It is well known that when data is contaminated by non-Gaussian noise, conventional linear systems may perform poorly. The paper presents an adaptive robust filter (adaptive preprocessor) for canceling impulsive components when the nominal process (or background noise) is a correlated, possibly nonstationary, Gaussian process. The proposed preprocessor does not require iterative and/or batch processing or prior knowledge about the nominal Gaussian process; consequently, it can be implemented in real time and adapt to changes in the environment. Based on simulation results, the proposed adaptive preprocessor shows superior performances over presently available techniques for cleaning impulse noise. Using the proposed adaptive preprocessor to clean the impulsive components in received data samples, conventional linear systems based on the Gaussian assumption can work in an impulsive environment with little if any modification. The technique is applicable to a wide range of problems, such as detection, power spectral estimation, and jamming or clutter suppression in impulsive environments. >

Adaptive robust impulse noise filtering

The theory and application of the class of spherically invariant random processes (SIRPs) are reviewed. An SIRP is a random process whose finite-dimensional distributions are scalar functions of quadratic forms in the corresponding sampled variables. Stochastic and system-theoretic properties are discussed, including a basic representation theorem which gives rise to a number of interesting properties concerning the detection, estimation, and interpretation of SIRPs. Applications are reviewed as well, including the use of SIRPs to model speech waveforms, radar clutter returns, and various radio propagation channel disturbances. The use of SIRP modeling in channel equalization and array processing is also described. Finally, some issues concerning the generation and simulation of SIRPs are discussed.

Spherically Invariant Random Processes: Theory and Applications

The generation of continuous random processes with jointly specified probability density and covariation functions is considered. The proposed approach is based on the interpretation of the simulated process as a stationary output of a nonlinear dynamic system, excited by white Gaussian noise and described by a system of a first-order stochastic differential equations (SDE). The authors explore how the statistical characteristics of the equation's solution depends on the form of its operator and on the intensity of the input noise. Some aspects of the approximate synthesis of stochastic differential equations and examples of their application to the generation of non-Gaussian continuous processes are considered. The approach should be useful in signal processing when it is necessary to translate the available a priori information on the real random process into the language of its Markov model as well as in simulation of continuous correlated processes with the known probability density function. >

Stochastic differential equations: an approach to the generation of continuous non-Gaussian processes

We propose the application of spherically invariant random processes for joint modeling of the fluctuations of the signal envelope and phase in narrowband wireless fading channels. In this model, the phase has a uniform distribution (which is very common in fading channels), while the envelope can be distributed according to an arbitrary distribution law (which includes Rayleigh as a special case). The great utility of the spherically invariant random processes, as a large family of non-Gaussian random processes, lies on their many Gaussian-like properties, which make them very flexible for multivariate statistical analysis, optimal estimation, simulation, and other signal processing issues. Empirical justifications are also given, which strongly support the acceptability of the model.

Signal modelling in wireless fading channels using spherically invariant processes

Recently the performance of digital communication systems in the presence of impulsive atmospheric noise has been evaluated assuming a noise model which is in excellent agreement with experimental results. We evaluate the bit error probability for coherent phase-shift keying (CPSK) signaling assuming the same atmospheric noise model but considering a more reasonable representation of the communication channel which accounts for the simultaneous presence of Gaussian (always present) atmospheric noise and signal fading.

Error Probability for Fading CPSK Signals in Gaussian and Impulsive Atmospheric Noise Environments

Determination of optimal receiver or detector and suboptimal estimator in the presence of additive atmospheric noise depends on the application of a mathematically tractable model of noise. In the tropics the atmospheric radio noise occurring mostly in the burst form above a relatively small continuous background does not deliver energy at a constant rate. This type of noise is non-Gaussian and has a very large dynamic range. The noise bursts consist of a number of short impulses. They are modelled here as the product of a narrow-band Gaussian noise and the reciprocal of a non-Gaussian random process. This paper includes the derivation of statistical information for the above noise viz, the probability distribution of amplitudes, and of separation between pulses, required for determining the error probabilities using various digital methods. This information can be used in filter optimization in digital systems, where the error probability is to be minimized.

A Model of HF Impulsive Atmospheric Noise

Correlation between atmospheric radio noise-burst amplitudes measured by the Aiya noise meter with different bandwidths was examined during periods of local thunderstorm activity. The investigations were carried over a frequency range of 100 kHz to 9 MHz and over a 6-dB bandwidth range of 300 Hz to 16 kHz. The correlation observed in all cases was so high that the standard error of estimate was nearly equal to the accuracy of measurement itself. This suggests that the phenomenon is deterministic rather than statistical. The practical utility of the result is discussed.

Correlation Between Atmospheric Radio Noise-Burst Amplitudes with Different Bandwidths

Short-term time characteristics of burst and quasi- continuous forms of atmospheric radio noise were investigated at Bangalore at a number of frequencies in the range 100 kHz-9 MHz and over a 300-Hz-16-kHz range of bandwidth. It was found that for all frequencies, bandwidths, and threshold levels the duration and spacing follow log-normal distributions. The duration of a pulse above a particular threshold is statistically independent of its spacing from an adjacent pulse. Further, the average duration varies approximately linearly with the threshold level. These results are expected to be of use in planning digital communications where atmospheric noise is the limiting factor in reception capability.

Suresh N. Gupta

Papers

A Model of HF Impulsive Atmospheric Noise

Correlation Between Atmospheric Radio Noise-Burst Amplitudes with Different Bandwidths

Short-Term Time Characteristics of Atmospheric Radio Noise Above Different Thresholds