The problem of computing intermodulation generated by a large number of narrowband carriers is examined. In general, narrowband carriers sharing a nonlinear repeater may have different power levels and different spectral shapes. Therefore, different kinds of intermodulation products will appear. It is well known that replacing identical contiguous carriers by a noise band may lead to a poor approximation when baseband computations involving carriers with peaked spectral shapes (e.g. SCPC/FM) are considered. However, it is shown here that this noise band representation offers an effective way to calculate the total RF intermodulation power corresponding to each kind of product and can therefore be viewed as a means of indirectly counting intermodulation products.>

When two or more frequency-modulated and/or digital carriers of various sizes and modulation formats are transmitted through a common memoryless nonlinear device with AM/AM and AM/PM characteristics such as a traveling-wave tube amplifier, interactions among the carriers will occur. One of the impairments caused by these interactions results in modulation-transfer noise effects. In particular, in satellite communications, depending on the manner multicarrier transponders are used, the modulation-transfer impairment manifests itself under various forms and subjective interference effects. This tutorial-review paper presents an introduction to this type of impairment, methods of analysis and examples, and measurement results. General practical guidelines are suggested for controlling these effects.

Interference from carriers which are frequency modulated by a spreading waveform is examined. A mixed spreading waveform, obtained by adding a line rate component to a frame rate component, is proposed. This spreading is shown to combine advantages which are offered by line rate and frame rate when used separately.

An analysis of the modulation transfer noise effects from a continuous (nonbursty) digital carrier to multiple FDM/FM carriers in a common memoryless nonlinear amplifier (e.g., satellite transponder TWTA) is presented. It is shown that the modulation transfer noise, which is caused by the random envelope variations of the digital carrier due to the random data patterns and filtering of the PSK pulses, consists of both discrete and continuous spectral components in the baseband of the FDM/FM carriers. Numerical examples in terms of the noise power ratio as well as a comparison between measured and computed results are given. In general, the discrete or tonal interference component at the symbol rate of the digital carrier is quite significant. Results of this paper should be useful in the planning of FDMA satellite transponders employing the mixed PSK-FM mode of operation.

This paper presents a power series expansion approach for evaluating modulation transfer noise effects fromLdigital carriers (continuous or bursty) toKFDM/FM carriers in a common memoryless nonlinear amplifier. The method allows for a complete characterization and assessment of this type of transmission impairment and its effects in satellite communications systems. The baseband modulation transfer noise in the FM carriers caused by the random envelope fluctuations due to filtering of PSK pulses and/or by the on-off bursting of the digital carriers can be calculated. Illustrative numerical results indicate that the mixed PSK-FM mode of operation in satellite transponders should be employed with great care since a number of 4 kHz channels in the basebands of the FM carriers may receive prohibitive interference.

This paper examines modulation transfer noise effects from TDMA carriers to FDM/FM carriers in a common memoryless nonlinear amplifier. The modulation transfer noise consists of discrete as well as continuous spectral components. Three types of discrete components are identified: those due to pulse filtering only, those due to on-off bursting only, and cross terms due to both mechanisms simultaneously. The continuous spectral component of the modulation transfer noise is due to pulse filtering only. A comparison of the relative intensities of all these noise components is also presented.

When several voice-activated SCPC/FM carriers are transmitted through a nonlinear satellite repeater, a large number of intermodulation products appear at the output. An analysis of the baseband effect of these products is presented, taking into account the random on-off pattern followed by each carrier, the random nature of the level of each modulating speech signal, and a precise definition of the carrier power spectral density which is conditioned on the fact that the carrier is on, assuming that this is the circumstance under which we want to examine interference effects on any particular carrier. The analysis shows that computing intermodulation baseband noise, simply by introducing a penalty factor into the noise that would result by treating intermodulation as if it were thermal noise, may lead to very conservative estimates of intermodulation effects. The paper is restricted to the situation in which all carriers have equal amplitudes, but the general analysis is still valid when this is not so. The extension is straightforward except for the difficulties in counting the number of products of each type.

It is well known that the Barankin bound is locally the tightest lower bound on the variance of any unbiased estimator. If the minimum-variance unbiased-parameter estimation problem is viewed as a minimum-norm problem in an appropriate Hilbert space, the Barankin bound has a very simple geometric interpretation. This interpretation also gives some insight into the influence of bias on the estimation error.