Paul H. Wittke

Carrier Transmission of Binary Data in a Restricted Band

The spectra of digital frequency modulation (FM) signals have been observed to be narrow compared with the spectra of digital baseband signals or the corresponding amplitude modulation (AM) and phase modulation (PM) signals. This suggests a high efficiency of transmission in terms of occupied bandwidth for binary FM. Here the desirability of digital FM systems is investigated further with an examination of the probability of bit error. The FM receiver considered consists of a predetection filter, a limiter-discriminator, and a postdetection filter. New results are presented on the effect of predetection bandwidth restriction on the error performance of binary FM systems for various frequency deviations. Theoretical results have been obtained by a Fourier analysis of the distorted FM signals and by Rices click analysis of FM noise. The data presented permits an optimum selection of system parameters such as frequency deviation ratio and predetection filter bandwidth. It is found that in narrow-band operation a peak-to-peak frequency deviation of about 0.7 times the bit rate and a bandpass filter bandwidth of about 1.0 times the bit rate yield a minimum probability of error. Experimental measurements have been made and there is, in general, good agreement with the theory. A comparison of the error performance of noncoherent binary FM, coherent AM, and coherent PM in a restricted band is made. Narrow-band noncoherent FM proves superior to AM in any bandwidth. In narrow-band operation, the noncoherent FM gives a somewhat better error performance than the coherent PM. For example, for an error rate of 10-4and a bandpass filter bandwidth of one times the bit rate, the performance of a noncoherent FM system is 0.7 dB better than that of a coherent PM system.

Signaling constellations for fading channels

The performance of various coherent 8-ary and 16-ary modulations in additive white Gaussian noise (AWGN) and slowly fading channels are analyzed. New expressions for the exact symbol error rates (SER) in fading with diversity combining are derived for any two-dimensional signaling format having polygonal decision boundaries. Maximal ratio combining, equal gain combining, and selection combining are considered. The SER formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine,which constellation has the lowest probability of error. For example, a star constellation such as that specified in the CCITT V.29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0.63 dB power in AWGN without sacrificing the phase error tolerance, while maintaining the same error rate. The sensitivity of each constellation to phase error is presented and comparisons are made. Six 8-ary signal sets and 11 16-ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels.

Optimization and performance evaluation of multicarrier transmission

Optimization of the performance of multicarrier transmission over a linear dispersive channel is presented. The optimum data and power assignment to the subcarriers are derived for both the conventional error probability criterion, and a new criterion based on the normalized mean-square error. The assignments and algorithms hold for channels where performance is degraded by additive noise, intersymbol and interchannel interference. Lower bounds on throughput are derived and are used to compare multicarrier performance with conventional single-carrier quadrature amplitude modulation (QAM) with both linear and decision feedback equalization. It is seen that multicarrier transmission can provide a significant improvement at low and intermediate channel signal-to-noise ratios. As an example, the optimization is applied to the high-speed digital subscriber loop, and multicarrier transmission is demonstrated to be superior to decision feedback equalized single-carrier QAM.

Error probabilities of two-dimensional M-ary signaling in fading

A new exact method for computing the average symbol error probability of two-dimensional M-ary signaling in slow fading is presented. The method is generally applicable to polygonal decision regions. The exact average symbol error rate of coherent 16-star-QAM is obtained and compared to that of 16-rectangular-QAM. New results for optimum ring ratios of 16-star-QAM in additive white Gaussian noise (AWGN) and in slow fading are also given.

PSK and DPSK trellis codes for fast fading, shadowed mobile satellite communication channels

The performance of 8-PSK and 8-DPSK trellis codes is presented for a class of fast fading, land mobile satellite communication channels. The fading model is Rician but, in addition, the line-of-sight path is subjected to a fast lognormal attenuation that represents tree shadowing. The fading parameters used in this study represent the degree of shadowing and are based on measured data. The primary application considered is for digital speech transmission and thus, bit error probabilities in the order of 10/sup -3/ are emphasized. Sensitivity of the bit error probability to amplitude fading, amplitude and phase fading, and decoding delay is presented. Performance is determined via digital computer simulation. Optimal four- and eight-state codes are determined and optimality is found to be dependent on the presence of lognormal shadowing. >

Low Complexity Decoders for Constant Envelope Digital Modulations

Digital angle modulations having input symbol memory can be demodulated using maximum likelihood sequence estimation (MLSE or Viterbi decoding). The demodulation of the more bandwidth efficient of these can require a large number of computations. In this paper, lower complexity decoding approaches are presented. These decoders use a predetermined processing order and a reduced number of survivor signals, S , at every-time NT . Processing is performed on the signal sequences using metrics (likelihoods) obtained by a matched filter bank similar to that needed for MLSE. The decoders can achieve asymptotic optimality of error rate while being computationally faster and simpler than MLSE for many modulations. In addition, error rate performance can be traded for complexity reduction. Expected performance has been verified for representative modulations.

Frequency-hopped spread-spectrum transmission with band-efficient modulations and simplified noncoherent sequence estimation

Frequency-hopped spread-spectrum transmission using band-efficient modulations that are phase-continuous during each hop, is presented. A range of system parameters is considered, including signaling spectrum, reception, system complexity, and performance in the presence of noise and jamming. The particular cases where the hopped modulation is minimum-shift-keying (MSK), duobinary minimum-shift-keying (DMSK), or tamed-FM (TFM), are studied in detail. Results are presented for various modulation indexes, rectangular and raised cosine pulse shapings, and a range of hop interval lengths. Sequence estimation on a hop-by-hop basis is considered. The noncoherent likelihood sequence receiver must keep all possible paths, and so the computation and complexity becomes large for system transmitting many bits per hop. Therefore, a simplified noncoherent Viterbi-like sequence estimation algorithm with reduced complexity is introduced. System performance has been evaluated in Gaussian noise, partial-band jamming and multiple-tone jamming, using bounds and a system simulation. The compact nature of the hopped spectrum, when a number of bits are transmitted per hop, offers greater spectrum utilization and the prospect of improved performance in the presence of multiple-tone jamming or interference. >

Cyclic prefixed single carrier transmission in ultra-wideband communications

This letter proposes cyclic prefixed single carrier transmission with frequency domain equalization (SC-FDE) as an alternative physical layer solution for UWB communications. The performance of SC-FDE over IEEE 802.15.3a UWB channel models is analyzed, simulated and compared with that of impulse based single carrier UWB (SC-UWB) and multicarrier UWB employing orthogonal frequency division multiplexing (OFDM-UWB). The impact of channel coding on the performance of OFDM and SC-FDE in UWB is also studied. Our results demonstrate performance advantage of the SC-FDE scheme, especially when implementation issues such as low complexity and low power consumption for UWB are taken into consideration. The performance of SC-FDE with diversity combining using oversampling is also investigated

Infinite series of interference variables with Cantor-type distributions

The sum of an infinite series of weighted binary random variables arises in communications problems involving intersymbol and adjacent-channel interference. If the weighting decays asymptotically at least exponentially and if the decay is not too slow, the sum has an unusual distribution which has neither a density nor a discrete mass function, and therefore cannot be manipulated with usual techniques. The distribution of the sum is given, and the calculus for dealing with the distribution is presented. It is shown that these Cantor-type random variables arise in a range of digital communications models, and exact explicit expressions for performance measures, such as the probability of error, may be obtained. Several examples are given. >

Effects of Pulse Shaping and Soft Decisions on the Performance of Digital FM with Discriminator Detection

Band-limited digital FM systems employing discriminator detection are analyzed. The error-rate performance of binary FM with premodulation shaping and duobinary FM with the same occupied bandwidth are compared. At bandwidths above 1.1 times the bit rate, it is found that binary FM gives a lower error rate than duobinary FM. For binary FM to meet lower bandwidth requirements, frequency deviation ratios below 0.4 times the bit rate must be used. At these low deviations, binary FM does not perform as well as duobinary FM with the same bandwidth. In addition, if a more complex receiver is used which makes use of Viterbi decoding after the discriminator, the performance can be made better than binary FM even at the larger occupied bandwidths.