This paper presents a method for evaluating the maximum bit error probability (BEP) of a digital communication system subjected to interference by measuring the amplitude probability distribution (APD) of the interfering noise. Necessary conditions for the BEP evaluation are clarified both for the APD measuring receiver and the communication receiver considered. A method of defining emission limits is presented in terms of APD so that the worst BEP of a communication system does not exceed a required permissible value. The methods provide a theoretical basis for a wide variety of applications such as emission requirements in compliance testing, dynamic spectrum allocations, characterization of an electromagnetic environment for introducing new radio systems, and evaluation of intra-system interference.

Non-stationary glint noise is often observed in a radar tracking system. The distribution of glint noise is non-Gaussian and heavy-tailed. Conventional recursive identification algorithms use the stochastic approximation (SA) method. However, the SA method converges slowly and is invalid for non-stationary noise. This paper proposes an adaptive algorithm, which uses the stochastic gradient descent (SGD) method, to overcome these problems. The SGD method retains the simple structure of the SA method and is suitable for real-world implementation. Convergence behavior of the SGD method is analyzed and closed-form expressions for sufficient step size bounds are derived. Since noise data are usually not available in practice, we then propose a noise extraction scheme. Combining the SGD method, we can perform on-line adaptive noise identification directly from radar measurements. Simulation results show that the performance of the SGD method is comparable to that of the maximum-likelihood (ML) method. Also, the noise extraction scheme is effective that the identification results from the radar measurements are close to those from pure glint noise data.

This study shows the effectiveness of the simulation probability density function (p. d. f. ) based on the Bhattacharyya bound from the point of view of the twisted distribution. As a result, the simulation p. d. f. related to the Bhattacharyya bound is asymptotically optimal for the trellis coded modulation scheme under some practical conditions. And the optimality is also confirmed by a numerical example.

The evaluation of a error probability of a trellis-coded modulation scheme by an ordinary Monte-Carlo simulation method is almost impossible since the excessive simulation time is required to evaluate it. The reduction of the number of simulation runs required is achieved by an importance sampling method, which is one of the variance reduction simulation methods. The reduction of it is attained by the modification of the probability density function, which makes errors more frequent. The error event simulation method, which evaluates the error probability of finite important error events, cannot avoid a truncation error. It is the fatal problem to evaluate the precision of the simulation result. The reason of it is how to design the simulation probability density function. We propose a evaluation method and the design methods of the simulation conditional probability density function. The proposed method simulates any error event starting at the fixed time, and the estimator of it has not the truncation error. The proposed design method approximate the optimum simulation conditional probability density function. By using the proposed method for an additive non-Gaussian noise case, the simulation time of the most effective case of the proposed method is less than 1/5600 of the ordinary Monte-Carlo method at the bit error rate of 10-6 under the condition of the same accuracy if the overhead of the selection of the error events is excluded. The simulation time of the same bit error rate is about 1/96 even if we take the overhead for the importance sampling method into account.

To evaluate the coding performance of a multilevel coding scheme for Rayleigh fading channel, a virtual automatic gain control and interleaving are applied to the scheme. The automatic gain control is assumed only for the theoretical evaluation of the performance. It is noted that the bit error-rate performance of the scheme for phase shift keying does not change whether the control is assumed or not. By the effect of the virtual automatic gain control and the interleaving, a fading channel with Gaussian noise is theoretically converted into an equivalent time-invariant channel with non-Gaussian noise. The probability density function of the converted non-Gaussian noise is derived. Then, the function is applied to a formula of the bit error-rate of the scheme for non-Gaussian noise. The formula is derived for phase shift keying by modifying that for pulse amplitude modulation. The coding performance for the non-Gaussian noise channel is evaluated by the formula, and the suitable coding with ideal interleaving is searched. As a result, the coding gain of 28 dB is obtained at the bit error-rate of 10-6 by using BCH code of length 31. This result is confirmed by a simulation for the fading channel. Then, the effectiveness of the formula for finite interleaving is evaluated. Finally, the usefulness of the formula, where the noise power is doubled, is shown for a case of a differential detection.

When bit error probability of a trellis-coded modulation (TCM) scheme becomes very small, it is almost impossible to evaluate it by an ordinary Monte-Carlo simulation method. Importance sampling is a technique of reducing the number of simulation samples required. The reduction is attained by modifying the noise to produce more errors. The low error rate can be effectively estimated by applying importance sampling. Each simulation run simulates a single error event, and importance sampling is used to make the error events more frequent. The previous design method of the probability density function in importance sampling is not suitable for the TCM scheme on an additive non-Gaussian noise channel. The main problem is how to design the probability density function of the noise used in the simulation. We propose a new design method of the simulation probability density function related to the Bhattacharyya bound. It is reduced to the same simulation probability density function of the old method when the noise is additive white Gaussian. By using the proposed method for an additive non-Gaussian noise, the reduction of simulation time is about 1/170 at bit error rate of 106 if the overhead of the calculation of the Bhattacharyya bound is ignored. Under the same condition, the reduction of the simulation time by the proposed method is 1/65 of the ordinary Monte-Carlo method even if we take the overhead for importance sampling into account.

A composite noise generator (CNG) is proposed for simulating the actual non-Gaussian noise and its applications are mentioned. Basing upon the actual measured result (APD) of induced noise from electric contact discharge arc, the APD is approximated by partial linearlization and shown that it can be simulated by a combination of plural Gaussian noise sources. Applying the CNG, quasi-peak (Q-P) detector is investigated and shown that the Q-P detector response is different for non-Gaussian noise when its time domain parameter is different even if its original APD is the same. For digital transmission error due to non-Gaussian noise, and for TV picture stained by the non-Gaussian noise, the CNG is applied to evaluate their performances and quality. The results obtained show that the CNG can be used as a standard non-Gaussian generator for several immunity tests for information equipments.

In the maximum-likelihood decoding under a non-Gaussian noise, the decoding region is bounded by complex curves instead of a perpendicular bisector corresponding to the Gaussian noise. Therefore, the error rate is not evaluated by the Euclidean distance. The Bhattacharyya distance is adopted since it can evaluate the error performance for a noise with an arbitrary distribution. Upper bound formulae of a bit error rate and an event error rate are obtained based on the error-weight-profile method proposed by Zehavi and Wolf. The method is modified for a non-Gaussian channel by using the Bhattacharyya distance instead of the Euclidean distance. To determine the optimum code for an impulsive noise channel, the upper bound of the bit error rate is calculated for each code having an encoder with given shift-register lehgth. The best code is selected as that having the minimum upper bound of the bit error rate. This method needs much computation time especially for a code with a long shift-register. To lighten the computation burden, a suboptimum search is also attempted. For an impulsive noise, modeled from an observation in digital subscriber loops, an optimum or suboptimum code is searched for among codes having encoders with a shift-register of up to 4 bits. By using a code with a 4-bit encoder, a coding gain of 20 dB is obtained at the bit error rate 10-5. It is 11 dB more than that obtained by Ungerboeck's code.

A random pulse stream (RPS) generator was developed for the noise immunity test of various digital system including communication system. By using this RPS generator along with the composite noise generator (CNG) developed formerly, the Middleton's "Class A" noise could be generated, and the total system (RPS+CNG) became more general noise simulator. In this paper, the configuration of CNG with newly developed RPS generator, and a typical example of Class A noise generated by this system are shown.