Probability and Measure

Cognitive radios have been proposed as a means to implement efficient reuse of the licensed spectrum. The key feature of a cognitive radio is its ability to recognize the primary (licensed) user and adapt its communication strategy to minimize the interference that it generates. We consider a communication scenario in which the primary and the cognitive user wish to communicate to different receivers, subject to mutual interference. Modeling the cognitive radio as a transmitter with side-information about the primary transmission, we characterize the largest rate at which the cognitive radio can reliably communicate under the constraint that (i) no interference is created for the primary user, and (ii) the primary encoder-decoder pair is oblivious to the presence of the cognitive radio.

Cognitive Radio: An Information-Theoretic Perspective

The problem of acoustic noise is becoming increasingly serious with the growing use of industrial and medical equipment, appliances, and consumer electronics. Active noise control (ANC), based on the principle of superposition, was developed in the early 20th century to help reduce noise. However, ANC is still not widely used owing to the effectiveness of control algorithms, and to the physical and economical constraints of practical applications. In this paper, we briefly introduce some fundamental ANC algorithms and theoretical analyses, and focus on recent advances on signal processing algorithms, implementation techniques, challenges for innovative applications, and open issues for further research and development of ANC systems.

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Recent Advances on Active Noise Control: Open Issues and Innovative Applications

Book review: Applied cryptography: Protocols, algorithms, and source code in C

Review Article: Power line communication technologies for smart grid applications: A review of advances and challenges

In active noise control there has been some research based in the modified filtered-X least mean square (LMS) algorithm (MFX-LMS). When the secondary path is perfectly modeled, this algorithm is able to perfectly eliminate it's effect. It is also easily adapted to allow the use of fast algorithms such as the recursive least square, or algorithms with good tracking performance based on the Kalman filter. This letter presents the results of a frequency domain analysis about the behavior of the MFX-LMS in the presence of secondary path modeling errors and a comparison with the FX-LMS algorithm. Namely, it states that for small values of the secondary path delay both algorithms perform the same, but that the step-size of the FX-LMS algorithm decreases with increasing delay, while the MFX-LMS algorithm is stable for an arbitrary large value for the secondary path delay, as long as the real part of the ratio of the estimated to the actual path is greater than one half (Re{S/spl circ//sub z//S/sub z/}>1/2). This means that for the case of no phase errors the estimated amplitude should be greater than half the real one and for the case of no amplitude errors the phase error should be less than 60/spl deg/. Analytical expressions for the limiting values for the step-size in the presence of modeling errors are given for both algorithms.

The behavior of the modified FX-LMS algorithm with secondary path modeling errors

Most Active Noise Control (ANC) systems use some form of the LMS [5] [9] algorithm due to its reduced computational complexity However, the problems associated with it are well-known, namely slow convergence and high sensitivity to the eigenvalue spread [3] [9] To overcome these problems the RLS algorithm is often used, but it is now widely known, that the RLS loses many of its good properties for a forgetting factor lower than one Namely, it has been shown that in some applications the LMS algorithm is actually better in tracking non-stationary systems than the RLS algorithm [2] [3] One approach, which works well with non-stationary systems, is to use some specialized form of the Kalman filter, which can be interpreted as a generalization of the RLS algorithm [1][3][4] The Kalman filter has a high computational complexity, similar to that of the RLS algorithm, which can make it costly for some applications Nevertheless, for narrow-band ANC, the number of taps is not very large [9], and the application of the Kalman filter in ANC may be easily handled by today DSP's In this paper, a specialized version of the Kalman filter fitted to ANC is developed; both control filter adaptation and secondary path modeling It is shown, throw computer experiments, that a large reduction in the residual noise can be achieved in non-stationary environments, compared with the LMS and RLS based algorithms, especially when on-line secondary path modeling is used

A Kalman filter approach to active noise control

Power-line communication (PLC) allows establishing digital communications without adding any new wires. It will turn one's house or neighborhood grid into a smart grid. PLC has some issues, namely, high noise at low frequencies and varying characteristic impedance. This paper addresses these issues to improve the signal-to-noise ratio by increasing the signal or reducing the noise. PLC MODEMs are subject to legislations that limit the signals in the line. The radiated signal is proportional to the current, but not to the input current, since the current forms a standing wave along the line. However, better performance can be achieved if the input current is measured. The receiver circuit of the transmitting MODEM can be used to estimate the input impedance. This paper presents a technique to use this new information to achieve better performance and to follow legislation changes in the band above 30 MHz. A study of the viability of using impulsive noise reduction techniques to further increase performance is also presented. The short noise pulses result in high correlation between the noises in different carriers. Impulse position detection should result in an increase in capacity.

Dealing With Unknown Impedance and Impulsive Noise in the Power-Line Communications Channel

In active noise control (ANC), online secondary path modeling can be achieved by adding a small auxiliary noise signal. If the secondary path changes are slow, then this signal can be low, but keeping the stability of the ANC system with sudden secondary path changes requires higher values for this signal, so auxiliary noise power scheduling is required. The proposed algorithm deals well with sudden (and strong) changes, due to the fast convergence of the secondary path model. It is compared with other similar algorithms in the literature. The ability to deal with different physical conditions without changing the algorithms parameters is also compared. The proposed algorithm increases the auxiliary noise to levels close to the acoustic noise when no cancelation is done and reduces it to lower levels when noise cancelation is being performed. In addition variants of the LMS that improve performance are proposed.

Auxiliary Noise Power Scheduling Algorithm for Active Noise Control with Online Secondary Path Modeling and Sudden Changes

While the LMS algorithm and its normalized version (NLMS), have been thoroughly used and studied. Connections between the Kalman filter and the RLS algorithm have been established however, the connection between the Kalman filter and the LMS algorithm has not received much attention. By linking these two algorithms, a new normalized Kalman based LMS (KLMS) algorithm can be derived that has some advantages to the classical one. Their stability is guaranteed since they are a special case of the Kalman filter. More, they suggests a new way to control the step size, that results in good convergence properties for a large range of input signal powers, that occur in many applications. They prevent high measurement noise sensitivity that may occur in the NLMS algorithm for low order filters, like the ones used in OFDM equalization systems. In these paper, different algorithms based on the correlation form, information form and simplified versions of these are presented. The simplified form maintain the good convergence properties of the KLMS with slightly lower computational complexity.

Paulo A. C. Lopes

Papers

The behavior of the modified FX-LMS algorithm with secondary path modeling errors

A Kalman filter approach to active noise control

Dealing With Unknown Impedance and Impulsive Noise in the Power-Line Communications Channel

Auxiliary Noise Power Scheduling Algorithm for Active Noise Control with Online Secondary Path Modeling and Sudden Changes

New Normalized LMS Algorithms Based on the Kalman Filter