High-rate analysis of channel-optimized vector quantization

High-rate analysis of channel-optimized vector quantizationThis paper considers the high-rate performance of channel optimized source coding for noisy discrete symmetric channels with random index assignment. Specifically, with mean squared error (MSE) as the performance metric, an upper bound on the asymptotic (i.e., high-rate) distortion is derived by assuming a general structure on the codebook. This structure enables extension of the analysis of the channel optimized source quantizer to one with a singular point density: for channels with small errors, the point density that minimizes the upper bound is continuous, while as the error rate increases, the point density becomes singular. The extent of the singularity is also characterized. The accuracy of the expressions obtained are verified through Monte Carlo simulations.

An Accurate Model for EESM and its Application to Analysis of CQI Feedback Schemes and Scheduling in LTE

The Effective Exponential SNR Mapping (EESM) is an indispensable tool for analyzing and simulating next generation orthogonal frequency division multiplexing (OFDM) based wireless systems. It converts the different gains of multiple subchannels, over which a codeword is transmitted, into a single effective flat-fading gain with the same codeword error rate. It facilitates link adaptation by helping each user to compute an accurate channel quality indicator (CQI), which is fed back to the base station to enable downlink rate adaptation and scheduling. However, the highly non-linear nature of EESM makes a performance analysis of adaptation and scheduling difficult; even the probability distribution of EESM is not known in closed-form. This paper shows that EESM can be accurately modeled as a lognormal random variable when the subchannel gains are Rayleigh distributed. The model is also valid when the subchannel gains are correlated in frequency or space. With some simplifying assumptions, the paper then develops a novel analysis of the performance of LTE's two CQI feedback schemes that use EESM to generate CQI. The comprehensive model and analysis quantify the joint effect of several critical components such as scheduler, multiple antenna mode, CQI feedback scheme, and EESM-based feedback averaging on the overall system throughput.

BER Analysis of Uplink OFDMA in the Presence of Carrier Frequency and Timing Offsets on Rician Fading Channels

In orthogonal frequency-division multiple access (OFDMA) on the uplink, the carrier frequency offsets (CFOs) and/or timing offsets (TOs) of other users with respect to a desired user can cause multiuser interference (MUI). Analytically evaluating the effect of these CFO/TO-induced MUI on the bit error rate (BER) performance is of interest. In this paper, we analyze the BER performance of uplink OFDMA in the presence of CFOs and TOs on Rician fading channels. A multicluster multipath channel model that is typical in indoor/ultrawideband and underwater acoustic channels is considered. Analytical BER expressions that quantify the degradation in BER due to the combined effect of both CFOs and TOs in uplink OFDMA with M-state quadrature amplitude modulation (QAM) are derived. Analytical and simulation BER results are shown to match very well. The derived BER expressions are shown to accurately quantify the performance degradation due to nonzero CFOs and TOs, which can serve as a useful tool in OFDMA system design.

Derating Based Hardware Optimizations in Soft Error Tolerant Designs

Ensuring reliable operation over an extended period of time is one of the biggest challenges facing present day electronic systems. The increased vulnerability of the components to atmospheric particle strikes poses a big threat in attaining the reliability required for various mission critical applications. Various soft error mitigation methodologies exist to address this reliability challenge. A general solution to this problem is to arrive at a soft error mitigation methodology with an acceptable implementation overhead and error tolerance level. This implementation overhead can then be reduced by taking advantage of various derating effects like logical derating, electrical derating and timing window derating, and/or making use of application redundancy, e. g. redundancy in firmware/software executing on the so designed robust hardware. In this paper, we analyze the impact of various derating factors and show how they can be profitably employed to reduce the hardware overhead to implement a given level of soft error robustness. This analysis is performed on a set of benchmark circuits using the delayed capture methodology. Experimental results show upto 23% reduction in the hardware overhead when considering individual and combined derating factors.

Design and analysis of a peer-to-peer based distributed clock synchronisation protocol for wireless sensor networks

Clock synchronisation is an important requirement for various applications in wireless sensor networks (WSNs). Most of the existing clock synchronisation protocols for WSNs use some hierarchical structure that introduces an extra overhead due to the dynamic nature of WSNs. Besides, it is difficult to integrate these clock synchronisation protocols with sleep scheduling scheme, which is a major technique to conserve energy. In this paper, we propose a fully distributed peer-to-peer based clock synchronisation protocol, named Distributed Clock Synchronisation Protocol (DCSP), using a novel technique of pullback for complete sensor networks. The pullback technique ensures that synchronisation phases of any pair of clocks always overlap. We have derived an exact expression for a bound on maximum synchronisation error in the DCSP protocol, and simulation study verifies that it is indeed less than the computed upper bound. Experimental study using a few TelosB motes also verifies that the pullback occurs as predicted.

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.

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.

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

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).

Analysis of Bandwidth-Unit-Vector-Distortion Tradeoff in PLL During Abnormal Grid Conditions

Phase-locked loops (PLLs) are necessary in applications which require grid synchronization. Presence of unbalance or harmonics in the grid voltage creates errors in the estimated frequency and angle of a PLL. The error in estimated angle has the effect of distorting the unit vectors generated by the PLL. In this paper, analytical expressions are derived which determine the error in the phase angle estimated by a PLL when there is unbalance and harmonics in the grid voltage. By using the derived expressions, the total harmonic distortion (THD) and the fundamental phase error of the unit vectors can be determined for a given PLL topology and a given level of unbalance and distortion in the grid voltage. The accuracy of the results obtained from the analytical expressions is validated with the simulation and experimental results for synchronous reference frame PLL (SRF-PLL). Based on these expressions, a new tuning method for the SRF-PLL is proposed which quantifies the tradeoff between the unit vector THD and the bandwidth of the SRF-PLL. Using this method, the exact value of the bandwidth of the SRF-PLL can be obtained for a given worst case grid voltage unbalance and distortion to have an acceptable level of unit vector THD. The tuning method for SRF-PLL is also validated experimentally.

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

The analysis of modulation schemes for the physical layer network-coded two way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. Depending on the signal set used at the end nodes, the minimum distance of the effective constellation seen at the relay becomes zero for a finite number of channel fade states referred as the singular fade states. The singular fade states fall into the following two classes: (i) the ones which are caused due to channel outage and whose harmful effect cannot be mitigated by adaptive network coding called the non-removable singular fade states and (ii) the ones which occur due to the choice of the signal set and whose harmful effects can be removed called the removable singular fade states. In this paper, we derive an upper bound on the average end-to-end Symbol Error Rate (SER), with and without adaptive network coding at the relay, for a Rician fading scenario. It is shown that without adaptive network coding, at high Signal to Noise Ratio (SNR), the contribution to the end-to-end SER comes from the following error events which fall as SNR-1: the error events associated with the removable and nonremovable singular fade states and the error event during the BC phase. In contrast, for the adaptive network coding scheme, the error events associated with the removable singular fade states fall as SNR-2, thereby providing a coding gain over the case when adaptive network coding is not used. Also, it is shown that for a Rician fading channel, the error during the MA phase dominates over the error during the BC phase. Hence, adaptive network coding, which improves the performance during the MA phase provides more gain in a Rician fading scenario than in a Rayleigh fading scenario. Furthermore, it is shown that for large Rician factors, among those removable singular fade states which have the same magnitude, those which have the least absolute value of the phase - ngle alone contribute dominantly to the end-to-end SER and it is sufficient to remove the effect of only such singular fade states.

End-to-End BER Analysis of Space Shift Keying in Decode-and-Forward Cooperative Relaying

Space shift keying (SSK) is a special case of spatial modulation (SM), which is a relatively new modulation technique that is getting recognized to be attractive in multi-antenna communications. Our new contribution in this paper is an analytical derivation of exact closed-form expression for the end-to-end bit error rate (BER) performance of SSK in decode-and-forward (1)1,) cooperative relaying. An incremental relaying (IR) scheme with selection combining (SC) at the destination is considered. In SSK, since the information is carried by the transmit antenna index, traditional selection combining methods based on instantaneous SNRs can not be directly used. To overcome this problem, we propose to do selection between direct and relayed paths based on the Euclidean distance between columns of the channel matrix. With this selection metric, an exact analytical expression for the end-to-end BER is derived in closed-form. Analytical results are shown to match with simulation results.

A POSTERIORI ERROR CONTROL OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC OBSTACLE PROBLEMS

In this article, we derive an a posteriori error estimator for various discontinuous Galerkin (DG) methods that are proposed in (Wang, Han and Cheng, SIAM J. Numer. Anal., 48: 708-733, 2010) for an elliptic obstacle problem. Using a key property of DG methods, we perform the analysis in a general framework. The error estimator we have obtained for DG methods is comparable with the estimator for the conforming Galerkin (CG) finite element method. In the analysis, we construct a non-linear smoothing function mapping DG finite element space to CG finite element space and use it as a key tool. The error estimator consists of a discrete Lagrange multiplier associated with the obstacle constraint. It is shown for non-over-penalized DG methods that the discrete Lagrange multiplier is uniformly stable on non-uniform meshes. Finally, numerical results demonstrating the performance of the error estimator are presented.

Analysis of modified microstrip line and its application

Analysis of a microstrip line with a symmetrically located aperture in its ground plane is reported in this paper. The solution is based on conformal mapping technique. Conformal mapping has been used to determine the characteristic impedance and effective permittivity of the line. The accuracy of results is within 5% error. An low pass filter has been designed based on the electrical parameters obtained using the proposed method.

BER Analysis of Space Shift Keying in Cooperative Multi-hop Multi-branch DF Relaying

Space shift keying (SSK) is an attractive modulation technique for multi-antenna communications. In SSK, only one among the available transmit antennas is activated during one channel use, and the index of the chosen transmit antenna conveys information. In this paper, we analyze the performance of SSK in multi-hop, multi-branch cooperative relaying systems. We consider the decode-and-forward relaying protocol, where a relay forwards the decoded symbol if it decodes the symbol correctly from the received signal. We derive closed-form expressions for the end-to-end bit error rate of SSK in this system. Analytical and simulation results match very well.