Two types of commutation signaling for combating multipath are introduced:M \times Nsignaling, in which the signal set cycles successively amongNdifferent sets ofMsigals each; andM + Nsignaling, in which the signal set at any time consists ofMmembers of an alphabet ofM + Nsignals,Nof which are inactive at any epoch. In both cases, the objective is to remove from use any signal sent recently enough that it is still "ringing" in the multipath channel. We consider the problems of minimization ofMandN, hence the total number signals used; analysis of2 \times Nsets (M = 2is almost uniformly optimal); analysis of the simplestM + Nset, i.e., a 2 + 1 set; and presentation of the results of simulation ofM \times NandM + Nsignaling through realistic urban/suburban radio channels. Comparison of these simulations to simulations of other antimultipath techniques is also made. The simulation results are due to Kamil [3].

We show the following results concerning the maximum number Nmaxof simultaneous users supportable by an asynchronous direct-sequence code-division multiple-access (CDMA) system using DPSK. (a) For a network of single-path nonfading links in which all users' signals arrive at any receiver with equal energies, Nmaxis 10-20 percent of the number of chipsMin the system's codes at bit error rates of 10-3to 10-5. (b) If typical urban/suburban multipath and fading phenomena occur and no power control ameliorates them, Nmaxfalls to 1-5 percent ofMeven under the best of circumstances (availability of multipath diversity and ideal multipath combining receivers). (c) If the links consist mostly of only single fading paths and no power control is available, direct-sequence CDMA becomes unusable. Power-control policies can be devised to overcome shadowing (slow fading) or near/far problems, thus partially restoring the Nmaxof (a). It is unlikely that power control will effectively combat fast fading, especially in single-path situations.

The best signal and worst jamming are derived for a detection system which uses a matched-filter receiver. The penalty for deviation from the best signal is determined.

The error spectrum at the output of an ideal FM discriminator is derived for the case where the source of the error is a weak scatter component, which perturbs a strong specular component in the transmission medium. Illustrative examples are given.

A binary transmission scheme in which the transmitter is turned on and off during each bit by an uncertainty variable fed back from the receiver through a noisy feedback channel is analyzed. In particular, the energy advantage of this scheme over ordinary binary transmission without feedback, as a function of error probability, bit rate, channel bandwidth, and the magnitude of the feedback noise is given.

In a previous paper, we found optimal signals for, and evaluated the performance of, a binary sequential detection system in which the detector constantly feeds back to the transmitter its "state of uncertainty" concerning what is being sent. In the present paper, we consider a similar system, which uses a nonsequential detector. Comparison of the results of the two papers shows that: 1) when the prescribed peak-to-average power ratio is small, the sequential system operates with a6-dB average-power advantage over the nonsequential system; 2) when the prescribed peak-to-average power ratio is large, the sequential system operates with a6-dB peak-power advantage over the nonsequential system. In both systems, the performance improves rapidly as the peak-power constraint is relaxed, i.e., as the prescribed peak-to-average power ratio is increased.

We consider a coherent white Gaussian channel, through which one of two signals is sent to a receiver which operates as a sequential detector. A noiseless delayless feedback link is assumed, which continuously informs the transmitter of the state of the receivers uncertainty concerning which signal was sent, and which also synchronizes the transmitter when the receiver has reached a decision. The transmitter, in turn, uses the output of the feedback link to modify its transmission so as to hasten the receiver's decision. The following problem is posed: Given average- and peak-power constraints on the transmitter and a prescribed error probability for the receiver, what signal waveforms should the transmitter use in order to minimize the average transmission time, and how should it utilize the fedback values of the receiver's uncertainty to modify these waveforms while transmission is in progress? We give partial solutions to these questions. In particular, we have shown that if the peak-to-average power ratio is allowed to be sufficiently large, substantial improvement of performance may be achieved through the use of uncertainty feedback.

The ideal probability-computingM-ary receiver is derived for a fading, noisy, multidiversity channel, in which the link fadings may be mutually correlated, as may the link noises. The results are interpreted in terms of block diagrams involving various filtering operations. Two special cases, those of very fast and very slow fading, are considered in detail.

In a tutorial exposition, the following topics are discussed: definition of a matched filter; where matched filters arise; properties of matched filters; matched-filter synthesis and signal specification; some forms of matched filters.

A sounding signal is transmitted through a transmission medium which may be characterized as a linear filter whose impulse response is random, i.e., drawn according to some probability law from an ensemble of possible impulse responses. To the output of the medium is added random noise; the resultant waveform is the received signal. A receiver is required to operate on this received signal so as to make a linear, minimum-mean-square-error estimate of the impulse response of the transmission medium. Two problems concerned with the design of such a sounding system are considered in this paper. The first is the determination of the transfer function of the optimum linear estimating filter in the receiver. The second is the optimization of the spectrum of the transmitted sounding signal.