This paper addresses the energy-latency trade-off in distributed application offloading, in which an energy-limited handset offloads totally or partially an application to one or several virtual machines (VMs) located in remote locations or access points (APs) close to the mobile terminal (MT). One of the APs (the serving AP) provides radio access to the MT and is connected to the VMs through non-ideal backhaul (BH) links. In this setting, we optimize the offloading strategy (including the joint optimization of radio and computational resources) to minimize the energy consumption at the MT subject to a maximum latency constraint. In addition, we propose robust designs to cope with imperfect acquisition of the channel state information (CSI) and the BH parameters. Our findings show that, as far as the energy-latency trade-off is concerned, the optimal order of activation of the VMs does not depend on their processing capabilities but the delays of the BH links. However, once a VM is selected to participate in the processing, the optimal amount of processing allocated to such VM depends on its computational capabilities as well as on the features (capacity and delay) of the BH link. Additionally, offloading decisions become more conservative as the uncertainty in CSI and BH parameters increases.
Rubio, J.; Pascual Iserte, A.; Palomar, D.P.; Goldsmith, A. IEEE transactions on signal processing Vol. 65, num. 1, p. 212-227 DOI: 10.1109/TSP.2016.2614794 Data de publicació: 2017-01-01 Article en revista
We present an approach to solve the nonconvex optimization problem that arises when designing the transmit covariance matrices in multiuser multiple-input multiple-output (MIMO) broadcast networks implementing simultaneous wireless information and power transfer (SWIPT). The MIMO SWIPT problem is formulated as a general multiobjective optimization problem, in which data rates and harvested powers are optimized simultaneously. Two different approaches are applied to reformulate the (nonconvex) multiobjective problem. In the first approach, the transmitter can control the specific amount of power to be harvested by power transfer whereas in the second approach the transmitter can only control the proportion of power to be harvested among the different harvesting users. We solve the resulting formulations using the majorization-minimization (MM) approach. The solution obtained from the MM approach is compared to the classical block-diagonalization (BD) strategy, typically used to solve the nonconvex multiuser MIMO network by forcing no interference among users. Simulation results show that the proposed approach improves over the BD approach both the system sum rate and the power harvested by users. Additionally, the computational times needed for convergence of the proposed methods are much lower than the ones required for classical gradient-based approaches.
Sala, J.; Vázquez, G.; López, R.; Sedighi, S.; Taherpour, A. IEEE transactions on signal processing Vol. 64, num. 23, p. 6269-6283 DOI: 10.1109/TSP.2016.2601290 Data de publicació: 2016-12-01 Article en revista
We establish the generalized likelihood ratio (GLR)
test for a Gaussian signal of known power spectral shape and
unknown rank-one spatial signature in additive white Gaussian
noise with an unknown diagonal spatial correlation matrix. This
is motivated by spectrum sensing problems in dynamic spectrum
access, in which the temporal correlation of the primary signal
can be assumed known up to a scaling, and where the noise is
due to an uncalibrated receive array. For spatially independent
identically distributed (i.i.d.) noise, the corresponding GLR test
reduces to a scalar optimization problem, whereas the GLR detector
in the general non-i.i.d. case yields a more involved expression,
which can be computed via alternating optimization methods. Low
signal-to-noise ratio (SNR) approximations to the detectors are
given, together with an asymptotic analysis showing the influence
on detection performance of the signal power spectrum and SNR
distribution across antennas. Under spatial rank-P conditions, we
show that the rank-one GLR detectors are consistent with a statistical
criterion that maximizes the output energy of a beamformer
operating on filtered data. Simulation results support our theoretical
findings in that exploiting prior knowledge on the signal power
spectrum can result in significant performance improvement.
Perez, A.; Caus, M.; Rostom, Z.; Le Ruyet, Didier; Kofidis, E.; Haardt, M.; Mestre, X.; Cheng, Y. IEEE transactions on signal processing Vol. 64, num. 21, p. 5733-5762 DOI: 10.1109/TSP.2016.2580535 Data de publicació: 2016-11-01 Article en revista
Next-generation communication systems have to comply with very strict requirements for increased flexibility in heterogeneous environments, high spectral efficiency, and agility of carrier aggregation. This fact motivates research in advanced multicarrier modulation (MCM) schemes, such as filter bank-based multicarrier (FBMC) modulation. This paper focuses on the offset quadrature amplitude modulation (OQAM)-based FBMC variant, known as FBMC/OQAM, which presents outstanding spectral efficiency and confinement in a number of channels and applications. Its special nature, however, generates a number of new signal processing challenges that are not present in other MCM schemes, notably, in orthogonal-frequency-division multiplexing (OFDM). In multiple-input multiple-output (MIMO) architectures, which are expected to play a primary role in future communication systems, these challenges are intensified, creating new interesting research problems and calling for new ideas and methods that are adapted to the particularities of the MIMO-FBMC/OQAM system. The goal of this paper is to focus on these signal processing problems and provide a concise yet comprehensive overview of the recent advances in this area. Open problems and associated directions for future research are also discussed.
Recent results have shown the benefits of widely
linear precoding (WLP) in the MIMO interference channel
(MIMO IC) assuming that all transmitters can follow the same
strategy. Motivated by a transitional scenario where legacy linear
transmitters coexist with widely linear ones, this work investigates
the general K-user MIMO IC in a heterogeneous (linear and
widely linear) transmitter deployment. In particular, we address
the maximization of the weighted sum-rate (WSR) for (widely)
linear transmit filters design through the use of the complexvalued
formulation. Since the maximum WSR problem is nonconvex,
and thus difficult to be solved, we formulate an equivalent
minimum weighted mean square error problem that allows
deriving closed-form expressions for (widely) linear transceivers.
Then an iterative procedure is proposed, which is proven to reach
a stationary point of the maximum WSR problem. Simulations
show that the proposed procedure allows increasing the sumrate
as compared to coordinated linear transceiver schemes. The
gains are larger and significant in two different non-exclusive
conditions: as the interference level increases or when the number
of antennas is low.
We consider the problem of multiantenna spectrum sensing (SS) in cognitive radios (CRs) when the receivers are assumed to be uncalibrated across the antennas. The performance of the Hadamard Ratio Detector (HRD) is analyzed in such a scenario. Specifically, we first derive the exact distribution of the HRD statistic under the null hypothesis, which leads to an elaborate but closed-form expression for the false-alarm probability. Then, we derive a simpler and tight closed-form approximation for both the false-alarm and detection probabilities by using a moment-based approximation of the HRD statistical distribution under both hypotheses. Finally, the accuracy of the obtained results is verified by simulations.
López, R.; Villares, J.; Riba, J.; Gappmair, W.; Mosquera, C. IEEE transactions on signal processing Vol. 63, num. 7, p. 1675-1683 DOI: 10.1109/TSP.2015.2396013 Data de publicació: 2015-04-01 Article en revista
Most signal-to-noise ratio (SNR) estimators use the receiver matched filter output sampled at the symbol rate, an approach which does not preserve all information in the analog waveform due to aliasing. Thus, it is relevant to ask whether avoiding aliasing could improve SNR estimation. To this end, we compute the corresponding data-aided (DA) and non-data-aided (NDA) Cramer-Rao bounds (CRBs). We adopt a novel dual filter framework, which is shown to be information-preserving under suitable conditions and considerably simplifies the analysis. It is shown that the CRB can be substantially reduced by exploiting any available excess bandwidth, depending on the modulation scheme, the SNR range, and the estimator type (DA or NDA).
Conventional implementations of the linearminimum mean-square (LMMSE) and minimum variance distortionless response (MVDR) estimators rely on the sample matrix inversion (SMI) technique, i.e., on the sample covariance matrix (SCM). This approach is optimal in the large sample size regime. Nonetheless, in small sample size situations, those sample estimators suffer a large performance degradation. Thus, the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations. To this aim, a twofold approach is proposed. First, shrinkage estimators are considered, as they are known to be robust to the small sample size regime. Namely, the proposed methods are based on shrinking the sample LMMSE or sample MVDR filters towards a variously called matched filter or conventional (Bartlett) beamformer in array processing. Second, random matrix theory is used to obtain the optimal shrinkage factors for large filters. The simulation results highlight that the proposed methods outperform the sample LMMSE and MVDR. Also, provided that the sample size is higher than the observation dimension, they improve classical diagonal loading (DL) and Ledoit-Wolf (LW) techniques, which counteract the small sample size degradation by regularizing the SCM. Finally, compared to state-of-the-art DL, the proposed methods reduce the computational cost and the proposed shrinkage of the LMMSE obtains performance gains.
Atzeni, I.; Garcia, L.; Scutari, G.; Palomar, D.P.; R. Fonollosa, Javier IEEE transactions on signal processing Vol. 62, num. 9, p. 2397-2412 DOI: 10.1109/TSP.2014.2307835 Data de publicació: 2014-05-01 Article en revista
The envisioned smart grid aims at improving the interaction between the supply-and the demand-side of the electricity network, creating unprecedented possibilities for optimizing the energy usage at different levels of the grid. In this paper, we propose a distributed demand-side management (DSM) method intended for smart grid users with load prediction capabilities, who possibly employ dispatchable energy generation and storage devices. These users participate in the day-ahead market and are interested in deriving the bidding, production, and storage strategies that jointly minimize their expected monetary expense. The resulting day-ahead grid optimization is formulated as a generalized Nash equilibrium problem (GNEP), which includes global constraints that couple the users' strategies. Building on the theory of variational inequalities, we study the main properties of the GNEP and devise a distributed, iterative algorithm converging to the variational solutions of the GNEP. Additionally, users can exploit the reduced uncertainty about their energy consumption and renewable generation at the time of dispatch. We thus present a complementary DSM procedure that allows them to perform some unilateral adjustments on their generation and storage strategies so as to reduce the impact of their real-time deviations with respect to the amount of energy negotiated in the day-ahead. Finally, numerical results in realistic scenarios are reported to corroborate the proposed DSM technique.
Riba, J.; Font-Segura, J.; Villares, J.; Vazquez, G. IEEE transactions on signal processing Vol. 62, num. 8, p. 1899-1912 DOI: 10.1109/TSP.2014.2303433 Data de publicació: 2014-04-01 Article en revista
Cyclostationary processes exhibit a form of frequency diversity. Based on that, we show that a digital waveform with symbol period T can be asymptotically represented as a rank-1 frequency-domain vector process which exhibits uncorrelation at different frequencies inside the Nyquist spectral support of 1/T. By resorting to the fast Fourier transform (FFT), this formulation obviates the need of estimating a cumbersome covariance matrix to characterize the likelihood function. We then derive the generalized likelihood ratio test (GLRT) for the detection of a cyclostationary signal in unknown white noise without the need of a assuming a synchronized receiver. This provides a sound theoretical basis for the exploitation of the cyclostationary feature and highlights an explicit link with classical square timing recovery schemes, which appear implicitly in the core of the GLRT. Moreover, to avoid the well-known sensitivity of cyclostationary-based detection schemes to frequency-selective fading channels, a parametric channel model based on a lower bound on the coherence bandwidth is adopted and incorporated into the GLRT. By exploiting the rank-1 structure of small spectral covariance matrices, the obtained detector outperforms the classical spectral correlation magnitude detector.
This work shows the existence of sampling walls in detection of wideband signals from Bernoulli nonuniform sampling (BNS) in the presence of noise uncertainty. A sampling wall is defined as the sampling density below which the target error probabilities, i.e., the missed detection and false alarm probabilities, cannot be guaranteed at a given signal to noise ratio (SNR) regardless the number of acquired samples. The BNS is adopted because it exhibits good tradeoff properties between complexity and performance. It is shown that BNS suffers from noise enhancement, which translates into a whitening effect in the correlation of the legacy signal. Contrarily to the existing literature, the signal detection problem is addressed without having to reconstruct neither the signal nor its spectrum. More specifically, the optimal low SNR detector is formulated as a generalized likelihood ratio test (GLRT) to exploit the available side information of the problem, i.e., the noise variance, the sampling density and the legacy signal autocorrelation. By deriving the asymptotic performance of the GLRT in the presence of noise uncertainty, explicit expressions for sampling walls are obtained as a function of the legacy signal occupancy, the SNR and the noise uncertainty. Further, numerical results are provided to assess the behavior of the sampling walls and signal detection performance.
This paper addresses the joint design of MIMO precoding and decoding matrices for filter bank multicarrier (FBMC) systems based on OQAM, known as FBMC/OQAM. Existing solutions that support multi-stream transmission only give satisfactory performance in scenarios with high coherence bandwidth channels. To make progress towards the application of FBMC/OQAM to MIMO channels, we study the design of novel solutions that provide robustness against the channel frequency selectivity and support multi-stream transmission. To this end, two techniques have been devised under the criterion of minimizing the sum mean square error. The non-circular nature of the OQAM symbols has not been ignored, making evident the convenience of performing a widely linear processing. The first technique keeps the complexity at a reasonable level but in exchange the original problem is relaxed yielding a suboptimal solution. With the objective of performing closer to the optimum solution, the second option iteratively computes precoders and equalizers by resorting to an alternating optimization method, which is much more complex. We have demonstrated via simulations that the first technique nearly achieves the same results as the iterative design. Simulation results show that the proposed low-complexity solution outperforms existing MIMO-FBMC/OQAM schemes in terms of bit error rate. As for the comparison with OFDM, the numerical results highlight that FBMC/OQAM remains competitive, with and without perfect channel state information, while it provides spectral efficiency gains. Under highly frequency selective channels the proposed technique significantly outperforms OFDM.
Atzeni, I.; Garcia, L.; Scutari, G.; Palomar, D.P.; R. Fonollosa, Javier IEEE transactions on signal processing Vol. 61, num. 10, p. 2454-2472 DOI: 10.1109/TSP.2013.2248002 Data de publicació: 2013-05 Article en revista
The electric energy distribution infrastructure is undergoing a startling technological evolution with the development of the smart grid concept, which allows more interaction between the supply-and the demand-side of the network and results in a great optimization potential. In this paper, we focus on a smart grid in which the demand-side comprises traditional users as well as users owning some kind of distributed energy source and/or energy storage device. By means of a day-ahead demand-side management mechanism regulated through an independent central unit, the latter users are interested in reducing their monetary expense by producing or storing energy rather than just purchasing their energy needs from the grid. Using a general energy pricing model, we tackle the grid optimization design from two different perspectives: a user-oriented optimization and an holistic-based design. In the former case, we optimize each user individually by formulating the grid optimization problem as a noncooperative game, whose solution analysis is addressed building on the theory of variational inequalities. In the latter case, we focus instead on the joint optimization of the whole system, allowing some cooperation among the users. For both formulations, we devise distributed and iterative algorithms providing the optimal production/storage strategies of the users, along with their convergence properties. Among all, the proposed algorithms preserve the users' privacy and require very limited signaling with the central unit.
We explore decentralized coordination of sectored
cellular networks to adapt the usage of downlink resources to
the instantaneous network conditions. The transmission frame
consists of an orthogonal bandwidth usage phase, where sectors
perform FDMA and power control over an agreed frequency
chunk, and a shared bandwidth usage phase where each sector
performs FDMA over the full available bandwidth without power
control (interference is not controlled in this phase by any means).
Decentralized network utility maximization with global optimality
guarantee is enabled by fixing this structure of the transmission
frame, which does not cause significant network-wide losses. Thus,
the ability to better balance the resources gained from coordination
generates some slack that can be used to either i) provide
higher-quality access, ii) increase the number of active users, or
iii) reduce deployment and maintenance costs by operating larger
Signal-to-noise ratio (SNR) estimators of linear modulation schemes usually operate at one sample per symbol at the matched filter output. In this paper we propose a new method
for estimating the SNR in the complex additive white Gaussian
noise (AWGN) channel that operates directly on the oversampled cyclostationary signal at the matched filter input. Exploiting cyclostationarity proves to be advantageous due to the fact that a signal-free Euclidean noise subspace can be identified such that only second order moments of the received waveform need to be computed. The proposed method is nondata-aided (NDA), as well as constellation and phase independent, and only requires prior timing synchronization to fully exploit the cyclostationarity property.
The estimator can also be applied to nonconstant modulus
constellations without requiring any tuning, which is a feature not found in existing approaches. Implementation aspects and simpler suboptimal solutions are also provided.
Distributed consensus algorithms for estimation of parameters or detection of events in wireless sensor networks have attracted considerable attention in recent years. A necessary condition to achieve a consensus on the average of the initial
values is that the topology of the underlying graph is balanced or symmetric at every time instant. However, communication
impairments can make the topology vary randomly in time, and instantaneous link symmetry between pairs of nodes is not
guaranteed unless an acknowledgment protocol or an equivalent approach is implemented. In this paper, we evaluate the convergence of the consensus algorithm in the mean square sense in wireless sensor networks with random asymmetric topologies. For the case of links with equal probability of connection, a closed form expression for the mean square error of the state along with
the dynamical range and the optimum value of the link weights that guarantee convergence are derived. For the case of links with
different probabilities of connection, an upper bound for the mean square error of the state is derived. This upper bound can be
computed for any time instant and can be employed to compute a link weight that reduces the convergence time of the algorithm.
Malinowski, S.; Artigas, J.; Guillemot, C.; Torres, L. IEEE transactions on signal processing Vol. 57, num. 10, p. 4154-4158 DOI: 10.1109/TSP.2009.2023359 Data de publicació: 2009-10-01 Article en revista
This correspondence considers the use of punctured
quasi-arithmetic (QA) codes for the Slepian–Wolf problem. These
entropy codes are defined by finite state machines for memoryless and
first-order memory sources. Puncturing an entropy coded bit-stream leads
to an ambiguity at the decoder side. The decoder makes use of a correlated
version of the original message in order to remove this ambiguity. A
complete distributed source coding (DSC) scheme based on QA encoding
with side information at the decoder is presented, together with iterative
structures based on QA codes. The proposed schemes are adapted to
memoryless and first-order memory sources. Simulation results reveal
that the proposed schemes are efficient in terms of decoding performance
for short sequences compared to well-known DSC solutions using channel
Emerging cellular networks are likely to handle users with heterogeneous quality of service requirements attending to the nature of their underlying service application, the quality of their wireless equipment, or even their contract terms. While sharing the same physical resources (power, bandwidth, transmission time), the utility they get from using them may be very different and arbitrage is needed to optimize the global operation of the network. In this respect, resource allocation strategies maximizing network utility under practical constraints are investigated in this paper. In particular, we focus on a cellular network with half-duplex, MIMO terminals and relaying infrastructure in the form of fixed and dedicated relay stations. Whereas orthogonal-frequency-division multiple access is assumed, it is seen as a frequency diversity enabler since path loss is the only channel state information (CSI) known at the transmitters, which is refreshed periodically. With this setup, the performance of a state-of-the art relay-assisted transmission protocol is characterized in terms of the ergodic achievable rates, for which novel concave lower bounds are developed. The use of these bounds allows us to derive two efficient algorithms computing resource allocations in polynomial time, which address the optimization of the uplink and downlink directions jointly. First, a global optimization algorithm providing one Pareto optimal solution maximizing network utility during the validity period of one CSI is studied, which acts as a performance upper bound. Second, a sequential optimization algorithm maximizing network utility frame by frame is considered as a simpler alternative. The performance of both schemes has been compared in practical scenarios, giving special attention to the performance-complexity and throughput-fairness tradeoffs.
Ordonez, L.; Palomar, D.P.; Pages, A.; R. Fonollosa, Javier; Garcia, L. IEEE transactions on signal processing Vol. 57, num. 6, p. 2336-2353 DOI: 10.1109/TSP.2009.2016253 Data de publicació: 2009-06 Article en revista
MIMO systems with perfect channel state information at both sides of the link can adapt to the instantaneous channel conditions to optimize the spectral efficiency and/or the reliability of the communication. A low-complexity approach is the use of linear MIMO transceivers which are composed of a linear precoder at the transmitter and a linear equalizer at the receiver. The design of linear transceivers has been extensively studied in the literature with a variety of cost functions. In this paper, we focus on the minimum BER design, and show that the common practice of fixing a priori the number of data symbols to be transmitted per channel use inherently limits the diversity gain of the system. By introducing the number of symbols in the optimization process, we propose a minimum BER linear precoding scheme that achieves the full diversity of the MIMO channel. For the cases of uncorrelated/semicorrelated Rayleigh and uncorrelated Rician fading, the average BER performance of both schemes is analytically analyzed and characterized in terms of two key parameters: the array gain and the diversity gain.
Ventosa, S.; Simon, C.; Schimmel, M.; Dañobeita, J.; Manuel, A. IEEE transactions on signal processing Vol. 56, num. 7, p. 2771-2780 DOI: 10.1109/TSP.2008.917029 Data de publicació: 2008-07 Article en revista
Simon, C.; Ventosa, S.; Schimmel, M.; Heldring, A.; Dañobeita, J.; Gallart, J.; Manuel, A. IEEE transactions on signal processing Vol. 55, num. 10, p. 4928-4937 Data de publicació: 2007-10 Article en revista
This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimation methods in the context of digital communications. The low- and high-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator - derived assuming Gaussian transmitted symbols - is compared with the performance of the optimal second-order estimator, which exploits the actual distribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimal second-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitude modulation (QAM) or amplitude-phase-shift keying (APSK). On the other hand, the Gaussian assumption can yield important losses at high SNR if the transmitted symbols are drawn from a constant modulus constellation such as phase-shift keying (PSK) or continuous-phase modulations (CPM). These conclusions are illustrated for the problem of direction-of-arrival (DOA) estimation of multiple digitally-modulated signals.
This paper considers a wireless communication
system with multiple transmit and receive antennas, i.e., a multiple-input-multiple-output (MIMO) channel. The objective is to design the transmitter according to an imperfect channel estimate, where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy. The robust transmission scheme is composed of an orthogonal space–time block code (OSTBC), whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them. At the receiver, the signal is detected assuming a perfect channel knowledge. The optimization problem corresponding to the design of the power allocation among the estimated eigenmodes, whose goal is the maximization of the signal-to-noise ratio (SNR), is transformed to a simple convex problem that can be easily solved. Different sources of errors are considered in the channel estimate, such as the Gaussian noise from the estimation process and the errors from the quantization of the channel estimate, among others. For the case of Gaussian noise, the robust power allocation admits a closed-form expression.
Finally, the benefits of the proposed design are evaluated and compared with the pure OSTBC and nonrobust approaches.
This paper provides a systematic approach to the
problem of nondata aided symbol-timing estimation for linear
modulations. The study is performed under the unconditional
maximum likelihood framework where the carrier-frequency
error is included as a nuisance parameter in the mathematical
derivation. The second-order moments of the received signal are
found to be the sufficient statistics for the problem at hand and they
allow the provision of a robust performance in the presence of a
carrier-frequency error uncertainty. We particularly focus on the
exploitation of the cyclostationary property of linear modulations.
This enables us to derive simple and closed-form symbol-timing
estimators which are found to be based on the well-known square
timing recovery method by Oerder and Meyr. Finally, we generalize
the OM method to the case of linear modulations with
offset formats. In this case, the square-law nonlinearity is found
to provide not only the symbol-timing but also the carrier-phase
This work provides a general framework for the design of second-order blind estimators without adopting any approximation about the observation statistics or the a priori distribution of the parameters. The proposed solution is obtained minimizing the estimator variance subject to some constraints on the estimator bias. The resulting optimal estimator is found to depend on the observation fourth-order moments that can be calculated analytically from the known signal model. Unfortunately, in most cases, the performance of this estimator is severely limited by the residual bias inherent to nonlinear estimation problems. To overcome this limitation, the second-order minimum variance unbiased estimator is deduced from the general solution by assuming accurate prior information on the vector of parameters. This small-error approximation is adopted to design iterative estimators or trackers. It is shown that the associated variance constitutes the lower bound for the variance of any unbiased estimator based on the sample covariance matrix. The paper formulation is then applied to track the angle-of-arrival (AoA) of multiple digitally-modulated sources by means of a uniform linear array. The optimal second-order tracker is compared with the classical maximum likelihood (ML) blind methods that are shown to be quadratic in the observed data as well. Simulations have confirmed that the discrete nature of the transmitted symbols can be exploited to improve considerably the discrimination of near sources in medium-to-high SNR scenarios.
This work provides a general framework for the design of second-order blind estimators without adopting any
approximation about the observation statistics or the a priori
distribution of the parameters. The proposed solution is obtained
minimizing the estimator variance subject to some constraints on
the estimator bias. The resulting optimal estimator is found to
depend on the observation fourth-order moments that can be calculated
analytically from the known signal model. Unfortunately,
in most cases, the performance of this estimator is severely limited
by the residual bias inherent to nonlinear estimation problems.
To overcome this limitation, the second-order minimum variance
unbiased estimator is deduced from the general solution by assuming
accurate prior information on the vector of parameters.
This small-error approximation is adopted to design iterative
estimators or trackers. It is shown that the associated variance
constitutes the lower bound for the variance of any unbiased
estimator based on the sample covariance matrix.
The paper formulation is then applied to track the angle-of-arrival
(AoA) of multiple digitally-modulated sources by means of
a uniform linear array. The optimal second-order tracker is compared
with the classical maximum likelihood (ML) blind methods
that are shown to be quadratic in the observed data as well. Simulations
have confirmed that the discrete nature of the transmitted
symbols can be exploited to improve considerably the discrimination
of near sources in medium-to-high SNR scenarios.
Many engineering problems that can be formulated
as constrained optimization problems result in solutions
given by a waterfilling structure; the classical example is the
capacity-achieving solution for a frequency-selective channel.
For simple waterfilling solutions with a single waterlevel and a
single constraint (typically, a power constraint), some algorithms
have been proposed in the literature to compute the solutions
numerically. However, some other optimization problems result in
significantly more complicated waterfilling solutions that include
multiple waterlevels and multiple constraints. For such cases, it
may still be possible to obtain practical algorithms to evaluate the
solutions numerically but only after a painstaking inspection of
the specific waterfilling structure. In addition, a unified view of
the different types of waterfilling solutions and the corresponding
practical algorithms is missing.
The purpose of this paper is twofold. On the one hand, it
overviews the waterfilling results existing in the literature from a
unified viewpoint. On the other hand, it bridges the gap between
a wide family of waterfilling solutions and their efficient implementation
in practice; to be more precise, it provides a practical
algorithm to evaluate numerically a general waterfilling solution,
which includes the currently existing waterfilling solutions and
others that may possibly appear in future problems.
This paper proposes a spatial filtering technique for
the reception of pilot-aided multirate multicode direct-sequence
code division multiple access (DS/CDMA) systems such as wideband
CDMA (WCDMA). These systems introduce a code-multiplexed
pilot sequence that can be used for the estimation of the
filter weights, but the presence of the traffic signal (transmitted
at the same time as the pilot sequence) corrupts that estimation
and degrades the performance of the filter significantly. This is
caused by the fact that although the traffic and pilot signals are
usually designed to be orthogonal, the frequency selectivity of the
channel degrades this orthogonality at hte receiving end. Here,
we propose a semi-blind technique that eliminates the self-noise
caused by the code-multiplexing of the pilot. We derive analytically
the asymptotic performance of both the training-only and
the semi-blind techniques and compare them with the actual simulated
performance. It is shown, both analytically and via simulation,
that high gains can be achieved with respect to training-onlybased