The optimal single symbol detector on the Rayleigh fading channel computes a functional quadratic form in the time continuous received signal. A drawback is that closed-form solutions of integral equations based on the channel statistics are required. This makes simplified discrete receivers attractive. A class of suboptimal receivers that transforms the received random process to a set of discrete observables is derived. The set of observables constitutes a random vector in a finite dimensional receiver signal space. Given this vector, the maximum likelihood detector computes a quadratic form in the received vector. The discretization implies a loss of information, therefore such a detector is not, in general, optimal given the received time continuous signal. The purpose is, however, to achieve close to optimal performance when the number of observables becomes large. This class of detectors is analyzed using exact error probability calculations, which reveal several interesting properties. The length of the observation interval and the number of discrete observables have significant influences on the error probability when the time variations of the fading process are rapid compared with the symbol duration. By increasing the number of observables, the error floor is lowered, and the implicit diversity order is increased. This implicit diversity arises as soon as more than one observable per symbol interval is used and is a consequence of the information bearing signal being a random process. Matched filter receivers use few discrete observables per symbol interval, and thus suffer from high error floors and low implicit diversity orders on fast fading channels. The error probability is highly dependent on the shapes and durations of the modulator waveforms. For instance, pulses of long duration give lower error probabilities than shorter pulses, and for a certain type of orthogonal waveforms there is no error floor.

Concatenated encoders are found in many digital communication systems. A concatenated receiver for such a system consists of a chain of independently working estimators ended with an outer detector. Each stage of the receiver chain corresponds to a certain code in the system. Maximum likelihood sequence detection with a concatenated receiver requires soft information consisting of symbol aposteriori probabilities to be transferred between the receiver stages. In this paper the optimal inner estimator is derived and further simplified into a new asymptotically optimal one by imposing a tree structure on the inner code. By mapping several suboptimal inner estimators onto the tree structure and noting which approximations they make, a theoretical performance ranking is obtained. The asymptotical performance of the optimal concatenated detector at high signal-to-noise ratios (SNRs) is investigated. The decision variables underlying the pairwise error event probability are shown to be asymptotically Gaussian and consequently a free Euclidean distance can be found for the optimal concatenated detector.

A mobile data system that uses two significantly different data rates on the air interface is described. In a cellular system it is the conditions prevailing for a mobile terminal at the cell border that is setting the limit for a reasonable data rate. However, there are conditions in the cell, e.g. a stationary terminal close to the base station, where it is possible to use a higher data rate. A system is described that is designed for 12.5 kHz LMR channels. The system uses a binary digital FM of GMSK-type as the default transmission mode, but it switches to multilevel CPM when radio conditions are found to be good by the terminal. Considerations on the choice of the number of levels, and on the performance and complexity of the multilevel signalling, are given. Criteria for deciding when conditions are good enough for a rate increase are also suggested.>