arXiv subjects

Luc Vandendorpe

Publications and source records attributed to Luc Vandendorpe.

At least 73 records · Page 4Linked to original sources

arXiv2015

Energy Efficient Precoder Design for MIMO-OFDM with Rate-dependent Circuit Power

This paper studies an energy efficient design of precoders for point-to-point multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. Differently from traditional approaches, the optimal power allocation strategy is studied by modelling the circuit power as a rate-dependent function. We show that if the circuit power is a constant plus an increasing and convex function of the transmission rate, the problem of minimizing the consumed energy per bit received can be reformulated as a convex fractional program and solved by means of a bisection algorithm. The impact of the some system parameters is investigated either analytically or by means of computational results.

cs.IT↗

arXiv2014

Compute-and-Forward on a Multi-User Multi-Relay Channel

In this paper, we consider a system in which multiple users communicate with a destination with the help of multiple half-duplex relays. Based on the compute-and-forward scheme, each relay, instead of decoding the users' messages, decodes an integer-valued linear combination that relates the transmitted messages. Then, it forwards the linear combination towards the destination. Given these linear combinations, the destination may or may not recover the transmitted messages since the linear combinations are not always full rank. Therefore, we propose an algorithm where we optimize the precoding factor at the users such that the probability that the equations are full rank is increased and that the transmission rate is maximized. We show, through some numerical examples, the effectiveness of our algorithm and the advantage of performing precoding allocation at the users. Also, we show that this scheme can outperform standard relaying techniques in certain regimes.

cs.IT↗

arXiv2014

Wideband Sensing and Optimization for Cognitive Radio Networks with Noise Variance Uncertainty

This paper considers wide-band spectrum sensing and optimization for cognitive radio (CR) networks with noise variance uncertainty. It is assumed that the considered wide-band contains one or more white sub-bands. Under this assumption, we consider throughput maximization of the CR network while appropriately protecting the primary network. We address this problem as follows. First, we propose novel ratio based test statistics for detecting the edges of each sub-band. Second, we employ simple energy comparison approach to choose one reference white sub-band. Third, we propose novel generalized energy detector (GED) for examining each of the remaining sub-bands by exploiting the noise information of the reference white sub-band. Finally, we optimize the sensing time ($T_o$) to maximize the CR network throughput using the detection and false alarm probabilities of the GED. The proposed GED does not suffer from signal to noise ratio (SNR) wall and outperforms the existing signal detectors. Moreover, the relationship between the proposed GED and conventional energy detector (CED) is quantified analytically. We show that the optimal $T_o$ depends on the noise variance information. In particular, with $10$TV bands, SNR=$-20$dB and $2$s frame duration, we found that the optimal $T_o$ is $28.5$ms ($50.6$ms) with perfect (imperfect) noise variance scenario.

stat.AP↗

arXiv2014

Joint Estimation of the Time Delay and the Clock Drift and Offset Using UWB signals

We consider two transceivers, the first with perfect clock and the second with imperfect clock. We investigate the joint estimation of the delay between the transceivers and the offset and the drift of the imperfect clock. We propose a protocol for the synchronization of the clocks. We derive some empirical estimators for the delay, the offset and the drift, and compute the Cramer-Rao lower bounds and the joint maximum likelihood estimator of the delay and the drift. We study the impact of the protocol parameters and the time-of-arrival estimation variance on the achieved performances. We validate some theoretical results by simulation.

stat.AP↗

arXiv2014

Statistics of the MLE and Approximate Upper and Lower Bounds - Part 1: Application to TOA Estimation

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared-error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accurateness of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation.

stat.AP↗

arXiv2014

Statistics of the MLE and Approximate Upper and Lower Bounds - Part 2: Threshold Computation and Optimal Signal Design

Threshold and ambiguity phenomena are studied in Part 1 of this work where approximations for the mean-squared-error (MSE) of the maximum likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate upper and lower bounds are derived. In this part we consider time-of-arrival estimation and we employ the MIE to derive closed-form expressions of the begin-ambiguity, end-ambiguity and asymptotic signal-to-noise ratio (SNR) thresholds with respect to some features of the transmitted signal. Both baseband and passband pulses are considered. We prove that the begin-ambiguity threshold depends only on the shape of the envelope of the ACR, whereas the end-ambiguity and asymptotic thresholds only on the shape of the ACR. We exploit the results on the begin-ambiguity and asymptotic thresholds to optimize, with respect to the available SNR, the pulse that achieves the minimum attainable MSE. The results of this paper are valid for various estimation problems.

stat.AP↗

arXiv2014

Sensing Throughput Tradeoff for Cognitive Radio Networks with Noise Variance Uncertainty

This paper proposes novel spectrum sensing algorithm, and examines the sensing throughput tradeoff for cognitive radio (CR) networks under noise variance uncertainty. It is assumed that there are one white sub-band, and one target sub-band which is either white or non-white. Under this assumption, first we propose a novel generalized energy detector (GED) for examining the target sub-band by exploiting the noise information of the white sub-band, then, we study the tradeoff between the sensing time and achievable throughput of the CR network. To study this tradeoff, we consider the sensing time optimization for maximizing the throughput of the CR network while appropriately protecting the primary network. The sensing time is optimized by utilizing the derived detection and false alarm probabilities of the GED. The proposed GED does not suffer from signal to noise ratio (SNR) wall (i.e., robust against noise variance uncertainty) and outperforms the existing signal detectors. Moreover, the relationship between the proposed GED and conventional energy detector (CED) is quantified analytically. We show that the optimal sensing times with perfect and imperfect noise variances are not the same. In particular, when the frame duration is 2s, and SNR is -20dB, and each of the bandwidths of the white and target sub-bands is 6MHz, the optimal sensing times are 28.5ms and 50.6ms with perfect and imperfect noise variances, respectively.

stat.AP↗

arXiv2014

USRP Implementation of Max-Min SNR Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks

This paper presents the Universal Software Radio Peripheral (USRP) experimental results of the Max-Min signal to noise ratio (SNR) Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks which is recently proposed in \cite{BogaMaxMinSNRJournal2013}. Extensive experiments are performed for different set of parameters. In particular, the effects of SNR, number of samples and roll-off factor on the detection performances of the latter algorithms are examined briefly. We have observed that the experimental results fit well with those of the theory. We also confirm that these algorithms are indeed robust against carrier frequency offset, symbol timing offset and noise variance uncertainty.

stat.AP↗

arXiv2013

Max-Min SNR Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks with Noise Variance Uncertainty

This paper proposes novel spectrum sensing algorithms for cognitive radio networks. By assuming known transmitter pulse shaping filter, synchronous and asynchronous receiver scenarios have been considered. For each of these scenarios, the proposed algorithm is explained as follows: First, by introducing a combiner vector, an over-sampled signal of total duration equal to the symbol period is combined linearly. Second, for this combined signal, the Signal-to-Noise ratio (SNR) maximization and minimization problems are formulated as Rayleigh quotient optimization problems. Third, by using the solutions of these problems, the ratio of the signal energy corresponding to the maximum and minimum SNRs are proposed as a test statistics. For this test statistics, analytical probability of false alarm ($P_f$) and detection ($P_d$) expressions are derived for additive white Gaussian noise (AWGN) channel. The proposed algorithms are robust against noise variance uncertainty. The generalization of the proposed algorithms for unknown transmitter pulse shaping filter has also been discussed. Simulation results demonstrate that the proposed algorithms achieve better $P_d$ than that of the Eigenvalue decomposition and energy detection algorithms in AWGN and Rayleigh fading channels with noise variance uncertainty. The proposed algorithms also guarantee the desired $P_f(P_d)$ in the presence of adjacent channel interference signals.

math.OC↗

arXiv2013

Linear Transceiver design for Downlink Multiuser MIMO Systems: Downlink-Interference Duality Approach

This paper considers linear transceiver design for downlink multiuser multiple-input multiple-output (MIMO) systems. We examine different transceiver design problems. We focus on two groups of design problems. The first group is the weighted sum mean-square-error (WSMSE) (i.e., symbol-wise or user-wise WSMSE) minimization problems and the second group is the minimization of the maximum weighted mean-squareerror (WMSE) (symbol-wise or user-wise WMSE) problems. The problems are examined for the practically relevant scenario where the power constraint is a combination of per base station (BS) antenna and per symbol (user), and the noise vector of each mobile station is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel downlink-interference duality based iterative solution. Each of these problems is solved as follows. First, we establish a new mean-square-error (MSE) downlink-interference duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. For the first group of problems, we have established symbol-wise and user-wise WSMSE downlink-interference duality.

math.OC↗

arXiv2013

Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems with Arbitrary Power Constraint: Generalized Duality Approach

This paper considers linear minimum meansquare- error (MMSE) transceiver design problems for downlink multiuser multiple-input multiple-output (MIMO) systems where imperfect channel state information is available at the base station (BS) and mobile stations (MSs). We examine robust sum mean-square-error (MSE) minimization problems. The problems are examined for the generalized scenario where the power constraint is per BS, per BS antenna, per user or per symbol, and the noise vector of each MS is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel duality based iterative solution. Each of these problems is solved as follows. First, we establish a novel sum average meansquare- error (AMSE) duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. To solve robust sum MSE minimization constrained with per BS antenna and per BS power problems, we have established novel downlink-uplink duality. On the other hand, to solve robust sum MSE minimization constrained with per user and per symbol power problems, we have established novel downlink-interference duality. For the total BS power constrained robust sum MSE minimization problem, the current duality is established by modifying the constraint function of the dual uplink channel problem. And, for the robust sum MSE minimization with per BS antenna and per user (symbol) power constraint problems, our duality are established by formulating the noise covariance matrices of the uplink and interference channels as fixed point functions, respectively.

math.OC↗

arXiv2013

Robust Transceiver Optimization for Downlink Coordinated Base Station Systems: Distributed Algorithm

This paper considers the joint transceiver design for downlink multiuser multiple-input single-output (MISO) systems with coordinated base stations (BSs) where imperfect channel state information (CSI) is available at the BSs and mobile stations (MSs). By incorporating antenna correlation at the BSs and taking channel estimation errors into account, we solve two robust design problems: 1) minimizing the weighted sum of meansquare- error (MSE) with per BS antenna power constraint, and 2) minimizing the total power of all BSs with per user MSE target and per BS antenna power constraints. These problems are solved as follows. First, for fixed receivers, we propose centralized and novel computationally efficient distributed algorithms to jointly optimize the precoders of all users. Our centralized algorithms employ the second-order-cone programming (SOCP) approach, whereas, our novel distributed algorithms use the Lagrangian dual decomposition, modified matrix fractional minimization and an iterative method. Second, for fixed BS precoders, the receivers are updated by the minimum mean-square-error (MMSE) criterion. These two steps are repeated until convergence is achieved. In all of our simulation results, we have observed that the proposed distributed algorithms achieve the same performance as that of the centralized algorithms. Moreover, computer simulations verify the robustness of the proposed robust designs compared to the non-robust/naive designs.

math.OC↗

arXiv2013

Robust Transceiver Optimization for Downlink Multiuser MIMO Systems

This paper addresses the joint transceiver design for downlink multiuser multiple-input multiple-output (MIMO) systems, with imperfect channel state information (CSI) at the base station (BS) and mobile stations (MSs). By incorporating antenna correlation at both ends of the channel and taking channel estimation errors into account, we solve two robust design problems: minimization of the weighted sum mean-square-error (MSE) and minimization of the maximum weighted MSE. These problems are solved as follows: first, we establish three kinds of MSE uplink-downlink duality by transforming only the power allocation matrices from uplink channel to downlink channel and vice versa. Second, in the uplink channel, we formulate the power allocation part of each problem ensuring global optimality. Finally, based on the solution of the uplink power allocation and the MSE duality results, for each problem, we propose an iterative algorithm that performs optimization alternatively between the uplink and downlink channels. Computer simulations verify the robustness of the proposed design compared to the non-robust/naive design.

math.OC↗

arXiv2013

Weighted Sum Rate Optimization for Downlink Multiuser MIMO Systems with per Antenna Power Constraint: Downlink-Uplink Duality Approach

This paper considers weighted sum rate maximization constrained with a per base station (BS) antenna power problem for multiuser multiple-input multiple-output (MIMO) systems. For this problem, we propose new downlink-uplink duality based solution. We solve the problem as follows. First, by introducing additional optimization variables, we reformulate our problem into an equivalent problem that incorporates a weighted sum mean-square-error (MSE) term. Second, we establish novel weighted sum MSE duality. The duality is established by modifying the input covariance matrix of the dual uplink problem, and formulating the noise covariance matrix of the uplink channel as a fixed point function. Third, we optimize the introduced variables and powers in the downlink channel by a Geometric Program (GP) method. Fourth, using the duality result and the solution of GP, we apply alternating optimization technique to solve the original downlink problem. In our simulation results, we have observed that the proposed duality based solution utilizes less power than that of existing algorithms.

math.OC↗

arXiv2013

Sum Rate Optimization for Coordinated Multi-Antenna Base Station Systems

This paper considers the joint precoder design problem for multiple-input single-output (MISO) systems with coordinated base stations (BSs). We consider maximization of the total sum rate with per BS antenna power constraint problem. For this problem, we propose a novel linear iterative algorithm. The problem is solved as follows. First, by introducing additional optimization variables and applying matrix fractional minimization, we reformulate the original problem as a new problem. Second, for the given precoder vectors of all users, we optimize the introduced variables of the latter problem using Geometric Programming (GP) method. Third, keeping the introduced variables constant, the precoder vectors of all users are optimized by using phase rotation technique. The second and third steps are repeated until convergence. We have shown that the proposed algorithm is guaranteed to converge. Moreover, for the total sum power constraint case, simulation results show that the proposed iterative algorithm achieves almost the same average performance as that of the algorithm which utilizes mean-square-error (MSE) uplink-downlink duality approach. We also show that our iterative algorithm can be used to solve sum rate maximization and weighted sum MSE minimization problems for an arbitrary power constraint.

math.OC↗

arXiv2013

Multi-cycle Cyclostationary based Spectrum Sensing Algorithm for OFDM Signals with Noise Uncertainty in Cognitive Radio Networks

This paper proposes a simple multi-cycle cyclostationary based signal detection (spectrum sensing) algorithm for Orthogonal Frequency Division Multiplexed (OFDM) signals in cognitive radio networks. We assume that the noise samples are independent and identically distributed (i.i.d) random variables all with unknown (imperfect) variance. Our detection algorithm employ the following three steps. First, we formulate the test statistics as a ratio of two quadratic cyclic autocorrelation functions. Second, we derive a closed form expression for the false alarm probability. Third, we evaluate the detection probability of our algorithm for a given false alarm probability. The theoretical probability of false alarm expression matches with that of the simulation result. Moreover, we have observed that the proposed multi-cycle algorithm exhibits significantly superior probability of detection compared to the existing low complexity cyclostationary based and the well known energy detection algorithms.

stat.AP↗

arXiv2013

Moment based Spectrum Sensing Algorithm for Cognitive Radio Networks with Noise Variance Uncertainty

This paper proposes simple moment based spectrum sensing algorithm for cognitive radio networks in a flat fading channel. It is assumed that the transmitted signal samples are binary (quadrature) phase-shift keying BPSK (QPSK), Mary quadrature amplitude modulation (QAM) or continuous uniformly distributed random variables and the noise samples are independent and identically distributed circularly symmetric complex Gaussian random variables all with unknown (imperfect) variance. Under these assumptions, we propose a simple test statistics employing a ratio of fourth and second moments. For this statistics, we provide analytical expressions for both probability of false alarm (Pf) and probability of detection (Pd) in an additive white Gaussian noise (AWGN) channel.We confirm the theoretical expressions by computer simulation. Furthermore, under noise variance uncertainty, simulation results demonstrate that the proposed moment based detector gives better detection performance compared to that of energy detector in AWGN and Rayleigh fading channels.

stat.AP↗

arXiv2013

On the Optimum Energy Efficiency for Flat-fading Channels with Rate-dependent Circuit Power

This paper investigates the optimum energy efficiency (EE) and the corresponding spectral efficiency (SE) for a communication link operating over a flat-fading channel. The EE is evaluated by the total energy consumption for transmitting per message bit. Three channel cases are considered, namely static channel with channel state information available at transmitter (CSIT), fast-varying (FV) channel with channel distribution information available at transmitter (CDIT), and FV channel with CSIT. A general circuit power model is considered. For all the three channel cases, the tradeoff between the EE and SE is studied. It is shown that the EE improves strictly as the SE increases from 0 to the optimum SE, and then strictly degrades as the SE increases beyond the optimum SE. The impact of κ, ρ and other system parameters on the optimum EE and corresponding SE is investigated to obtain insight.Some of the important and interesting results for all the channel cases include: (1) when κ increases the SE corresponding to the optimum EE should keep unchanged if ϕ(R) = R, but reduced if ϕ(R) is strictly convex of R; (2) when the rate-independent circuit power ρ increases, the SE corresponding to the optimum EE has to be increased. A polynomial-complexity algorithm is developed with the bisection method to find the optimum SE. The insight is corroborated and the optimum EE for the three cases are compared by simulation results.

cs.OH↗