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

This paper investigates the performance of cyclic prefixed single carrier with frequency domain equalization (SC-FDE) transmission over the ultra-wideband (UWB) propagation environment. The performance of SC-FDE over IEEE 802.153a UWB channel models is analyzed, simulated and compared with that of impulse based single carrier UWB (SC-UWB) and multicarrier UWB (MC-UWB) employing orthogonal frequency-division-multiplexing (OFDM). The impact of channel coding with different code rates on the performance of OFDM and SC-FDE in UWB is also studied. Our results demonstrate conclusive performance advantage of the SC-FDE scheme, especially when implementation issues such as low complexity and low power consumption for UWB are taken into account.

Energy detection of frequency-shift keying (FSK) signals is the optimum noncoherent detection technique yielding a minimum bit-error rate (BER) on the additive white Gaussian noise channel. It is usually used when carrier phase estimation is difficult. When FSK signals are passed through a frequency-selective multipath fading channel, the multipath delay in the channel results in a multitone waveform being received during each signaling interval. An effective practical sequence estimation receiver for this situation is proposed. It makes use of energy detectors followed by a Viterbi (1979) or sequence estimator that uses an energy difference metric. Statistical properties of the detection variable are derived. Analytical upper and lower bounds on the BER are derived and the results compared with computer simulations to show the effectiveness of the technique.

For channels which suffer predominantly from additive noise and intersymbol interference, the decision-feedback equalizer has provided a relatively simple solution for reducing the effects of interfering symbols at the input to the decision device. A technique is developed that enables fast, accurate calculation of the error performance of decision-feedback equalization for a number of channel models. The method is to calculate the n-step transition probability for an associated Markov process and then use this transition probability as an approximation to the stationary probability distribution. For systems with finite memory, it is proved that the method converges. If the signal-to-noise ratio (SNR) is high and the signal amplitude is more than twice the worst-case interference, it is shown that the convergence is rapid. Numerical results indicate that the convergence is rapid enough to make this an efficient method of calculation, even for channels for which the interference does not fully satisfy this condition. Two examples are given here, but the technique has been tested on most of the examples that have been presented in the literature. The method yields results in closer agreement with simulation results than previous results obtained using bounding techniques, especially at low to moderate SNRs, and requires less computation.

The energy detection of continuous phase frequency shift keying (CP-FSK) signals is the optimum noncoherent detection technique yielding a minimum bit error rate (BER) on the additive white Gaussian noise (AWGN) channel. This scheme is usually used when carrier phase estimation is difficult. When a CP-FSK signal is passed through a frequency selective multipath fading channel, inter-symbol interference (ISI) is introduced which distorts the received signal waveform. However, this ISI can be compensated and the BER improved by use of sequence estimation at the output of the energy detectors. In this paper, we derive an analytical upper bound as well as a lower bound on the BER for this scheme on the multipath fading channels and compare the results with the computer simulation to show the effectiveness of the technique.

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.

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.

Several treatments of interference problems are examined with a view to determine whether doubtful mathematical assumptions about the existence of probability density functions affect the conclusions. Most derivations can be recast so that the existence of a density function is not necessary for the conclusions to be valid.

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.

The performance of trellis-coded FSK modulation with noncoherent detection is presented, as applicable to a frequency-hopped spread spectrum communication system or a conventional FSK system. Nonorthogonal tone spacing is considered as a parameter to control bandwidth occupancy of the hopped signal and to allow an increased number of users. Soft decision decoding with a maximum metric decoder is employed. The metrics considered are the energy metric with and without perfect jammer state information as well as a practical self-normalized metric that compensates for jamming or interference. Performance analyses for full and partial band, and both noise and multitone jammings are presented. For nonorthogonal tone spacing, the signals are correlated, and so Chernoff bounds on the pairwise error probability for energy detectors with correlated signals are presented and evaluated. These bounds supplement earlier performance estimates for trellis coded FSK. To assess the tightness of the bounds, simulations have been carried out, with results that come within 1 to 3 dB of the bounds. System performance is evaluated for 2, 4 and 8-state trellis codes with tone spacings of 1/3T, 1/2T, 2/3T and 1/T Hz.>

The symbol error probability of Gaussian MSK using differential detection in a Rician fast fading channel is investigated. In the analysis, the effect of the infinite sequence of intersymbol interference inherent in this modulation is included exactly, and the performance can be evaluated at narrow shaping bandwidths where the intersymbol interference is extensive. Numerical results are presented for parameters typically encountered in the satellite-to-mobile channel.>

Sums of infinite sequences of weighted binary random variables arise in communications problems involving signal-dependent interferences. In many cases of practical importance, the distribution functions of these sums are singular and often of Cantor type; they are continuous but do not have a density function. For this reason, special methods of calculating expectations are needed. Results of this type are derived. The method is used to compute error probabilities for differential detection of minimum shift keying, and for noncoherent detection of frequency shift keying. In each case the model assumed is a Rician fading channel.>

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.>

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.>

A derivation of the joint distribution of the amplitude and angle of a sinusoid in Gaussian noise is given. No assumptions about the structure of the noise at the output of the post-detection filter are required. However, it is assumed that the Gaussian noise at the input is generated by passing white noise through the bandpass equivalent of a single-pole low-pass filter. Hence, the noise is a two-dimensional Ornstein-Uhlenbeck or Gauss-Markov process. In practice, a higher-order bandpass filter would be encountered in FM reception. However, the approach is intended as a first step towards the goal of an understanding of the phase process. The method used is to derive and solve the Fokker-Planck partial differential equation that governs the joint distribution. An explicit integral formula for the solution is obtained. The integral is, in general, rather difficult to evaluate. A further integration over amplitude is required if the angle distribution rather than the joint distribution is required. For some special-cases, where the filtering time is large and the signal-to-noise power ratio is very large or very small, explicit approximate expressions are given.>

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.>

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.

Of the more band-efficient constant envelope digital modulations, duobinary FM is attractive in terms of its potential error performance, as indicated by the minimum distance of the signal structure. In this paper, the error performance of narrow-band duobinary FM, with discriminator detection in an additive Gaussian noise background, is evaluated for a range of system bandwidthsBTand frequency deviation ratiosh. The effects of intersymbol interference, due to the restricted bandwidth, are taken into account in the analysis. In addition, at the narrower bandwidths,0.5 \leq BT < 1.0, the filtered background noise is correlated, and these effects are included. It is shown that with the usual duobinary detector, "clicks," which are a major contributor to errors in conventional digital FM, do not contribute significantly to errors for the low frequency deviation ratios which are commonly used. The error rate theory agrees well with results obtained experimentally. The deviation ratios that give the best error performance for a given system bandwidth are presented. In a narrower bandwidth such asBT = 1/2, where duobinary FM is proposed, duobinary FM with a frequency deviation ratio ofh = 0.7performs better than binary FM.

Approximately 400 sets of field measurements were made on public switched telephone network connections from a location in Canada, to two locations in Australia and to 11 locations spread across the United Kingdom, to observe the properties of echos pertinent to high-speed full-duplex voiceband data transmission. The observations have been analyzed to give statistics on the duration, delay, and level of talker echo. Also, results on listener echo are included. The stability of echos is important in the design of echo cancelling and full-duplex digital transmission equipment, and so data are presented on the modulations of the echo or the phase roll that was observed and their stability. Results are included for calls placed over both cable and satellite circuits.

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-timeNT. 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.

This paper gives a straightforward method of obtaining an explicit expression for the spectrum of a correlative encoded digital FM signal. An investigation of the band occupancy for various encoding schemes with rectangular, as well as raised-cosine pulse shaping, is carried out. Correlative encodings that are spectrally more efficient than minimum shift keying (MSK) and that promise an improved error performance are shown. In addition, if a small degradation in error performance is tolerated, substantial increases in band efficiency are possible. For example, with the polynomial(1 + 2D + D^{2})/4the signal is spectrally 47 percent more efficient than MSK and with an SNR performance degradation of only 1.1 dB.

This paper presents a technique for optimizing the baseband pulse shapes in digital angle modulated signals to minimize the fraction of out-of-band power for a given channel bandwidth. As examples of practical interest, the optimization is carried out for channel bandwidths up to three times the bit rate and for the range of modulation indices usually encountered in digital transmission. Results for MSK-type signals appear as a special case.

Some numeric results are presented from a distribution-free analysis of how many design patterns to sample from each of two classes, for stationary, discrete-measurement pattern classifiers. A table of design sample size partitions is presented, that maximizes the mean accuracy, given the total number of design patterns and the prior class probabilities. The maximization is also over the measurement complexity (total number of resolvable measurement values). It is shown that the optimal sample size partitions are biased, in that fewer patterns should be taken of the more probable class than is implied by the prior class probabilities. An insensitivity to nonoptimal partitions is exhibited, which appears to be similar to that seen in other Bayesian decision problems.

The calculation of the autocorrelation function of the output of a randomly frequency-modulated oscillator with a non-linear tuning characteristic is similar to the calculation of the characteristic function of a functional of the form\int_{I}h(t', \tau) V(y(t')) dt'. This functional has arisen in a number of other stochastic problems, and so the techniques which have been applied to these problems may be used to obtain results for the nonlinear frequency-modulator. For example, if as a first approach to a nonlinear frequency-modulation a linear plus square-law modulator characteristic and a Gaussian modulating signal are assumed, a technique similar to that used in the analysis of the square-law detector by Kac and Siegert, and Emerson, may be applied. Then an expression for the autocorrelation function of the oscillator output is obtained in terms of two finite Wiener-Hopf integral equations. For an important class of kernels, these equations may be solved and the autocorrelation function evaluated. As an example, the calculation is carried out for a low-pass modulating signal. Results for phase modulation are included also.