A considerable amount of literature exists on the problem of selecting an efficient set ofNdigita... more A considerable amount of literature exists on the problem of selecting an efficient set ofNdigital signals with in-phase and quadrature components for use in a suppressed carrier data transmission system. However, the signal constellation which minimizes the probability of error in Gaussian noise, under an average power constraint, has not been determined when the number of signals is greater than
The effect of digital implementation on the gradient (steepest descent) algorithm commonly used i... more The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered. It is shown that digitally implemented adaptive gradient algorithms can exhibit effects which are significantly different from those encountered in analog (infinite precision) algorithms. This is illustrated by considering the often quoted result of stochastic
IRE transactions on communications systems, Jul 1, 1977
A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped dela... more A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped delay line equalizers. These adaptive algorithms accelerate the rate of convergence of the equalizer tap weights to those which minimize the output mean-squared error of a data transmission system. Accelerated convergence of the estimated gradient algorithm is effected by premultiplying the correction term in the algorithm by a matrix which is an estimate of the inverse of the channel correlation matrix. The various algorithms differ in the manner in which this estimate is sequentially computed. Depending on the degree of complexity available, the equalizer convergence time may be reduced more than an order of magnitude from that required by the simple gradient algorithm.
Up to this point in the text, we have made two key assumptions in discussing the structures descr... more Up to this point in the text, we have made two key assumptions in discussing the structures described in Chapter 7: we have assumed arbitrary receiver complexity and we have also assumed that the channel characteristics are known at the receiver. For the maximum likelihood sequence estimation receiver, implemented via the Viterbi algorithm, the number of states was allowed to grow without bound and the observables used to compute the transition metrics are outputs of a (presumed known) filter matched to the channel. In the optimum linear receiver, the matched filter appears again along with a tapped delay line equalizer of arbitrary length. In the optimum linear receiver which does not use a matched filter, the tap weights are dependent on the channel covariance matrix. In practice, the channel characteristics are generally not known. If a dialed telephone line is used, the channel is different on each call. Even for private or leased channels, the characteristics may be known only within certain limits. For many channels, such as fading radio systems, phase perturbations and other time-varying channel variations are present, requiring constant tracking to avoid deterioration of performance. The optimum receivers we have described in the preceding chapters would be of academic interest only if it were not possible to adapt the parameters appearing in their structures to accurately model the actual channel or a function of the channel, such as its inverse.
A considerable amount of literature exists on the problem of selecting an efficient set ofNdigita... more A considerable amount of literature exists on the problem of selecting an efficient set ofNdigital signals with in-phase and quadrature components for use in a suppressed carrier data transmission system. However, the signal constellation which minimizes the probability of error in Gaussian noise, under an average power constraint, has not been determined when the number of signals is greater than
The effect of digital implementation on the gradient (steepest descent) algorithm commonly used i... more The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered. It is shown that digitally implemented adaptive gradient algorithms can exhibit effects which are significantly different from those encountered in analog (infinite precision) algorithms. This is illustrated by considering the often quoted result of stochastic
IRE transactions on communications systems, Jul 1, 1977
A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped dela... more A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped delay line equalizers. These adaptive algorithms accelerate the rate of convergence of the equalizer tap weights to those which minimize the output mean-squared error of a data transmission system. Accelerated convergence of the estimated gradient algorithm is effected by premultiplying the correction term in the algorithm by a matrix which is an estimate of the inverse of the channel correlation matrix. The various algorithms differ in the manner in which this estimate is sequentially computed. Depending on the degree of complexity available, the equalizer convergence time may be reduced more than an order of magnitude from that required by the simple gradient algorithm.
Up to this point in the text, we have made two key assumptions in discussing the structures descr... more Up to this point in the text, we have made two key assumptions in discussing the structures described in Chapter 7: we have assumed arbitrary receiver complexity and we have also assumed that the channel characteristics are known at the receiver. For the maximum likelihood sequence estimation receiver, implemented via the Viterbi algorithm, the number of states was allowed to grow without bound and the observables used to compute the transition metrics are outputs of a (presumed known) filter matched to the channel. In the optimum linear receiver, the matched filter appears again along with a tapped delay line equalizer of arbitrary length. In the optimum linear receiver which does not use a matched filter, the tap weights are dependent on the channel covariance matrix. In practice, the channel characteristics are generally not known. If a dialed telephone line is used, the channel is different on each call. Even for private or leased channels, the characteristics may be known only within certain limits. For many channels, such as fading radio systems, phase perturbations and other time-varying channel variations are present, requiring constant tracking to avoid deterioration of performance. The optimum receivers we have described in the preceding chapters would be of academic interest only if it were not possible to adapt the parameters appearing in their structures to accurately model the actual channel or a function of the channel, such as its inverse.
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