Error performance of a digitally processed binary ESK frequencyhopping receiver in the presence of large Doppler

Analysis is made of the effects of Doppler on the error rate performance of a low data rate binary FSK frequency hopping receiver, employing a discrete Fourier transform (DFT) technique for baseband detection. Bit detection decision is made by locating the maximum of the DFT outputs which, in the frequency domain, are assumed to be separated by 1/T where T is the bit period. Both the worst case and average error performances are obtained and presented as a function of E_b/N₀ for various values of M where E_b/N₀ is the signal bit energy-to-noise density ratio and M is the degree of freedom associated with the Doppler uncertainty window. The E _b/N₀ degradation as a function of M is also presented     

Roundoff error analysis of the discrete Wigner distribution usingfixed-point arithmetic

The issue of roundoff noise effects in the implementation of the discrete Wigner distribution using fixed-point arithmetic is addressed. The sign-magnitude number representation is assumed throughout the analysis. The measure of roundoff noise effects in an algorithm is the output noise-to-signal ratio. Using a statistical model, an analytical expression of the noise-to-signal ratio is derived as a function of the wordlength b and the transform length N. The noise-to-signal ratio is obtained by evaluating the signal and noise powers at different points in the algorithm, then reflecting to the output both signal and noise powers. Based on the derived noise-to-signal ratio is is noted that if the transform length is doubled, then) one additional bit is required in the wordlength to maintain a constant noise-to-signal ratio. It is demonstrated through the software simulations that the predicted noise-to-signal ratio is a good closed-form estimate of the `true' roundoff error. It is also found from the simulation that the wordlength b and the transform length N=2^v must satisfy the condition b- v⩾4     

Performance limits of coded multilevel DPSK in cellular mobileradio

Performance limits of coded multilevel differential PSK (MDPSK) in multipath Rayleigh fading channels are described. The simple Gaussian metric is assumed for reasons for practicality even though it is not the maximum likelihood. The channel cutoff rate, R₀ of MDPSK is analyzed based on the metric. Account is taken of additive white Gaussian noise (AWGN), cochannel interference, and multipath channel delay spread. For the analysis of the spectrum efficiency of a cellular mobile radio system employing coded MDPSK, its service area is defined as the area in which, with a bit rate of R information bit/symbol (R⩽R₀), reliable communications are possible. Three optimal information bit rates are determined from the channel cutoff rate to minimize the required average signal energy per information bit-to-noise power spectral density ratio (E_b/N₀) to maximize the tolerable r.m.s. delay spread τ_r.m.s. and to maximize the spectrum efficiency     

On minimizing the peak-to-average power ratio for the sum of N sinusoids

A new derivation is presented of a previously known relationship for phasing N equal-amplitude, equally spaced (in frequency) sinusoids so that the peak-to-average power ratio of their sum is 2.6 dB. The method of derivation provides intuitive insight into why this result is possible, and shows that the 2.6 dB figure is obtained independently of N as long as N is large. Any phase or frequency modulation can be applied simultaneously to all N sinusoids without altering this result     

Continuous phase quadrature phase shift keyed signaling techniquewith coding

A continuous phase quadrature phase shift keyed (CPQPSK) modulation technique is presented. This method utilizes a conventional QPSK modulator and a phase trajectory converter to approximate M=4, h=1/4 continuous phase signal and allows low cost, low complexity, and high rate (>1 Gbit/s) CPM modem implementation for bandwidth efficient transmission through nonlinear satellite channels. Using a communications analysis computer program it has been found that CPQPSK has 99 percent out-of-band power of 0.8R (MSK has 99 percent out-of-band power of 1.2 R where R is defined as bit rate), continuous phase trajectories, and nearly constant envelope amplitude. Simulation of realistic hardware designs indicate that the CPQPSK will require an Eb/No of 14 dB to achieve a bit error rate (BER) of 10^-6. Forward error correcting techniques using block codes with an overhead of 10 percent indicate that the Eb/No requirements can be reduced to 11.2 dB for 10^-6 BER     

Nonequiprobable signaling on the Gaussian channel

Signaling schemes for the Gaussian channel based on finite-dimensional lattices are considered. The signal constellation consists of all lattice points within a region R, and the shape of this region determines the average signal power. Spherical signal constellations minimize average signal power, and in the limit as N →∞, the shape gain of the N-sphere over the N-cube approaches πe/6≈1.53 dB. A nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension. A signal constellation, Ω is partitioned into T subconstellations Ω₀ , . . ., Ω_τ-1 of equal size by scaling a basic region R. Signal points in the same subconstellation are used equiprobably, and a shaping code selects the subconstellation Ω_i with frequency f_i. Shaping codes make it possible to achieve any desired fractional bit rate. The schemes presented are compared with equiprobable signaling schemes based on Voronoi regions of multidimensional lattices. For comparable shape gain and constellation expansion ratio, the peak to average power ratio of the schemes presented is superior. Furthermore, a simple table lookup is all that is required to address points in the constellations. It is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework     

A novel multilevel coherent optical system: 4-quadrature signaling

A novel multilevel coherent optical system is proposed. It is based on the exploitation of the property that the electromagnetic field propagating in a single-mode optical fiber can be represented by a four-dimensional vector whose components are the phase and quadrature terms of the two polarization components of the electrical field. This allows a wider use of the resources of the electromagnetic field for information transmission in order to obtain a spectrally efficient modulation format with a limited end. The net performance gain with respect to multilevel amplitude and phase modulation (N-APK) and N-PSK increases with an increase in the number of levels N. For instance, for N=32 the gain is 1.6 and 7.7 dB with respect to N-APK and N-PSK systems. The effect of laser phase noise on the system performance is evaluated     

Design of bipolar imaging devices (BASIS): analysis of random noise

A design methodology for a bipolar imaging device, the base-stored image sensor (BASIS), has been established by theoretical analysis and experimental verification for random noise. The random noise in BASIS is dominated by the shot noise in readout and transient reset operation. The theoretical analysis has been carried out by introducing the probability density functions for these operations. The readout noise depends on the base-to-collector junction capacitance C_bc , the emitter common current gain h_FE, the storage capacitor C_T, and the emitter voltage V _E. The reset noise has been confirmed to be given by thermal noise. The theoretical results coincide well with the experimental results obtained by TEG devices. An expression for the S/N ratio has been derived theoretically. It is found that h_FE should be made as large as possible and ( C_bc+C_be) as small as possible to improve the S/N ratio for random noise, where C _be is the base-to-emitter junction capacitance     

Diffusion and noise in GaAs material and devices

The variation of the diffusion coefficient D(E) versus the electric field strength E is determined at 300 K in n-type GaAs (N_D=3×10^-17 cm^-3 ), using pulsed high-frequency noise measurements. D(E) is found to increase slightly at low field, then to decrease down to one tenth of its ohmic value near the threshold field. Long (⩾4 μm) real n⁺-n-n⁺ Gunn diodes, with an arbitrary doping profile, can be modeled. Comparisons are made, and excellent agreement is found, between experimental and theoretical characteristics of two real diodes, with notch and with gradual doping profiles. The doping profile N_D(x ) is shown to have a considerable influence on the diode behavior, in regard to the electric field profile as well as the noise characteristics. Using the impedance field method, the noise current is modeled and found to by very sensitive in the D(E) variation law, in particular in the range of 2.5-4 kV/cm. The agreement between the experimental noise and the computed noise of real diodes is quite satisfactory when using the D(E) determined     

Digital frequency estimation in burst mode QPSK transmission

In burst digital transmission using PSK (phase shift keying) modulation with coherent detection, the recovery of the carrier reference phase and the symbol clock is a key aspect. If all users have a common clock synchronization, symbol timing needs not to be recovered in each burst. A digital processor for carrier recovery without preambles, in the presence of frequency offset, is considered. As an example, a 2 Mb/s QPSK transmission system is considered in which E _b/N_o=10 dB, and the burst and estimation interval length L=15. Using the algorithm described and averaging eight successive estimated frequency offsets, in order to eliminate anomalous errors, the BER (bit error rate) degradation is equal to 0.14 dB when Δf=20 kHz     

Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_m for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E_b/N₀) and E_b is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

The sublinear relationship between index change and carrier densityin 1.5 and 1.3 μm semiconductor lasers

The carrier-induced index change was measured using a novel injection-reflection technique in combination with differential carrier lifetime data. The observed relation between index change and injected carrier density at bandgap wavelength is nonlinear and is approximately given by δn_act=-6.1×10^-14 ( N)^0.66 for a 1.5-μm laser and δn _act=-1.3×10^-14 (N)^0.68 for a 1.3-μm laser. The carrier-induced index change for a 1.3-μm laser at 1.53-μm wavelength is smaller and is given by δn _act=-9.2×10^-16 (N)^0.72      

A 16-b 320-kHz CMOS A/D converter using two-stage third-orderΣΔ noise shaping

The design and measured performance of a two-stage third-order ΣΔ (sigma-delta) analog-to-digital (A/D) converter is described. The A/D converter achieves a 96-dB dynamic range and a maximum signal-to-noise-plus-distortion ratio (S/(N+ D)) r.m.s./r.m.s. of 93 dB with 320-kHz output rate and an oversampling ratio of 64. An analysis of the integrator gain error is presented. The modulator is realized in a 1.2-μm double-metal single-poly CMOS process with an active area of 1.6 mm². This modulator operates from a 5-V power supply and a single reference voltage     

Efficient fiber-optic structure with applications to sensor arrays

A fiber-optic structure which performs the functions of sensing and telemetry with a minimum of components and with efficient utilization of optical power is described. This structure, referred to as a recursive lattice array, requires N+1 couplers and N fiber sensing loops to realise N sensors. It is shown that for pulsed operation, the duty cycle approaches 100% and the maximum sampling rate is 1/(N+1)T, with T denoting the transit time of a single sensing loop. In the ideal (lossless) case, the power returned to the receiver from any sensor is -10 log 2N referred to the input, compared with previously reported, nonrecursive structures for which this figure-of-merit is -20 log N. Expressions for the optimum coupler tap ratios for two different cases of interest are derived: first, for the case in which all the coupler tap ratios are equal, and second, for the case where they may assume different values. The magnitudes of decaying recirculating terms which add noise to the desired primary returns from each sensor are estimated. Methods for reducing the magnitudes of the undesired terms are outlined     

Upper bounds on capacity for a constrained Gaussian channel

A low-pass and a bandpass additive white Gaussian noise channel with a peak-power constraint imposed on otherwise arbitrary input signals are considered. Upper bounds on the capacity of such channels are derived. They are strictly less than the capacity of the channel when the peak-power constrain is removed and replaced by the average-power constraint, for which the Gaussian inputs are optimum. This provides the answer to an often-posed question: peak-power limiting in the case of bandlimited channels does reduce capacity, whereas in infinite bandwidth channels it does not, as is well known. For an ideal low-pass filter of bandwidth B, the upper bound is Blog 0.934P/(N₀B) for P/( N₀B)≫1, where P is the peak power of the input signal and N₀/2 is the double-sided power spectral density of the additive white Gaussian noise     

A linear lightwave Benes network

The authors consider linear lightwave networks with a single waveband that have N inputs, each with a transmitter, and N outputs, each with a receiver, interconnected by optical links, broadcast stars, and wavelength-independent 2×2 switches. The transmitters and receivers can tune to C different wavelengths. The authors describe a rearrangeably nonblocking network that is a modification of the Benes network and uses transmitters that are fixed tuned and switches with two states. The network uses [1+o(1)] N/log₂(N/C) switches, which is shown to be nearly the minimum number. It is also shown that, if C =o(log N), then a rearrangeably nonblocking network requires [1+o(1)]Nlog₂N switches even if the switches have more than two states     

Maximum likelihood estimation of the parameters of discretefractionally differenced Gaussian noise process

A maximum-likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced Gaussian noise from an observation set of finite size N. The procedure does not involve the computation of any matrix inverse or determinant. It requires N²/2+O(N) operations. The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d. A Cramer-Rao bound on the variance of any unbiased estimate of d obtained from a finite-sized observation set is derived. It is shown experimentally that the maximum-likelihood estimate of d is unbiased and efficient when finite-size data sets are used in the estimation procedure. The proposed procedure is extended to deal with noisy observations of discrete fractionally differenced Gaussian noise     

Quantization loss in convolutional decoding

The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E_b/N₀) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E_b/N₀ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL     

The Cramer-Rao lower bound for signals with constant amplitude andpolynomial phase

The authors derive the Cramer-Rao lower bound (CRLB) for complex signals with constant amplitude and polynomial phase, measured in additive Gaussian white noise. The exact bound requires numerical inversion of an ill-conditioned matrix, while its O(N ^-1) approximation is free of matrix inversion. The approximation is tested for several typical parameter values and is found to be excellent in most cases. The formulas derived are of practical value in several radar applications, such as electronic intelligence systems (ELINT) for special pulse-compression radars, and motion estimation from Doppler measurements. Consequently, it is of interest to analyze the best possible performance of potential estimators of the phase coefficients, as a function of signal parameters, the signal-to-noise ratio, the sampling rate, and the number of measurements. This analysis is carried out     

Truncation length for Viterbi decoding

A bound is derived and analyzed for the bit error rate (BER) of a Viterbi decoder with survivor truncation. Estimates of the SNR (signal-to-noise ratio) loss on the AWGN (additive white Gaussian noise) channel due to truncation are obtained for convolutional codes. Larger truncation lengths are required than the smallest value that does not effectively decrease the code's free distance, especially at low E _b/N₀