Dyonisius Dony Ariananda

A survey on spectrum sensing techniques for cognitive radio

Spectrum sensing is an important functionality of cognitive radio (CR). Accuracy and speed of estimation are the key indicators to select the appropriate spectrum sensing technique. Conventional spectrum estimation techniques which are based on short time Fourier transform (STFT) suffer from familiar problems such as low frequency resolution, high variance of estimated power spectrum and high side lobes/leakages. Methods such as multitaper spectrum estimation successfully alleviate these infarctions but exact a high price in terms of complexity. On these accounts, it appears that the filter bank spectrum estimation formulated by F. Boroujeny and wavelet based spectrum estimates are the most promising and pragmatic approaches for CR applications. This article surveys and appraises available literature on various spectrum sensing techniques and discusses spectrum sensing as a key element of CR system design.

Compressive Wideband Power Spectrum Estimation

In several applications, such as wideband spectrum sensing for cognitive radio, only the power spectrum (a.k.a. the power spectral density) is of interest and there is no need to recover the original signal itself. In addition, high-rate analog-to-digital converters (ADCs) are too power hungry for direct wideband spectrum sensing. These two facts have motivated us to investigate compressive wideband power spectrum sensing, which consists of a compressive sampling procedure and a reconstruction method that is able to recover the unknown power spectrum of a wide-sense stationary signal from the obtained sub-Nyquist rate samples. It is different from spectrum blind sampling (SBS), which aims at reconstructing the original signal instead of the power spectrum. In this paper, a solution is first presented based on a periodic sampling procedure and a simple least-squares reconstruction method. We evaluate the reconstruction process both in the time and frequency domain. Then, we examine two possible implementations for the compressive sampling procedure, namely complex Gaussian sampling and multicoset sampling, although we mainly focus on the latter. A new type of multicoset sampling is introduced based on the so-called minimal sparse ruler problem. Next, we analyze the statistical properties of the estimated power spectrum. The computation of the mean and the covariance of the estimates allows us to calculate the analytical normalized mean squared error (NMSE) of the estimated power spectrum. Further, when the received signal is assumed to contain only circular complex zero-mean Gaussian i.i.d. noise, the computed mean and covariance can be used to derive a suitable detection threshold. Simulation results underline the promising performance of our proposed approach. Note that all benefits of our method arise without putting any sparsity constraints on the power spectrum.

Power Spectrum Blind Sampling

Power spectrum blind sampling (PSBS) consists of a sampling procedure and a reconstruction method that is capable of perfectly reconstructing the unknown power spectrum of a signal from the obtained samples. In this letter, we propose a solution to the PSBS problem based on a periodic sampling procedure and a simple least squares (LS) reconstruction method. For this PSBS technique, we derive the lowest possible average sampling rate, which is much lower than the Nyquist rate of the signal. Note the difference with spectrum blind sampling (SBS) where the goal is to perfectly reconstruct the spectrum and not the power spectrum of the signal, in which case sub-Nyquist rate sampling is only possible if the spectrum is sparse. In the current work, we can perform sub-Nyquist rate sampling without making any constraints on the power spectrum, because we try to reconstruct the power spectrum and not the spectrum. In many applications, such as spectrum sensing for cognitive radio, the power spectrum is of interest and estimating the spectrum is basically overkill.

Direction of arrival estimation using sparse ruler array design

In this paper, a new direction of arrival (DOA) estimation approach is addressed for the case of more sources than physical receiving antennas by considering a novel nonuniform array design. The new design utilizes the concept of minimum sparse rulers which are rulers having incomplete marks. The differences between marks in a sparse ruler cover all lags of the autocorrelation. In array processing, this set of differences can be used as a basis to construct a virtual uniform linear array having a higher number of antennas than the actual linear array. In order to attain the required rank condition of the observation matrix, the most recent spatial smoothing method is used. The MUSIC algorithm can then be applied leading to the desired high resolution result. It is also possible to compromise the resolution for a lower complexity level by exploiting the least-squares approach to generate the angular spectrum.

Compressive Covariance Sensing: Structure-based compressive sensing beyond sparsity

Compressed sensing deals with the reconstruction of signals from sub-Nyquist samples by exploiting the sparsity of their projections onto known subspaces. In contrast, this article is concerned with the reconstruction of second-order statistics, such as covariance and power spectrum, even in the absence of sparsity priors. The framework described here leverages the statistical structure of random processes to enable signal compression and offers an alternative perspective at sparsity-agnostic inference. Capitalizing on parsimonious representations, we illustrate how compression and reconstruction tasks can be addressed in popular applications such as power-spectrum estimation, incoherent imaging, direction-of-arrival estimation, frequency estimation, and wideband spectrum sensing.

Wideband power spectrum sensing using sub-Nyquist sampling

Compressive sampling (CS) is famous for its ability to perfectly reconstruct a sparse signal based on a limited number of measurements. In some applications, such as in spectrum sensing for cognitive radio, perfect signal reconstruction is not really needed. Instead, only statistical measures such as the power spectrum or equivalently the auto-correlation sequence are required. In this paper, we introduce a new approach for reconstructing the power spectrum based on samples produced by sub-Nyquist rate sampling. Depending on the compression rate, the entire problem can be presented as either under-determined or over-determined. In this paper, we mainly focus on the over-determined case, which allows us to employ a simple least-squares (LS) reconstruction method. We show under which conditions this LS reconstruction method yields a unique solution, without including any sparsity constraints.

Multi-coset sampling for power spectrum blind sensing

Power spectrum blind sampling (PSBS) consists of a sampling procedure and a reconstruction method that is able to recover the unknown power spectrum of a random signal from the obtained sub-Nyquist-rate samples. It differs from spectrum blind sampling (SBS) that aims to recover the spectrum instead of the power spectrum of the signal. In this paper, a PSBS solution is first presented based on a periodic sampling procedure. Then, a multi-coset implementation for this sampling procedure is developed by solving the so-called minimal sparse ruler problem, and the coprime sampling technique is tailored to fit into the PSBS framework as well. It is shown that the proposed multi-coset implementation based on minimal sparse rulers offers advantages over coprime sampling in terms of reduced sampling rates, increased flexibility and an extended range of estimated auto-correlation lags. These benefits arise without putting any sparsity constraint on the power spectrum. Application to sparse power spectrum recovery is also illustrated.

Cooperative compressive wideband power spectrum sensing

Compressive sampling is a popular approach to relax the rate requirement on the analog-to-digital converters and to perfectly reconstruct wideband sparse signals sampled below the Nyquist rate. However, there are some applications, such as spectrum sensing for cognitive radio, that demand only power spectrum recovery. For wide-sense stationary signals, power spectrum reconstruction based on samples produced by a sub-Nyquist rate sampling device is possible even without any sparsity constraints on the power spectrum. In this paper, we examine an extension of our proposed power spectrum reconstruction approach to the case when multiple sensors cooperatively sense the power spectrum of the received signals. In cognitive radio networks, this cooperation is advantageous in terms of the channel diversity gain as well as a possible sampling rate reduction per receiver. In this work, we mainly focus on how far this cooperative scheme promotes the sampling rate reduction at each sensor and assume that the channel state information is available. We concentrate on a centralized network where each sensor forwards the collected measurements to a fusion centre, which then computes the cross-spectra between the measurements obtained by different sensors. We can express these cross-spectra of the measurements as a linear function of the power spectrum of the original signal and attempt to solve it using a least-squares algorithm.

Direction of arrival estimation for more correlated sources than active sensors

Abstract In this paper, a new direction of arrival (DOA) estimation method for more correlated sources than active receiving antennas is proposed. The trick to solve this problem using only second-order statistics is to consider a periodic scanning of an underlying uniform array, where a single scanning period contains several time slots and in different time slots different sets of antennas are activated leading to a dynamic non-uniform array with possibly less active antennas than sources in each time slot. We collect the spatial correlation matrices of the active antenna arrays for all time slots and are able to present them as a linear function of the spatial correlation matrix of the underlying array. We provide a necessary and sufficient condition for this system of equations to be full column-rank, which allows for a least squares (LS) reconstruction of the spatial correlation matrix of the underlying array. Some practical greedy algorithms are presented to design dynamic arrays satisfying this condition. In a second step, we use the resulting spatial correlation matrix of the underlying array to estimate the DOAs of the possibly correlated sources by spatial smoothing and MUSIC. Alternatively, we can express this matrix as a linear function of the correlation matrix of the sources (incoming signals) at a grid of investigated angles, and solve this system of equations using either LS or sparsity-regularized LS (possibly assisted by additional constraints), depending on the grid resolution compared to the number of antennas of the underlying array.

Direction of arrival estimation of correlated signals using a dynamic linear array

In this paper, we evaluate a new second-order statistics based direction of arrival (DOA) estimation method for possibly coherent sources by considering a uniform linear array (ULA) as the underlying array, and a periodic scanning where a single scanning period consists of several time slots and in different time slots, different sets of antennas in the ULA are activated leading to a dynamic array having possibly less active sensors per time slot than correlated sources. The spatial correlation matrices of the output of the antenna arrays for all time slots are collected and they can be presented as a linear function of the correlation matrix of the incoming signal at the investigated angles. Depending on the number of investigated angles, the number of time slots per scanning period, and the number of active antennas per time slot, it is possible to present our system of linear equations as an over-determined system. As long as the rank condition of the system matrix is satisfied, it is possible to first reconstruct the spatial correlation matrix of the outputs of the underlying array using LS. Given this spatial correlation matrix, we offer three alternatives. First, we can estimate the correlation matrix of the incoming signal at the investigated angles using LS. However, this option is vulnerable to a so-called grid mismatch effect. In order to mitigate this effect, we also propose structured total least-squares (S-TLS) as a second option in order to reconstruct the correlation matrix of the incoming signal at the perturbed investigated angles given the reconstructed spatial correlation matrix of the outputs of the underlying array. As a third option, we can also apply spatial smoothing and multiple signal classification (MUSIC) on the reconstructed spatial correlation matrix of the underlying array to directly obtain the DOA estimates.