A methodology is presented for designing systolic structures for recursive algorithms, especially for recursive filtering algorithms. A direct mapping methodology is used to map the dependence graph of the recursive algorithms onto systolic architectures. The mapping procedures are given and illustrated by examples. The methods for minimizing the computation time or the pipeline period and improving the utilization efficiency of the array are also discussed. In particular, the problems of the recursive state-space filtering algorithms are considered.>

The authors extend the LMS (least mean squares) adaptation algorithm to state-space recursive filtering. Based on the state equations in the time domain, gradients for all parameters are formulated by matrix derivative linear operations and are calculated recursively. The stability of the filter during the adaptive process is guaranteed by adding the constraints of a specified system matrix A. Simulation results show that any desired state-space system can be achieved by initializing the system properly. Since the adaptive state-space filtering requires intensive computations and all computations involved are matrix operations, a high-speed VLSI architecture is presented for real-time or near real-time applications.>

A nonuniform sampling digital phase-locked loop (DPLL) is proposed with a sequential loop filter, in which two additional phase comparators are added conjointly with an estimation-decision circuit controlling the two distinct modes, acquisition and tracking, in which the loop is to work. These additions provide more freedom to deal with the conflicting requirements of minimum acquisition time and maximum noise rejection in the presence or absence of frequency drift. Using a pseudo-two-dimensional random-walk filter, the stationary phase-error variance and the mean acquisition time have been evaluated by means of a numerical analysis. The comparison between the theoretical analysis and the experiments has proven to be very satisfactory. Substantial reduction of the acquisition time, without severely degrading the noise reduction performance, has been achieved. The improved ability of this modified loop to track frequency drift was also demonstrated. A digital loop "quasi-bandwidth" measure was used in the evaluation of the loop performance, thus allowing for a comparison with other digital loops and to a limited extent with a first-order analog loop. The usual difference in performance favoring the analog loop for high signal-to-noise ratio is shown to be substantially reduced and can be lowered by an appropriate choice of parameters.

A modified BPSK modulation technique using premodulation filtering is presented. The modified BPSK modulator achieves a smooth phase transition from 0 to π rad by going through an intermediate value of\pi/2rad. The resultant PSK signal has a very low AM component, particularly suitable for data transmission through nonlinear channels. Experimental tests performed in a channel having a high degree of AM nonlinearity (AM-to-AM conversion), have shown that the modified BPSK signal, when passed through a hard-limiter, has a spectrum with greatly reduced spectral sidelobes compared to the conventional BPSK signal. The modified BPSK signal has spectral lines at the carrier frequency plus multiples of the signaling frequency, which in some cases might be useful for timing recovery in the demodulation process.

The problem of equalizing a discrete signal that has been transmitted through a channel selected at random from an ensemble of channels is considered. Using mean-square error as the performance index, the minimum number of adjustable parameters required to achieve a given level of performance is sought. For certain special cases, it is shown that, using nonrecursive sampled data filters, the optimum tap weights are given by the eigenvectors of the matrix formed from the covariances of the channel's impulse response. A numerical algorithm is developed to find the optimum equalizer structure for a wide class of channels with the restriction that the number of channels in the given ensemble is finite. Results worked out for several examples show that the optimum equalizer structure requires significantly fewer adjustable parameters than the standard transversal equalizer in order to obtain the same level of performance.