An exact expression for the output autocorrelation function of an FM discriminator is derived when the input of the FM discriminator is an FM signal, cochannel interference and Gaussian noise. The modulating baseband signals for the FM signal and the cochannel interference are assumed FDM signals whose statistics are modeled by a stationary Gaussian random process. The interaction among signal, interference and noise are determined by which the NPR (noise-power-ratio) can be calculated.>

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.

The Bessel function expansion has been used [1] to approximate the TWTA nonlinear characteristics to assist in the evaluation of intelligible crosstalk between FDM/FM carriers using the Shimbo-Pontano method [2]. In particular, the arbitrary constant α was chosen to be in the range of 100-1000. This correspondence presents a further theoretical clarification on the selection of suitable values for α, which was briefly explained in [3]. In this analysis, it is shown that the suitably chosen values for α (as given in the main text) cannot be large (roughly,\alpha \leq 1.6).

A method of evaluating double intelligible crosstalk between two frequency division multiplexed frequency modulated (FDM/FM) carriers accessing the same earth station high-power amplifier (HPA) and satellite transponder traveling wave tube amplifier (TWTA) has been developed. The analysis takes into consideration the AM/AM and AM/PM characteristics of the two cascaded memoryless nonlinear amplifiers, and the amplitude and group delay variations of transmission paths preceding the first nonlinear amplifier and of the path between the two nonlinear amplifiers. Results of the double intelligible crosstalk evaluation show the existence of significant distortion cross terms caused by the two cascaded nonlinearities and filters, in addition to individual distortion terms by each nonlinearity. Specific illustrative examples are discussed, and some practical suggestions are given for controlling crosstalk impairment effects in satellite channels with double cascaded nonlinear amplifiers.

Increased frequency reuse in satellite systems will result in increased levels of cochannel interference. Such interference can in fact become the limiting factor affecting system performance. In this paper, the effects of cochannel interference on the bit error rate (BER) of a QPSK satellite system are analyzed. A nonlinear satellite transponder having a specified AM-AM and AM-PM transfer characteristic is assumed. An arbitrary number of up- and downlink interferers is considered. The theoretical results are compared with results obtained from time-domain computer simulations. Two facets of the cochannel interference problem which are of particular interest are investigated: the non-Gaussian nature of the interference and the small-signal suppression which may occur for uplink interferers.

An investigation of ways to improve the capacity in a dedicated SCPC transponder has resulted in the development of a method for optimizing the transponder capacity and link performance in preassigned multilevel SCPC systems. The main approach is to form different groups of carriers based on the traffic requirement, and on typical characteristics of the link destinations such as variations in the satellite e.i.r.p. and downlink path loss, and differences in the receive earth station antenna size. The Fletcher-Powell optimization technique is used to determine the set of optimum carrier levels at the transponder TWTA input. Application of the method to a number of preassigned multilevel frequency plans in a global transponder environment clearly indicates that the total carrier-to-noise ratios for all the links can be optimized at any specified CNR value, and that the optimized capacities are substantially higher than that of the basic two-level system. The implementation of multilevel plans is fairly simple if all downlink carrier levels can be monitored at some reference station in the SCPC network to reasonably control the uplink e.i.r.p. levels.

The theoretical relationships are presented for determining the output amplitude and phase of each small signal when commonly amplified with a large signal by a memoryless nonlinear amplifier. Both the amplitude and phase of each output small signal depend on the input amplitude of the large signal and on the AM/AM and AM/PM characteristics of the nonlinear amplifier. If the nonlinear amplifier is a hard limiter without AM/PM conversion, then the well-known result can also be derived from a general formula developed in this paper. A numerical example is given and confirmed by laboratory measurement.

This is in reply to the comments made by Messrs. X. T. Vuong and H. J. Moody on "A general theory for intelligible crosstalk between frequency-division multiplexed angle-modulated carriers." We do want to express our gratitude for the editorial comments which were made by Messrs. Vuong and Moody which could be of help to the reader. The comments of substance however we feel are in many cases misleading and in certain cases incorrect. An item by item assessment of each of the fifteen (15) points which were raised follows below.

A problem associated with signal power control during multicarrier transmission in the presence of an amplifier nonlinearity in a satellite communications channel is analyzed. The problem is to calculate input carrier power levels wheii output carrier power levels are given. The Fletcher-Powell optimization technique is used for a small number of transmitted carriers, and an example shows the effect of weak signal suppression in the presence of large signal(s) because of nonlinear effects. This technique is applied to three types of transponder nonlinearities to illustrate realistic cases. The Gaussian assumption is used for a large number of carriers. Cases in which one or two input signals are much larger than the other signals are also treated.

It is commonly known that, in order to calculate the demodulated noise power of the wanted frequency division multiplexedfrequency modulated (FDM-FM) signal due to interference, the convolution between the power spectra of the wanted FM signal and interference is required to be obtained. This concise paper shows a simple approach to calculate this convolution without direct calculation of the power spectrum of the FDMFM signal when the power spectrum of the interference is given (by measurements or calculation) and the highest and lowest channel frequencies of the baseband signal and rms frequency deviation of the wanted FDM-FM signal are known. Since the calculation of the FDM-FM signal power spectrum is not an easy problem in some cases, this approach makes much simpler an accurate evaluation of the output noise power due to interference.

A new method for calculating intelligible crosstalk between frequency-division multiplexed (FDM) angle-modulated carriers has been developed and is directly applicable to multicarrier operation in communications satellite systems. The analysis is general in scope and accounts for both the nonlinear amplitude and phase characteristics of the amplifying device by the use of a complex Bessel function expansion. Group delay and amplitude variation preceding the input of the nonlinear device are modeled using a Fourier series expansion. FDM baseband loading is also considered in the analysis. A comparison of theoretical results with measurement shows good agreement.

A unified approach is presented for evaluation of the error probabilities of a class of digital communications systems in additive noise and interference. This class of systems includes coherent systems such asM-ary amplitude-shift keying (ASK),M-ary phase-shift keying (PSK), andM-ary amplitude-and-phase keying (APK); it also includes differential coherent systems such as binary differential PSK (DPSK). The noise is not necessarily Gaussian. The interference can be intersymbol interference, co-channel interference, adjacent-channel interference, any of their linear combinations, or intermodulation prodducts at the output of some nonlinear device. This approach essentially expands the characteristic function of the interferences into a power series so that the desired error probability can be evaluated as the sum of terms representing perturbations around the error probability due to additive noise alone. Bounds on three kinds of truncation errors, which are simple and applicable to all aforementioned digital systems, are obtained. As a result, any desired accuracy in the evaluation of the error probabilities can be achieved with this approach. In the special case in which the noise is Gaussian, explicit bounds on truncation errors are also obtained. Examples are given to illustrate how the unified analysis can be applied to evaluate the error probabilities of various digital systems. More specifically, the combined effects of Gaussian noise, intersymbol interference, and co-channel interference on the error performance ofM-ary coherent PSK and APK (MCPSK and MCAPK) systems are computed. The probability of error of a binary DPSK (BDPSK) system in the presence of Gaussian noise and intersymbol interference is analyzed. The intermodulation products at the output of a hardlimiter are also determined.

A useful method is presented for the evaluation of the error probability ofM-ary phase-shift-keyed systems with Gaussian noise and intersymbol interference. By regarding a portion of the intersymbol interference as an equivalent Gaussian noise, this method suggests first calculating the probability of error caused by the combined effects of the Gaussian noise and the equivalent noise. Necessary correction terms are then added to the calculation to take into account the fact that the intersymbol interference is actually non-Gaussian. It is shown that with this method any desired accuracy can be theoretically achieved in the evaluation of the probability of error. This method has been programmed for numerical computations. Some examples are also given for illustrative purposes.

This paper analyzes the threshold characteristic of FM signals. An exact solution, obtained previously [1] for Gaussian base-band modulation, is generalized in order to obtain the autocorrelation function of the output signal plus noise of an FM discriminator for the case of more general baseband signals. For an application of the general results, sinusoidal modulation is analyzed in detail. It is shown that, under appropriate conditions, the heuristic result obtained by Rice [3] for sinusoidal modulation can be derived from the exact solution that is obtained here.

An analysis of the threshold characteristic of FM signals when modulated by a Gaussian baseband signal and demodulated by an ideal FM discriminator has been derived. It is shown that there are two components in the demodulated output due entirely to modulation. This analysis serves also to unify the work of Rice [8], Wang [9], and Blachman [16].