A digital modulation method based on quadrature-carrier multiplexing of two N-dimensional biorthogonal signal sets is proposed. An embodiment of the proposed method referred to as quadrature frequency/phase modulation (QFPM), and its continuous phase modification CP QFPM, are described. QFPM results when two NFSK/2PSK (combined frequency and phase shift keying) signals are quadrature-carrier multiplexed. The power efficiency of QFPM and CP QFPM on the AWGN (additive white Gaussian noise) channel is always superior when compared to that of quadrature-amplitude modulation (QAM), and their bandwidth efficiency is demonstrated to be under certain conditions comparable or better than that of QAM. Both schemes possess a self-synchronization capability. The demonstrated performance characteristics of QFPM and CP QFPM suggest that they may be competitive with respect to QAM on channels where little or no filtering is desired.>

It is shown that the classical additive white Gaussian noise (AWGN) channel design can be retained for the fading channel with any degree of fading, if carried out with the appropriate signal set size M=M/sub min/. The size of the signal set M/sub min/ is shown to depend upon the number of parallel transitions between a given pair of states and the throughput rate. In the proposed multiple trellis-coded modulation (MTCM) scheme with a modified design (MTCM (MD)), the output bits from a rate m/m+1 trellis encoder are assigned multiple signals from an M/sub min/-PSK signal set. Compared to the MTCM with set partitioning proposed for the fading channel (SPF) design, the MTCM (MD) scheme provides the same signal diversity and the same or increased values of the branch distance product, and always leads to increased value of d/sup 2/(free). As a result, the performance is always improved on the Rician fading channel due to the increased d/sup 2/(free), and is improved on any fading channel when an increase in branch distance produce P takes place. When compared to the MTCM with the set partitioning optimum for the AWGN channel (SPA) design, the MTCM (MD) scheme, under certain conditions, provides the same value of d/sup 2/(free) as the MTCM (SPA) design, and is then asymptotically optimum for both the AWGN channel and the fading channels.>

A new modulation scheme that produces a constant envelope continuous phase signal set with a compact power spectrum and power efficiency better than that of MSK is proposed. The scheme can be implemented by quadrature-carrier multiplexing of two frequency/phase modulated signals of the type NFSK/2PSK, both with the same frequency in each transmission interval, and with sinusoidal symbol shapes. The generated signal can be viewed in each transmission interval as an MSK signal at one of the N frequencies and is referred to as multifrequency minimum shift keying (MF MSK). Modulation, demodulation, and synchronization circuits are described, and the spectral properties and power efficiency on the AWGN channel are analyzed. Combining a number of attractive attributes such as constant envelope, excellent spectral properties, high power efficiency, and self-synchronization capability, the proposed modulation format lends itself to a variety of applications, one of them being the digital satellite link.>

The authors explore the trellis coding of continuous-phase quadrature frequency/phase modulated (CPQFPM) signal sets and continuous-phase FPM (CPFPM) signal sets, which are embodiments of the quadrature biorthogonal modulation (QBOM) technique. Conventional TCM and multiple TCM schemes with these modulation formats are examined using both the AWGN channel and the Rician fading channel design. Asymptotic coding gains in d/sup 2/(free) are tabulated for trellis-coded rate 3/4, 5/6, and 6/7 QFPM schemes, in comparison with uncoded modulations (8AMPM, 32AMPM) and other trellis-coded modulations (TCM (2FSK/4PSK 16QAM, 64QAM), MTCM (2FSK/8PSK)) of equivalent throughput rate. Performance gains on the Rician fading channel are demonstrated by increased values of the design parameters for this channel, namely symbol diversity L/sub min/ and branch distance product P.>

Multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets (MTCM/FPM) is investigated for performance on the additive white Gaussian noise (AWGN) channel and on the one-sided normal, Rayleigh and Rician fading channels. The Nakagami-m fading model is used as an alternative to the Rician fading model to calculate the error probability upper bound for trellis-coded schemes on the fading channel. The likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed. The design criteria for the one-sided normal fading channel, modeled by the Nakagami-m distribution, are observed to be the same as those for the Rayleigh-fading channel. For the MTCM/FPM schemes, it is demonstrated that the set partitioning designed to maximize symbol diversity (optimum for fading channels) is optimum for performance on the AWGN channel as well. The MTCM/FPM schemes demonstrate improved performance over MTCM/MPSK schemes and TCM/FPM schemes on the AWGN channel and the fading channel.>

A modified sequential procedure for testing binary hypotheses with different means, proposed by C.C. Lee and J.B. Thomas (ibid., vol.IT-30, no.1, p.16-23, Jan. 1984), is generalized for application to the case of multiple hypotheses with different means/variances of the Gaussian distribution. The method constitutes a two-threshold test for fixed-size packages of samples with a sequential procedure of discarding the package for which no decision is reached and subsequently testing a new package. The objective is to find an optimum package size N/sub 0/ which leads to the minimum overall average sample number (ASN) for a given overall error probability. An optimization algorithm is developed to extend the application of the Lee-Thomas procedure to the M-ary case. Performance characteristics of the generalized two-threshold (GTT) test procedure are compared with those of conventional sequential as well as fixed-sample-size (FSS) methods. It is shown for the M-ary different means/variances cases that for low error rates the number of samples required by the GTT test is, on the average, approximately half that needed by a FSS test. However, it is somewhat more than the ASN obtained with a conventional sequential test. With decreasing error probabilities the GTT test performance approaches that of conventional sequential methods.>

A sequential multiple hypotheses test for the unknown parameters of a Gaussian distribution is developed. The case of a known variance but an unknown mean belonging to the set (00,01,''' ,Om_l} is considered as well as that of a known mean but an unknown variance belonging to the set\{\sigma^{2}_{0}, \sigma^{2}_{1},\cdots ,\sigma^{2}_{m-1}\}. Analytical expressions are developed for the algorithm performance, i.e., the average length of the test and the error probability. The results are compared with a Bayes algorithm and show that the new algorithm needs about half as many samples. As far as the authors are aware this is the firstmary sequential algorithm for which the performance has been found analytically. Because of the performance of this algorithm and the fact that it is a natural generalization of the binary sequential test, it is felt that the algorithm may be optimum or close to optimum.

This paper deals with the design of adaptive algorithms for reception of a narrowband signal with an unknown envelope in a noisy channel (Gaussian noise). We here consider a system (with a "real teacher") which learns from the samples classified by this self-learning system (decision directed adaptive receiver). By using those samples which are accepted as learning samples, the parameters of the unknown envelope are estimated. The envelope's parameters appear in the form of coefficients of the generalized Fourier series expansion of the signal (with respect to eigenfunctions of appropriate integral equation). It is possible to utilize any orthonormal set with respect to the interval(0, T)under the usual assumption, that the complex autocovariance function isR(\tau) = N\delta (\tau)(i.e., that the noise bandwidth is much greater than both1/Tand the signal bandwidth andNis the unilateral spectral density of the noise in the neighborhood of the signal spectrum). We present expressions that enable the upper bound estimates of the error probability to be found for the derived algorithms. The results obtained for the binary detection are readily generalized to the case of anM-ary signal.