Josep Sala-Alvarez

Statistical reference criteria for adaptive signal processing in digital communications

A general criterion for the design of adaptive systems in digital communications called the statistical reference criterion is proposed. The criterion is based on imposition of the probability density function of the signal of interest at the output of the adaptive system, with its application to the scenario of highly powerful interferers being the main focus of this paper. The knowledge of the PDF of the wanted signal is used as a discriminator between signals so that interferers with differing distributions are rejected by the algorithm. Its performance is studied over a range of scenarios. Equations for gradient-based coefficient updates are derived, and the relationship with other existing algorithms like the minimum variance and the Wiener criterion are examined.

Multiantenna GLR Detection of Rank-One Signals With Known Power Spectrum in White Noise With Unknown Spatial Correlation

Multiple-antenna detection of a Gaussian signal with spatial rank one in temporally white Gaussian noise with arbitrary and unknown spatial covariance is considered. This is motivated by spectrum sensing problems in the context of dynamic spectrum access in which several secondary networks coexist but do not cooperate, creating a background of spatially correlated broadband interference. When the temporal correlation of the signal of interest is assumed known up to a scale factor, the corresponding Generalized Likelihood Ratio Test is shown to yield a scalar optimization problem. Closed-form expressions of the test are obtained for the general signal spectrum case in the low signal-to-noise ratio (SNR) regime, as well as for signals with binary-valued power spectrum in arbitrary SNR. The two resulting detectors turn out to be equivalent. An asymptotic approximation to the test distribution for the low-SNR regime is derived, closely matching empirical results from spectrum sensing simulation experiments.

A fast OFDM-CDMA user demultiplexing architecture

A fast algorithm based on a butterfly structure is presented that demultiplexes the symbols of a particular type of MC-MA (multi-carrier multiple-access) modulation previously proposed for indoor radio communications. A special transform is used to packetize the different symbols on the down-link such that the code sequences associated with the different symbols are transmitted synchronously at the base station. The input to the FFT bins is defined as a symbol-dependent combination of Walsh-Hadamard codes. We derive a fast architecture that can combine the common redundancy found in the Walsh-Hadamard and the inverse Fourier transform. In the direct implementation, the receiver would compute the IFFT (as in OFDM) before the Walsh-Hadamard transform. The proposed algorithm evaluates both transforms in a single step. A general expression for the butterfly weights is derived and the savings in computational complexity in terms of the frame length is evaluated.

SINR profile for spectral efficiency optimization of SIC receivers in the many-user regime

In dense wireless scenarios, and particularly under high traffic loads, the design of efficient random access protocols is necessary. Some candidate solutions are based on Direct-Sequence Spread Spectrum (DS-SS) combined with a Successive Interference Cancellation (SIC) demodulator, but the performance of these techniques is highly related to the distribution of the users received power. In that context, this paper presents a theoretical analysis to calculate the optimum user SINR profile at the decoder maximizing the spectral efficiency in bps/Hz for a specific modulation and practical Forward Error Correction (FEC) code. This solution is achieved by means of Variational Calculus operating in the asymptotic large-user case. Although a constant SINR function has been typically assumed in the literature (the one maximizing capacity), the theoretical results evidence that the optimum SINR profile must be an increasing function of the users received power. Its performance is compared with that of the uniform profile for two representative scenarios with different channel codes in a slightly overloaded system. The numerical results show that the optimum solution regulates the network load preventing the aggregate throughput from collapsing when the system is overloaded. In scenarios with a large number of transmitters, this optimum solution can be implemented in an uncoordinated manner with the knowledge of a few public system parameters.

Correlated Multiple Antennas Spectrum Sensing Under Calibration Uncertainty

We address the problem of spectrum sensing in cognitive radios (CRs) when the secondary user (SU) is equipped with a multiantenna receiver. We consider scenarios with correlation between the received channels at different antennas and unequal per-antenna noise variances to accommodate calibration errors. First, we derive the exact as well as the asymptotic performance of the genie-aided (benchmark) detector with perfect knowledge of the antenna correlation coefficients, the primary user (PU) signal power and the noise covariance matrix. Then, we consider the sensing problem in which the SU is non-cognizant of the per-antenna noise variances, the PU signal power and the correlation of channel gains, starting with a specific treatment of the two-antenna case. For a general multiantenna receiver, we propose combining the derived test statistics among all antenna pairs. The related optimization problem to obtain the optimum combination weights is analyzed, which requires the analytical performance characterization of the constituent two-antenna detector. Thus, we compute the exact performance of the proposed detector in a special case (a particular case of the Hadamard ratio test) in terms of its detection and false alarm probabilities. Performance analyses are verified with simulations, showing that the proposed detector outperforms several recently-proposed multiantenna detectors for CR in the scenarios considered.

On the Performance of Hadamard Ratio Detector-Based Spectrum Sensing for Cognitive Radios

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.

Optimum energy allocation for massive spread-spectrum multiple access in networks of uncoordinated energy-limited terminals

This paper derives the energy allocation policy that maximizes the aggregate spectral efficiency of an uncoordinated spread-spectrum multiple access network operating in the large-user regime and subject to a long-term per-user average energy constraint. Focusing on a network of autonomous energy-limited devices, we consider that the receiver operates under noise-dominant conditions and that every transmitter is able to estimate accurately its own slowly time-varying channel with no feedback from the receiver. The aggregate spectral efficiency is derived in terms of the statistical distribution of the channel power gains and of the Packet Error Rate (PER) curve of the common modulation and error correcting code employed by all users. Using Variational Calculus, we obtain a closed-form expression for the optimum energy profile at low average Es/N0 and prove that the aggregate spectral efficiency converges to a non-vanishing value if the user population is large and terminals implement an uncoordinated admission control based on the known PER curve.

Multiantenna GLR Detection of Rank-One Signals With Known Power Spectral Shape Under Spatially Uncorrelated Noise

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.

Stochastic dynamic models in PHY abstraction

Physical Layer (PHY) abstraction aims to model link performance and accelerate system-level analyses of communication systems by reducing simulation complexity and their associated computational costs. We examine a Physical Layer (PHY) abstraction approach based on Stochastic Dynamic Systems (SDS) for easing the requirement of expensive Monte Carlo system-level evaluations. We present the framework, recently applied in simplified models for Successive Interference Cancellation (SIC) receivers in the finite and large user limits, and refine the analysis for a related scheme named Successive Interference Blocking (SIB), with the objective of evaluating performance metrics such as the Packet Error Rate using a probability particle algorithm for approximating the equivalent SDS.