High frequency (HF) communications are of vital importance for modern military operations. However, HF channels are touchy and unpredictable, prone to noise, fading, jamming, and interference. Therefore, a number of prediction tools for channel selection have been developed. However, existing tools do not consider the local actual electromagnetic interference at receivers located on navy and army platforms. Measurements on military platforms show that also the local interference environment can be crucial and has large variations in frequency and time. In this paper we analyze the levels and dynamics of local interference from a typical military platform. We show that the variations regarding interference waveform can be very large between two consecutive seconds of measurement. This means that the interference impact in terms of bit error probability also will be very large between such consecutive seconds. The overall conclusion is that future methods for HF-frequency selection would be significantly improved by considering the characteristics of local interference from electrical equipment.

We consider spectrum sensing of signals encoded with an orthogonal space-time block code (OSTBC). We propose a CFAR detector based on knowledge of the eigenvalue multiplicities of the covariance matrix which are inherent owing to the OSTBC and derive theoretical performance bounds. In addition, we show that the proposed detector is robust to a carrier frequency offset, and propose a detector that deals with timing synchronization using the detector for the synchronized case as a building block. The proposed detectors are shown numerically to perform well.

Cognitive radio is a new concept of reusing spectrum in an opportunistic manner. Cognitive radio is motivated by recent measurements of spectrum utilization, showing unused resources in frequency, time and space. Introducing cognitive radios in a primary network inevitably creates increased interference to the primary users. Secondary users must sense the spectrum and detect primary users' signals at very low SNR, to avoid causing too much interference.This dissertation studies this detection problem, known as spectrum sensing.

The fundamental problem of spectrum sensing is to discriminate an observation that contains only noise from an observation that contains a very weak signal embedded in noise. In this work, detectors are derived that exploit known properties of the second-order moments of the signal. In particular, known structures of the signal covariance are exploited to circumvent the problem of unknown parameters, such as noise and signal powers or channel coefficients.

The dissertation is comprised of six papers, all in different ways related to spectrum sensing based on second-order statistics. In the first paper, we considerspectrum sensing of orthogonal frequency-division multiplexed (OFDM) signals in an additive white Gaussian noise channel. For the case of completely known noise and signal powers, we set up a vector-matrix model for an OFDM signal with a cyclic prefix and derive the optimal Neyman-Pearson detector from first principles. For the case of completely unknown noise and signal powers, we derive a generalized likelihood ratio test (GLRT) based on empirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise or signal powers.

In the second paper, we create a unified framework for spectrum sensing of signals which have covariance matrices with known eigenvalue multiplicities. We derive the GLRT for this problem, with arbitrary eigenvalue multiplicities under both hypotheses. We also show a number of applications to spectrum sensing for cognitive radio.

The general result of the second paper is used as a building block, in the third and fourth papers, for spectrum sensing of second-order cyclostationary signals received at multiple antennas and orthogonal space-time block coded (OSTBC) signals respectively. The proposed detector of the third paper exploits both the spatial and the temporal correlation of the received signal, from knowledge of the fundamental period of the cyclostationary signal and the eigenvalue multiplicities of the temporal covariance matrix.

In the fourth paper, we consider spectrum sensing of signals encoded with an OSTBC. We show how knowledge of the eigenvalue multiplicities of the covariance matrix are inherent owing to the OSTBC, and propose an algorithm that exploits that knowledge for detection. We also derive theoretical bounds on the performance of the proposed detector. In addition, we show that the proposed detector is robust to a carrier frequency offset, and propose another detector that deals with timing synchronization using the detector for the synchronized case as a building block.

A slightly different approach to covariance matrix estmation is taken in the fifth paper. We consider spectrum sensing of Gaussian signals with structured covariance matrices, and propose to estimate the unknown parameters of the covariance matrices using covariance matching estimation techniques (COMET). We also derive the optimal detector based on a Gaussian approximation of the sample covariance matrix, and show that this is closely connected to COMET.

The last paper deals with the problem of discriminating samples that containonly noise from samples that contain a signal embedded in noise, when the variance of the noise is unknown. We derive the optimal soft decision detector using a Bayesian approach. The complexity of this optimal detector grows exponentially with the number of observations and as a remedy, we propose a number of approximations to it. The problem under study is a fundamental one andit has applications in signal denoising, anomaly detection, and spectrum sensing for cognitive radio.

The ever-increasing demand for higher data rates in wireless communications in the face of limited or underutilized spectral resources has motivated the introduction of cognitive radio. Traditionally, licensed spectrum is allocated over relatively long time periods and is intended to be used only by licensees. Various measurements of spectrum utilization have shown substantial unused resources in frequency, time, and space [1], [2]. The concept behind cognitive radio is to exploit these underutilized spectral resources by reusing unused spectrum in an opportunistic manner [3], [4]. The phrase cognitive radio is usually attributed to Mitola [4], but the idea of using learning and sensing machines to probe the radio spectrum was envisioned several decades earlier (cf., [5]).

In this work, we consider spectrum sensing of OFDM signals. We deal withthe inevitable problem of a carrier frequency offset, and propose modificationsto some state-of-the-art detectors to cope with that. Moreover, the (modified)detectors are implemented using GNU radio and USRP, and evaluated over aphysical radio channel. Measurements show that all of the evaluated detectorsperform quite well, and the preferred choice of detector depends on thedetection requirements and the radio environment.

In this paper, we create a unified framework for spectrum sensing of signals which have covariance matrices with known eigenvalue multiplicities. We derive the generalized likelihood-ratio test (GLRT) for this problem, with arbitrary eigenvalue multiplicities under both hypotheses. We also show a number of applications to spectrum sensing for cognitive radio and show that the GLRT for these applications, of which some are already known, are special cases of the general result.

We point out an error in a derivation in the recent paper [1], and provide a correct and much shorter calculation of the result in question. In passing, we also connect the results in [1] to the literature on array signal processing and on principal component analysis, and show that the main findings of [1] follow as special cases of standard results in these fields.

We consider spectrum sensing of a second-order cyclostationary signal receivedat multiple antennas. The proposed detector exploits both the spatial andthe temporal correlation of the received signal, from knowledge of thefundamental period of the cyclostationary signal and the eigenvaluemultiplicities of the temporal covariance matrix. All other parameters, suchas the channel gains or the noise power, are assumed to be unknown. The proposeddetector is shown numerically to outperform state-of-the-art detectors forspectrum sensing of anOFDM signal, both when using a single antenna and with multiple antennas.

We consider spectrum sensing of OFDM signals in an AWGN channel. For  the case of completely known noise and signal powers, we set up  a vector-matrix model for an OFDM signal with a cyclic prefix and  derive the optimal Neyman-Pearson detector from first  principles. The optimal detector exploits the inherent correlation  of the OFDM signal incurred by the repetition of data in the cyclic  prefix, using knowledge of the length of the cyclic prefix and the  length of the OFDM symbol. We compare the optimal detector to the energy  detector numerically. We show that the energy detector is  near-optimal (within 1 dB SNR) when the noise variance is  known. Thus, when the noise power is known, no substantial gain can  be achieved by using any other detector than the energy detector.

For the case of completely unknown noise and signal powers, we  derive a generalized likelihood ratio test (GLRT) based onempirical second-order statistics of  the received data. The proposed GLRT detector exploits the  non-stationary correlation structure of the OFDM signal and does not  require any knowledge of the noise power or the signal power. The  GLRT detector is compared to state-of-the-art OFDM signal detectors,  and shown to improve the detection performance with 5 dB SNR in  relevant cases.

In this work, we consider spectrum sensing of Gaussian signals with structured covariance matrices. We show that the optimal detector based on the probability distribution of the sample covariance matrix is equivalent to the optimal detector based on the raw data, if the covariance matrices are known. However, the covariance matrices are unknown in general. Therefore, we propose to estimate the unknown parameters using covariance matching estimation techniques (COMET). We also derive the optimal detector based on a Gaussian approximation of the sample covariance matrix, and show that this is closely connected to COMET.