Performance analysis of fixed gain amplify-and-forward relaying with time-efficient cascaded channel estimation

In a cooperative system with an amplify-and-forward relay, the cascaded channel training protocol enables the destination to estimate the source-destination channel gain and the product of the source-relay (SR) and relay-destination (RD) channel gains using only two pilot transmissions from the source. Notably, the destination does not require a separate estimate of the SR channel. We develop a new expression for the symbol error probability (SEP) of AF relaying when imperfect channel state information (CSI) is acquired using the above training protocol. A tight SEP upper bound is also derived; it shows that full diversity is achieved, albeit at a high signal-to-noise ratio (SNR). Our analysis uses fewer simplifying assumptions, and leads to expressions that are accurate even at low SNRs and are different from those in the literature. For instance, it does not approximate the estimate of the product of SR and RD channel gains by the product of the estimates of the SR and RD channel gains. We show that cascaded channel estimation often outperforms a channel estimation protocol that incurs a greater training overhead by forwarding a quantized estimate of the SR channel gain to the destination. The extent of pilot power boosting, if allowed, that is required to improve performance is also quantified.

Decoherence suppression by parallelization

Decoherence as an obstacle in quantum computation is viewed as a struggle between two forces [1]: the computation which uses the exponential dimension of Hilbert space, and decoherence which destroys this entanglement by collapse. In this model of decohered quantum computation, a sequential quantum computer loses the battle, because at each time step, only a local operation is carried out but g*(t) number of gates collapse. With quantum circuits computing in parallel way the situation is different- g(t) number of gates can be applied at each time step and number gates collapse because of decoherence. As g(t) ≈ g*(t) competition here is even [1]. Our paper improves on this model by slowing down g*(t) by encoding the circuit in parallel computing architectures and running it in Single Instruction Multiple Data (SIMD) paradigm. We have proposed a parallel ion trap architecture for single-bit rotation of a qubit.

Multiuser detection in large-dimension multicode MIMO-CDMA systems with higher-order modulation

In this paper, we are interested in high spectral efficiency multicode CDMA systems with large number of users employing single/multiple transmit antennas and higher-order modulation. In particular, we consider a local neighborhood search based multiuser detection algorithm which offers very good performance and complexity, suited for systems with large number of users employing M-QAM/M-PSK. We apply the algorithm on the chip matched filter output vector. We demonstrate near-single user (SU) performance of the algorithm in CDMA systems with large number of users using 4-QAM/16-QAM/64-QAM/8-PSK on AWGN, frequency-flat, and frequency-selective fading channels. We further show that the algorithm performs very well in multicode multiple-input multiple-output (MIMO) CDMA systems as well, outperforming other linear detectors and interference cancelers reported in the literature for such systems. The per-symbol complexity of the search algorithm is O(K2n2tn2cM), K: number of users, nt: number of transmit antennas at each user, nc: number of spreading codes multiplexed on each transmit antenna, M: modulation alphabet size, making the algorithm attractive for multiuser detection in large-dimension multicode MIMO-CDMA systems with M-QAM.

Energy-efficient training for antenna selection in time-varying channels

Training for receive antenna selection (AS) differs from that for conventional multiple antenna systems because of the limited hardware usage inherent in AS. We analyze and optimize the performance of a novel energy-efficient training method tailored for receive AS. In it, the transmitter sends not only pilots that enable the selection process, but also an extra pilot that leads to accurate channel estimates for the selected antenna that actually receives data. For time-varying channels, we propose a novel antenna selection rule and prove that it minimizes the symbol error probability (SEP). We also derive closed-form expressions for the SEP of MPSK, and show that the considered training method is significantly more energy-efficient than the conventional AS training method.

Joint data detection and dominant singular mode estimation in time varying reciprocal MIMO systems

This paper proposes an algorithm for joint data detection and tracking of the dominant singular mode of a time varying channel at the transmitter and receiver of a time division duplex multiple input multiple output beamforming system. The method proposed is a modified expectation maximization algorithm which utilizes an initial estimate to track the dominant modes of the channel at the transmitter and the receiver blindly; and simultaneously detects the un known data. Furthermore, the estimates are constrained to be within a confidence interval of the previous estimate in order to improve the tracking performance and mitigate the effect of error propagation. Monte-Carlo simulation results of the symbol error rate and the mean square inner product between the estimated and the true singular vector are plotted to show the performance benefits offered by the proposed method compared to existing techniques.

Quadrature approximation properties of the spiral-phase quadrature transform

The notion of the 1-D analytic signal is well understood and has found many applications. At the heart of the analytic signal concept is the Hilbert transform. The problem in extending the concept of analytic signal to higher dimensions is that there is no unique multidimensional definition of the Hilbert transform. Also, the notion of analyticity is not so well under stood in higher dimensions. Of the several 2-D extensions of the Hilbert transform, the spiral-phase quadrature transform or the Riesz transform seems to be the natural extension and has attracted a lot of attention mainly due to its isotropic properties. From the Riesz transform, Larkin et al. constructed a vortex operator, which approximates the quadratures based on asymptotic stationary-phase analysis. In this paper, we show an alternative proof for the quadrature approximation property by invoking the quasi-eigenfunction property of linear, shift-invariant systems. We show that the vortex operator comes up as a natural consequence of applying this property. We also characterize the quadrature approximation error in terms of its energy as well as the peak spatial-domain error. Such results are available for 1-D signals, but their counter part for 2-D signals have not been provided. We also provide simulation results to supplement the analytical calculations.

Modulation Diversity for Spatial Modulation Using Complex Interleaved Orthogonal Design

In this paper, we propose modulation diversity techniques for Spatial Modulation (SM) system using Complex Interleaved Orthogonal Design (CIOD). Specifically, we show that the standard SM scheme can achieve a transmit diversity order of two by using the CIOD meant for two transmit antenna system without incurring any additional system complexity or bandwidth requirement. Furthermore, we propose a low-complexity maximum likelihood detector for our CIOD based SM schemes by exploiting the structure of the CIOD. We show with our simulation results that the proposed schemes offer transmit diversity order of two and give a better symbol error rate performance than the conventional SM scheme.

Antenna Selection in Interference-Constrained Underlay Cognitive Radios: SEP-Optimal Rule and Performance Benchmarking

In the underlay mode of cognitive radio, secondary users are allowed to transmit when the primary is transmitting, but under tight interference constraints that protect the primary. However, these constraints limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which exploit spatial diversity with less hardware, help improve secondary system performance. We develop a novel and optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained multiple-input-single-output secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gain of the channel from the secondary transmit antenna to the primary receiver and from the secondary transmit antenna to the secondary receive antenna. We also propose a simpler, tractable variant of the optimal rule that performs as well as the optimal rule. We then analyze its SEP with L transmit antennas, and extensively benchmark it with several heuristic selection rules proposed in the literature. We also enhance these rules in order to provide a fair comparison, and derive new expressions for their SEPs. The results bring out new inter-relationships between the various rules, and show that the optimal rule can significantly reduce the SEP.

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Antenna selection in spatial modulation systems

Novel transmit antenna selection techniques are conceived for Spatial Modulation (SM) systems and their symbol error rate (SER) performance is investigated. Specifically, low-complexity Euclidean Distance optimized Antenna Selection (EDAS) and Capacity Optimized Antenna Selection (COAS) are studied. It is observed that the COAS scheme gives a better SER performance than the EDAS scheme. We show that the proposed antenna selection based SM systems are capable of attaining a significant gain in signal-to-noise ratio (SNR) compared to conventional SM systems, and also outperform the conventional MIMO systems employing antenna selection at both low and medium SNRs.

Language models for online handwritten Tamil word recognition

N-gram language models and lexicon-based word-recognition are popular methods in the literature to improve recognition accuracies of online and offline handwritten data. However, there are very few works that deal with application of these techniques on online Tamil handwritten data. In this paper, we explore methods of developing symbol-level language models and a lexicon from a large Tamil text corpus and their application to improving symbol and word recognition accuracies. On a test database of around 2000 words, we find that bigram language models improve symbol (3%) and word recognition (8%) accuracies and while lexicon methods offer much greater improvements (30%) in terms of word recognition, there is a large dependency on choosing the right lexicon. For comparison to lexicon and language model based methods, we have also explored re-evaluation techniques which involve the use of expert classifiers to improve symbol and word recognition accuracies.

Performance analysis of adaptive physical layer network coding for wireless two-way relaying

The performance analysis of adaptive physical layer network-coded two-way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. The deep channel fade conditions which occur at the relay referred as the singular fade states fall in the following two classes: (i) removable and (ii) non-removable singular fade states. With every singular fade state, we associate an error probability that the relay transmits a wrong network-coded symbol during the BC phase. It is shown that adaptive network coding provides a coding gain over fixed network coding, by making the error probabilities associated with the removable singular fade states contributing to the average Symbol Error Rate (SER) fall as SNR-2 instead of SNR-1. A high SNR upper-bound on the average end-to-end SER for the adaptive network coding scheme is derived, for a Rician fading scenario, which is found to be tight through simulations. Specifically, it is shown that for the adaptive network coding scheme, the probability that the relay node transmits a wrong network-coded symbol is upper-bounded by twice the average SER of a point-to-point fading channel, at high SNR. Also, it is shown that in a Rician fading scenario, it suffices to remove the effect of only those singular fade states which contribute dominantly to the average SER.

Channel training signal design for reciprocal multiple antenna systems with beamforming

Fast and efficient channel estimation is key to achieving high data rate performance in mobile and vehicular communication systems, where the channel is fast time-varying. To this end, this work proposes and optimizes channel-dependent training schemes for reciprocal Multiple-Input Multiple-Output (MIMO) channels with beamforming (BF) at the transmitter and receiver. First, assuming that Channel State Information (CSI) is available at the receiver, a channel-dependent Reverse Channel Training (RCT) signal is proposed that enables efficient estimation of the BF vector at the transmitter with a minimum training duration of only one symbol. In contrast, conventional orthogonal training requires a minimum training duration equal to the number of receive antennas. A tight approximation to the capacity lower bound on the system is derived, which is used as a performance metric to optimize the parameters of the RCT. Next, assuming that CSI is available at the transmitter, a channel-dependent forward-link training signal is proposed and its power and duration are optimized with respect to an approximate capacity lower bound. Monte Carlo simulations illustrate the significant performance improvement offered by the proposed channel-dependent training schemes over the existing channel-agnostic orthogonal training schemes.

SEP-optimal adaptive gain and transmit power amplify-and-forward relaying

Amplify-and-forward (AF) relay based cooperation has been investigated in the literature given its simplicity and practicality. Two models for AF, namely, fixed gain and fixed power relaying, have been extensively studied. In fixed gain relaying, the relay gain is fixed but its transmit power varies as a function of the source-relay (SR) channel gain. In fixed power relaying, the relay's instantaneous transmit power is fixed, but its gain varies. We propose a general AF cooperation model in which an average transmit power constrained relay jointly adapts its gain and transmit power as a function of the channel gains. We derive the optimal AF gain policy that minimizes the fading- averaged symbol error probability (SEP) of MPSK and present insightful and tractable lower and upper bounds for it. We then analyze the SEP of the optimal policy. Our results show that the optimal scheme is up to 39.7% and 47.5% more energy-efficient than fixed power relaying and fixed gain relaying, respectively. Further, the weaker the direct source-destination link, the greater are the energy-efficiency gains.

Accurate performance analysis of single and opportunistic AF relay cooperation with imperfect cascaded channel estimates

Given the significant gains that relay-based cooperation promises, the practical problems of acquisition of channel state information (CSI) and the characterization and optimization of performance with imperfect CSI are receiving increasing attention. We develop novel and accurate expressions for the symbol error probability (SEP) for fixed-gain amplify-and-forward relaying when the destination acquires CSI using the time-efficient cascaded channel estimation (CCE) protocol. The CCE protocol saves time by making the destination directly estimate the product of the source-relay and relay-destination channel gains. For a single relay system, we first develop a novel SEP expression and a tight SEP upper bound. We then similarly analyze an opportunistic multi-relay system, in which both selection and coherent demodulation use imperfect estimates. A distinctive aspect of our approach is the use of as few simplifying approximations as possible, which results in new results that are accurate at signal-to-noise-ratios as low as 1 dB for single and multi-relay systems. Using insights gleaned from an asymptotic analysis, we also present a simple, closed-form, nearly-optimal solution for allocation of energy between pilot and data symbols at the source and relay(s).