In a wireless system with Intelligent Reflective Surfaces (IRS) containing many passive elements, we consider the problem of channel estimation. All the links from the transmitter to the receiver via each IRS elements (or groups) are estimated. We show that the estimation performance are dependent on the setting of the IRS, and design an optimal channel estimation scheme where the IRS elements follow an optimal series of activation patterns. The optimal design is guided by results for the minimum variance unbiased estimation. The IRS setting during the channel estimation period mimics the discrete Fourier transforms. We show theoretically and with simulations that the estimation variance is one order smaller compared to existing methods with on/off IRS activation patterns as proposed in the literature.

In this paper, we consider methods for improving far-field speech recognition using dereverberation based on sparse multi-channel linear prediction. In particular, we extend successful methods based on nonconvex iteratively reweighted least squares, that look for a sparse desired speech signal in the short-term Fourier transform domain, by proposing sparsity promoting convex functions. Furthermore, we show how to improve performance by applying regularization into both the reweighted least squares and convex methods. We evaluate the methods using large scale simulations by mimicking the application scenarios of interest. The experiments show that the proposed convex formulations and regularization offer improvements over existing methods with added robustness and flexibility in fairly different acoustic scenarios.

Multi-pitch estimation concerns the problem of estimating the fundamental frequencies (pitches) and amplitudes/phases of multiple superimposed harmonic signals with application in music, speech, vibration analysis, and other fields. In this paper we formulate a complex-valued multi-pitch estimator via a semidefinite programming method for continuous sparse optimization over an infinite dictionary of vectors of complex exponentials and extend this to real-valued data via a real semidefinite program with the same dimensions (i.e. half the size). We further impose a continuous frequency constraint naturally occurring from assuming a Nyquist sampled signal by adding an additional semidefinite constraint. In our numerical experiments, the proposed estimator shows superior performance compared to state-of-the-art methods for separating two closely spaced fundamentals and approximately achieves the asymptotic Cramér-Rao lower bound.

The harmonic chirp signal model has only very recently been introduced for modelling approximately periodic signals with a time-varying fundamental frequency. A number of estimators for the parameters of this model have already been proposed, but they are either inaccurate, non-robust to noise, or very computationally intensive. In this paper, we propose a fast algorithm for the harmonic chirp summation method which has been demonstrated in the literature to be accurate and robust to noise. The proposed algorithm is orders of magnitudes faster than previous algorithms which is also demonstrated via timing studies.

Fundamental frequency estimation is a very important task in many applications involving periodic signals. For computational reasons, fast autocorrelation-based estimation methods are often used despite parametric estimation methods having superior estimation accuracy. However, these parametric methods are much more costly to run. In this paper, we propose an algorithm which significantly reduces the computational cost of an accurate maximum likelihood-based estimator for real-valued data. The computational cost is reduced by exploiting the matrix structure of the problem and by using a recursive solver. Via benchmarks, we demonstrate that the computation time is reduced by approximately two orders of magnitude. The proposed fast algorithm is available for download online.

In linear prediction of speech, the 1-norm error minimization criterion has been shown to provide a valid alternative to the 2-norm minimization criterion. However, unlike 2-norm minimization, 1-norm minimization does not guarantee the stability of the corresponding all-pole filter and can generate saturations when this is used to synthesize speech. In this paper, we introduce two new methods to obtain intrinsically stable predictors with the 1-norm minimization. The first method is based on constraining the roots of the predictor to lie within the unit circle by reducing the numerical range of the shift operator associated with the particular prediction problem considered. The second method uses the alternative Cauchy bound to impose a convex constraint on the predictor in the 1-norm error minimization. These methods are compared with two existing methods: the Burg method, based on the 1-norm minimization of the forward and backward prediction error, and the iteratively reweighted 2-norm minimization known to converge to the 1-norm minimization with an appropriate selection of weights. The evaluation gives proof of the effectiveness of the new methods, performing as well as unconstrained 1-norm based linear prediction for modeling and coding of speech.

Employing sparsity criteria in linear prediction of speech has been proven successful for several analysis and coding purposes. However, sparse linear prediction comes at the expenses of a much higher computational burden and numerical sensitivity compared to the traditional minimum variance approach. This makes sparse linear prediction difficult to deploy in real-time systems. In this paper, we present a step towards real-time implementation of the sparse linear prediction problem using hand-tailored interior-point methods. Using compiled implementations the sparse linear prediction problems corresponding to a frame size of 20ms can be solved on a standard PC in approximately 2ms and orders faster than with general purpose software.

The modulation accuracy described by an error vector magnitude is a critical parameter in modern communication systems - defined originally as a performance metric for transmitters but now also used in receiver design and for more general signal analysis. The modulation accuracy is a measure of how far a test signal is from a reference signal at the symbol values when some parameters in a reconstruction model are optimized for best agreement. This paper provides an approach to computation of error vector magnitude as described in several standards from measured or simulated data. It is shown that the error vector magnitude optimization problem is generally non-convex. Robust estimation of the initial conditions for the optimizer is suggested, which is particularly important for a non-convex problem. A Bender decomposition approach is used to separate convex and non-convex parts of the problem to make the optimization procedure simpler and robust. A two step global optimization method is suggested where the global step is the grid method and the local method is the Newton method. A number of test cases are shown to illustrate the concepts.

With the advent of ubiquitous computing there are two design parameters of wireless communication devices that become very important: power efficiency and production cost. Compressive sensing enables the receiver in such devices to sample below the Shannon-Nyquist sampling rate, which may lead to a decrease in the two design parameters. This paper investigates the use of Compressive Sensing (CS) in a general Code Division Multiple Access (CDMA) receiver. We show that when using spread spectrum codes in the signal domain, the CS measurement matrix may be simplified. This measurement scheme, named Compressive Spread Spectrum (CSS), allows for a simple, effective receiver design. Furthermore, we numerically evaluate the proposed receiver in terms of bit error rate under different signal to noise ratio conditions and compare it with other receiver structures. These numerical experiments show that though the bit error rate performance is degraded by the subsampling in the CS-enabled receivers, this may be remedied by including quantization in the receiver model. We also study the computational complexity of the proposed receiver design under different sparsity and measurement ratios. Our work shows that it is possible to subsample a CDMA signal using CSS and that in one example the CSS receiver outperforms the classical receiver.

In this paper, we consider the problem of minimizing a non-smooth convex problem using first-order methods. The number of iterations required to guarantee a certain accuracy for such problems is often excessive and several methods, e.g., restart methods, have been proposed to speed-up the convergence. In the restart method a smoothness parameter is adjusted such that smoother approximations of the original non-smooth problem are solved in a sequence before the original, and the previous estimate is used as the starting point each time. Instead of adjusting the smoothness parameter after each restart, we propose a method where we modify the smoothness parameter in each iteration. We prove convergence and provide simulation examples for two typical signal processing applications, namely total variation denoising and l1-norm minimization. The simulations demonstrate that the proposed method require fewer iterations and show lower complexity compared to the restart method.

We consider lossy compression of image sequences using l1-compression with overcomplete dictionaries. As a fidelity measure for the reconstruction quality, we incorporate the recently proposed structural similarity index measure, and we show that this leads to problem formulations that are very similar to conventional l1 compression algorithms. In addition, we develop efficient large-scale algorithms used for joint encoding of multiple image frames.

We consider the problem of lossy compression of images using sparse representations from overcomplete dictionaries. This problem is in principle easy to solve using standard algorithms for convex programming, but often the large dimensions render such an approach intractable. We present a highly efficient method based on recently developed first-order methods, which enables us to compute sparse approximations of entire images with modest time and memory consumption.

We investigate link quality metrics (LQMs) based on mutual information (MI) for fast link adaptation (FLA) in IEEE 802.11n wireless local area network (WLAN) with convolutional coding and higher order modulations. The LQMs are scalar quantities that map the receiver's post-decoding behaviour in a frequency-selective channel into an equivalent behaviour in an AWGN channel. From this metric the expected packet error rate (PER) can be predicted. Two LQMs are presented that are derived from the SINRs of all sub-carriers and streams: the effective SNR and the effective mutual information. The effective mutual information is the mean mutual information including a correction factor which improves the PER estimation accuracy in various highly frequency-selective channels. The FLA algorithm dynamically selects a modulation and coding scheme (MCS) that maximizes the throughput (TP), while keeping the average PER over time below a target value. Furthermore, we present methods of searching for the most suitable MCS. Practical performance bounds are obtained by means of simulations. We show that both investigated LQMs yield accurate PER estimates and that the resulting TP of the FLA algorithm used in a 2 x 2 MIMO bit-interleaved coded modulation (BICM) OFDM system that performs channel estimation is only 1.7 dB from the performance bound of the TP.