Establishing frame and burst synchronism in TDMA requires detection of a known, approximately periodic signal corrupted by noise. This paper presents a Markovian modeling approach to analyzing the performance of a sync detector that repeatedly compares the output of ann-bit binary correlator to an acceptance/rejection threshold. The detector is defined to be in one of two modes of operation: INITIAL ACQUISITION, during which it seeks to identify the start of a frame; and RETENTION, in which periodic detection of the frame (and burst) is essential for TDMA operations. During acquisition, then-bit sync word is assumed embedded in random data, and bit errors are assumed uncorrelated. The acquisition models permit ready computation of acquisition-time statistics and the probability of false acquisition. The retention models identify paths by which synchronism can be lost, their probability of occurrence, and a resulting mean time to loss of synchronism. Unlike the acquisition models, account is taken of the deterministic data pattern immediately preceding the sync word, and sources of timing error that alter the sync word's ideally periodic arrival. The models presented in this paper allow the detector's key performance indexes to be assessed as a function of its external environment: bit-error rate, timing uncertainty, and data pattern preceding the sync word; and internal parameters: sync word pattern, correlation detection threshold, detection aperture widths, number of consecutive detections before acquisition can be declared, and the number of tolerable consecutive sync word misses before synchronism is declared lost.

This paper deals with the passage ofmsignals along with additive Gaussian noise through a memoryless bandpass nonlinearity. It offers a method for finding the fundamental zone output attributable to anyninput signals (including their intermodulation) which at the same time specifies the equivalent new nonlinearity seen by these signals. The fundamental (i.e, bandpass) transfer characteristic of the original nonlinearity is arbitrary and may include AM-to-PM conversion. The approach is a generalization of Blachman's treatment of the problem for a signal-plus-noise jnpdt. The analysis is based on the author's previously reported stochastic decomposition method for multiple signals feeding a bandpass nonlinearity.

The need to predict overall link availability in a satellite communications system has motivated efforts to devise theoretical and empirical models to predict fade statistics for line of site propagation between an earth station and a satellite. Investigators have largely concentrated on measuring and analyzing the key propagation phenomena, especially attenuation and depolarization due to rainfall, and deriving simple parametric models which relate rain drop geometry, frequency, and available local meteorological data to probability distributions of attenuation and depolarization. However, in allocating margins for carrier-to-noise ratios, the designers of operational satellite systems still rely mainly on operational experience, and where limited experience is available margins tend to be conservative. While this approach may be the most practical with limited experimental and theoretical information, the sufficient variability of earth station to earth station link behavior suggests that without more detailed knowledge of the underlying mechanisms, system inefficiencies and unexpected problems may arise. Furthermore, an accurate link model is essential in the proper assessment of new systems, especially those systems using the 14/12 GHz, or higher, allocated satellite frequency bands. This paper derives the long term probability distribution of C/N over a complete satellite link that includes the effects of signal attenuation due to transmitting earth station pointing error, up-path propagation, geostationary satellite position error, down-path propagation, and receiving earth station pointing error. Non-tracking and tracking antennas subject to wind loading are considered, and the effects of the non-linear Satellite power transfer characteristic and the correlation of up- and down-link pointing losses due to satellite position error are accounted for. Results presented for 6/4 GHz links show that the satellite non-linear transponder, the proportion of noise in the up- and down-links, and satellite station keeping all affect the net fade distribution. It is therefore demonstrated that system parameters as well as uppath and down-path propagation statistics determine fade margin requirements for a satellite link.

The application of 14/12 GHz and higher allocated frequency bands in commercial satellite communications systems has been retarded by the problem of slow deep fading due principally to rain attenuation on the earth-station-to-satellite and satellite-satellite-to-earthstation radio links. The large carrier-to-noise ratio(C/N)margins required to ensure good link performance for a large percentage of time may be excessive, and a more sophisticated method of dealing with fading is required. The methods available fall broadly into two categories, one employing diversity and the other adaptive compensation techniques. This paper examines a link compensation method, namely up-link power control at the transmitting earth station, that effectively reduces the effects of both up- and down-link fading in a frequency-division multiple-access (FDMA) satellite system having a large number of accesses. The transmitted level of each carrier accessing the satellite transponder is dynamically adjusted to compensate the combination of up- and down-link fading experienced by the carrier. While this leads to wide variations in individual carrier levels into the satellite, the assumed independence of fades on the down-link to each of the receiving earth stations means that variations in multicarrier TWT operating point tend to be small (providing no one earth station receives a highly disproportionate share of the traffic). By essentially pooling among many links the effects of deep fades simultaneously present on only a few links, this technique will reduceC/Nvariations on individual carriers, thereby reducing required fade margins. This paper derives expressions for the earth-station-to-earth-station link fade probability density function (pdf) with and without transmit power control. The theoretical effects of noisy estimates of the up- and down link fades and quantization of the transmitted powers are considered. Simple asymptotic expressions applicable when the number of accesses is large are also derived. Computed results demonstrate that transmit power control can substantially reduce the fade margins required in homogeneous single channel per carrier (SCPC) systems operating in the 14/12 GHz band. Some detection and control problems associated with a practical implementation of the scheme are introduced.

This correspondence presents a simple bandwidthefficient rule for assigning carrier frequencies that ensures that all fundamental product terms up to a desired order fall on distinct frequencies, thereby facilitating their measurement.

Evaluating the capacity of a satellite communication system requires accurate prediction of the combined effects of up and down-path fading. This correspondence derives an expression for the resultant channel fade probability distribution as a function of up- and down-path fade distributions and the satellite TW input-output (I/O) power transfer characteristic, and demonstrate that power limiting in the satellite has a substantial effect.

When constant-amplitude signals and noise constitute the input to a bandpass device exhibiting a nonlinear input-output power characteristic and AM/PM conversion, the relative signal levels may change and intermodulation (IM) products are produced. A new and totally general method of evaluating the complex Fourier coefficient of any desired output component is presented. The analysis is based on repeated extraction using expected values of output signals dependent on one or more of the input signals, and makes use of joint envelope-phase probability distributions of the input conditioned on given signal phases. Several analytical examples demonstrating the application of the method and its advantages are discussed. Numerical results are presented for 2, 4, and 100 equal carriers into several types of soft limiters with quadratic AM/PM conversion.

When an angle-modulated signal plus noise constitute the input to a bandpass device exhibiting a nonlinear input-output power characteristic and AM to PM conversion, the noise component of the output has altered first- and second-order statistics. A method of evaluating the two-dimensional first-order statistics of this noise is presented. The effect on signal detectability of a nonlinearity inserted between two channel noise sources is studied; expressions for the mean square received phase error and probability of error (for coherent digital phase modulation) are derived. The hard limiting satellite channel, with Gaussian noise on the up and down links, is examined in detail, and it is demonstrated that the limiter can significantly affect signal detectability.