocol when the number of relays is greater than two. Also included is a DMT optimal code construction for the NAF protocol.

Ternary function and circuit design using ternary multiplexers

The recent trend towards minimizing the interconnections in large scale integration (LSI) circuits has led to intensive investigation in the development of ternary circuits and the improvement of their design. The ternary multiplexer is a convenient and useful logic module which can be used as a basic building block in the design of a ternary system. This paper discusses a systematic procedure for the simplification and realization of ternary functions using ternary multiplexers as building blocks. Both single level and multilevel multiplexing techniques are considered. The importance of the design procedure is highlighted by considering two specific applications, namely, the development of ternary adder/subtractor and TCD to ternary converter.