In this paper, we consider the problem of quickly detecting an abrupt change in linear regression models. Specifically, an observer sequentially obtains a sequence of observations, whose underlying linear model changes at an unknown time. Moreover, the pre-change linear model is perfectly known by the observer but the post-change linear model is unknown. The observer aims to design an efficient online algorithm to detect the presence of the change via his sequential observations. Based on different assumptions on the change-point, both non-Bayesian and Bayesian problem formulations are considered in this paper. In the non-Bayesian setting, the change-point is modeled as a fixed but unknown constant. Two performance metrics, namely the worst case detection delay (WADD) and the average run length to false alarm (ARL2FA), are adopted to evaluate the performance of detection algorithms. In the Bayesian setting, the change-point is modeled as a geometrically distributed random variable. For this case, the average detection delay (ADD) and the probability of false alarm (PFA) are used as performance metrics. We further propose a novel algorithm, namely the parallel-sum algorithm, for the purpose of change detection. For both setups, we analyze the proposed algorithm and show that it offers good performance while requiring low computational complexity.

Spectrum sensing is a key technology enabling the cognitive radio system. In this paper, the problem of how to quickly and accurately find an unoccupied channel from a large amount of potential channels is considered. The cognitive radio system under consideration is equipped with a narrow band sensor, hence it can only sense those potential channels in a sequential manner. In this scenario, we propose a novel two-stage mixed-observation sensing strategy. In the first stage, which is named as scanning stage, the sensor observes a linear combination of the signals from a pair of channels. The purpose of the scanning stage is to quickly identify a pair of channels such that at least one of them is highly likely to be unoccupied. In the second stage, which is called refinement stage, the sensor only observers the signal from one of those two channels identified from the first stage, and selects one of them as the unoccupied channel. The problem under this setup is an ordered two concatenated Markov stopping time problem. The optimal solution is solved using the tools from the multiple stopping time theory. It turns out that the optimal solution has a rather complex structure, hence a low complexity algorithm is proposed to facilitate the implementation. In the proposed low complexity algorithm, the cumulative sum test is adopted in the scanning stage and the sequential probability ratio test is adopted in the refinement stage. The performance of this low complexity algorithm is analyzed when the presence of unoccupied channels is rare. Numerical simulation results show that the proposed sensing strategy can significantly reduce the sensing time when the majority of potential channels are occupied.

For high-frequency surface wave radar (HFSWR), the unwanted radio wave originated from the ionosphere is commonly called ionospheric clutter. Its presence seriously affects the performance of the HFSWR and extremely degrades the radar capability to detect target over long distances. To solve this problem, this paper proposes a two-step method for ionospheric clutter mitigation with two-dimensional dual-polarized received array. The proposed method first performs parameter estimation of the clutter, and then gives a polarimetric-adaptive-based oblique projection filter (PAB-OPF) to suppress the clutter. In the first step, due to the fact that vertically and horizontally polarized antennas are at different array elements for reducing mutual coupling and hardware cost, 2-D DOAs are estimated to give phase compensation for polarization phase delay estimation. In the second step, the PAB-OPF is proposed to eliminate phase inconsistency by matching different polarization phase delays for different vertically polarized antennas, and then to suppress the clutter efficiently in space-polarization domain. Error analysis and computational complexity of the proposed method are derived. Experimental results are shown to illustrate the superiority of the proposed method for ionospheric clutter suppression.