Limiter-discriminator detection of a coherent optical heterodyneM-ary CPFSK receiver

The performance of a coherent optical M-ary continuous-phase frequency-shift-keying (CPFSK) receiver using limiter-discriminator (L-D) detection is investigated. It is shown that L-D detection of CPFSK optical signals offers the best performance for a large normalized IF beat spectral linewidth, ΔνT. When the modulation index is unity, the receiver is immune to laser phase noise and can produce (M/4) exp (-SNR) symbol error probability, which may be considered as the upper bound if the optimal modulation index is used (SNR is the signal-to-noise ratio per symbol). Optimum modulation indexes are 0.8 and 1 at ΔνT=1% and ΔνT=2%, respectively, for M=4, 8, and 16     

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     

Multiple differential detection of continuous phase modulationsignals

A sequence estimation algorithm for the differential detection of the continuous phase modulation (CPM) signals, yielding significant gains in BER performance and with considerable resistivity to fading, is introduced. These advantages, along with the reduced hardware complexity, low cost, and fast synchronization which characterize the differential detector, make the proposed receiver useful for land mobile radio and mobile-satellite communications. The new receiver is based on multiple differential detection. The multiple differential detection strategy provides the decoder with more information regarding the transmitted data and applies a noise decorrelation process on the received signal, useful to the sequence estimation. The algorithm is derived in a general form, and can be applied on any CPM scheme, with any degree of complexity. The authors have evaluated the receiver for two of the most popular CPM schemes, the tamed frequency modulation (TFM) and Gaussian minimum-shift keying (GMSK) (with B₁ T=0.25), in the presence of additive white Gaussian noise (AWGN) and Rician fading. The BER performance evaluation results indicated significant gains and considerable reduction of error floors. In AWGN improvements close to 9 dB have been verified     

Coding of optical on-off keying signals impaired by phase noise

The benefits of coding for an optical communication system that employs binary on-off keying and heterodyne detection are quantified. The system is impaired by laser phase noise as well as by additive white Gaussian noise (AWGN). A receiver structure especially designed to mitigate the effects of phase noise in the presence of AWGN is assumed. This special receiver structure requires a wider-band front-end IF filter than would be required for a phase-noise-free signal. The results, computed for several different coding schemes, indicate that the benefits of coding are large and the costs are small. For a linewidth-to-bit-rate ratio (βT) of 0.64 (for example, 45 Mb/s and 29 MHz linewidth), a half-rate binary code that can correct 3 bit errors provides a 50% reduction in the required IF filter bandwidth (and, therefore, the required IF) and about 5 dB of reduction in required laser power. The benefits of coding are greatest under high-βT conditions, corresponding to low bit rates where coders and decoders are most practical to implement     

Spectral efficiency of optical FDM systems impaired by phase noise

The required frequency spacings between channels in an optical frequency division multiplexing (FDM) network are considered. The minimum permissible spacings consistent with meeting bit error rate (BER) objectives are derived. The assumed transmission uses on-off keying (OOK), at a data rate 1/T (in bits per second), via external modulation of a laser source having linewidth β (in hertz). The assumed receiver consists of an optical channel selection filter followed by a p-i-n photodiode and a postdetection integrate-and-dump circuit. The analysis estimates the adjacent channel interference (ACI)-induced floor on BER for the middle of three FDM channels, as a function of frequency spacing and linewidth-to-bit rate ratio (βT). For BER=10^-9 and βT ranging from 0.32 to 5.12, the required channel spacing ranges from 5.2 to 27.5 bit rates. The multiplying factors associated with using (wide-deviation) frequency shift keying (FSK), coherent (heterodyne) detection, and infinitely many FDM channels, respectively, are estimated to be 2.0, at most 3.0, and at most 1.37     

Error probability of M-ary FSK with differential phasedetection in satellite mobile channel

Formulas are derived for the error probability of M-ary frequency shift keying (FSK) with differential phase detection in a satellite mobile channel. The received signal in this channel is composed of a specular signal, a diffuse signal, and white Gaussian noise; hence, the composite signal is fading and has a Rician envelope. The error probability is shown to depend on the following system parameters: (1) the signal-to-noise ratio; (2) the ratio of powers in the specular and diffuse signal components; (3) the normalized frequency deviation; (4) the normalized Doppler frequency; (5) the maximum normalized Doppler frequency; (6) the correlation function of the diffuse component, which depends on the normalized Doppler frequency and the type of the antenna; (7) the number of symbols; and (8) the normalized time delay between the specular and diffuse component (t _d/T) where 1/T is the symbol rate. Except for T_d/T, all normalized parameters are the ratios of the parameter value and symbol rate. The Doppler frequency depends on the velocity of the vehicle and the carrier frequency. The error probability is computed as a function of the various parameters. The bit error probability is plotted as a function of signal-to-noise ratio per bit and other system parameters     

Adjacent channel and cochannel interferences in CPFSK systems withnonlinear transmitters and limiter-discriminator detection

The performance of continuous-phase FSK (frequency-shift keying) systems with rectangular modulation pulse shaping and limiter-discriminator detection is analytically evaluated in the presence of transmission nonlinearities as well as adjacent channel and cochannel interference. Consideration of modulation pulses with length τ, shorter than symbol time, T, is investigated. The algorithm developed to evaluate bit-error probability shows that the choice τ/T=1, and even more so in the presence of adjacent channel interference. Moreover, for τ/T=0.5, numerical results are reported that describe system performance under different working conditions and can be used to develop design criteria     

The bandwidth performance of a two-element adaptive array withtapped delay-line processing

The bandwidth performance of a two-element adaptive array with a tapped delay line behind each element is examined. It is shown how the number of taps and the delay between taps affect the bandwidth performance of the array. An array with two weights and one delay behind each element is found to yield optimal performance (equal to that obtained with continuous-wave interference) for any value of intertap delay between zero and T₉₀/B, where T ₉₀ is a quarter-wavelength delay time and B is the fractional signal bandwidth. Delays less that T₉₀ yield optimal performance but result in large array weights. Delays larger than T₉₀/B yield suboptimal signal-to-interference-plus-noise ratio when each element has only two weights. For delays between T₉₀/B and 4T₉₀/B , the performance is suboptimal with only two taps but approaches the optimal if more taps are added to each element. Delays larger than T₉₀/B result in suboptimal performance regardless of the number of taps used     

Effect of conduction-band discontinuity on lasing characteristicsof 1.5 μm InGaAs/In(Ga)AlAs MQW-FP lasers

The characteristic temperature (T₀), relaxation frequency (f_r), differential gain (dg /dn) and nonlinear gain coefficient (ϵ) of 1.5-μm InGaAs/In(Ga)AlAs multiple-quantum-well (MQW) Fabry-Perot (FP) lasers grown by gas source molecular beam epitaxy (GSMBE) are reported. It is found that T₀ is little affected by the difference in the conduction band discontinuity. A maximum T₀ value of 86 K is obtained. The dg/dn and ϵ∈ were calculated from the slope of the f_r versus √ power plot and the damping K-factor. It is demonstrated that dg/dn and ϵ of InGaAs/In(Ga)AlAs MQW lasers increase with an increase in the conduction band discontinuity     

A multiple scattering solution for the effective permittivity of asphere mixture

A recursive algorithm for calculating the exact solution of a random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a one-sphere T matrix. The scattering from two spheres is expressed in terms of two-sphere T matrices, which are related to the one-sphere T matrix. A recursive algorithm to deduce the (n+1)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N² algorithm rather than the normal N³ algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible     

Optimization of offset for OQPSK with time limited pulses

The optimum offset for offset quaternary phase shift keying (OQPSK) in the presence of carrier phase error is determined for some time limited pulse shapes. It is shown that, for certain pulse shapes, T/2 is optimum in a minimum probability of error sense. In the case of bipolar pulse shaping it is seen that T/2 is not the optimum. It is shown that OQPSK with shaped pulses may be much more robust with respect to carrier phase errors than OQPSK with non-return-to-zero pulses     

A storage-efficient method for solving banded Toeplitz systems

A method is presented for solving the banded Toeplitz system Tx=y by decomposing T into its asymptotic upper and lower triangular factors (which are banded and Toeplitz) and a rank-p correction matrix, where p is the bandwidth of T. This way of representing T requires only O(p²) words of storage and allows computation of x in O(2Np) operations. A similar method is presented for the case in which T is bi-infinite and y is zero outside a finite region     

Data predistortion techniques using intersymbol interpolation

Two data predistortion techniques are presented that compensate for high-power amplifier (HPA) nonlinearities in digital microwave radio systems by employing quadrature amplitude-modulation (QAM) signal formats. The first one is a T/2-spaced predistortion technique that ensures distortion-free HPA output at two points per symbol interval T. The second is a T/3-spaced predistortion technique which cancels nonlinear distortion at the HPA output at three points per symbol interval. As opposed to conventional data predistortion, which can only compensate for warping of the signal constellation, the new techniques are effective against intersymbol interference. Using the 64- and 256-QAM signal constellations, it is shown that the proposed techniques lead to a very efficient utilization of the available HPA power. It is shown that, of the two techniques, the T/3-spaced data predistortion employs narrower transmit-pulse shaping and achieves higher protection against adjacent-channel interference at the expense of some additional complexity     

Multistable fiber-optic Michelson interferometer with electroopticfeedback exhibiting 95 stable states

The multistable behavior of a fiber-optic Michelson interferometer with electrooptic feedback using a piezoelectric phase modulator is investigated. A linear stability analysis of the third-order differential equation used to describe the system reveals the number of stable states increases with the ratio τ/T of the system time constant (τ) and the feedback delay time (T). In laboratory investigations 95 stable states were achieved with τ/T>50     

Convergence and steady-state behavior of a phase-splittingfractionally spaced equalizer

The eigenstructure, the initial convergence, and the steady-state behavior of a phase-splitting fractionally spaced equalizer (PS-FSE) are analyzed. It is shown that the initial convergence rate of a T/3 or, in general, a T/M, PS-FSE employing the least-mean-square (LMS) stochastic gradient adaptive algorithm is half that of a symbol rate equalizer (SRE) or a complex fractionally spaced equalizer (CFSE) with the same time span. It is also shown that the LMS adaptive PS-FSE with symbol rate update converges to a Hilbert transformer followed by a matched filter in cascade with an optimal SRE, and thus forms an optional receiver structure. The LMS PS-FSE is computationally more efficient and introduces less system delay than the CFSE     

On linear inductance- and capacitance-time conversions usingNIC-type configurations

The problem of linear inductance- and capacitance-time (L/T, C/T) conversion is approached through the systematic study of four approaches to building astable multivibrators using piecewise linear resistances obtained from one operational amplifier (OA) negative impedance converter (NIC) configuration. A new L/T converter with grounded inductance is found. Formulas for the time period taking into consideration the losses as well as the OA saturation output resistance are derived     

A T1 ones-density controller based on finite-statemachines

T1 clock recovery equipment requires that transmitted data not contain long sequences of 0 bits. For this reason, equipment that interfaces to T1 networks must meet a ones-density specification that ensures that 1 bit occurs frequently enough. Most schemes for meeting this specification require a substantial amount of overhead that consumes a significant portion of the available bandwidth. In this paper, and approach that meets the ones-density requirement with very little wasted bandwidth is described. Two practical coding schemes based on the approach are presented. The first, a block coding scheme, requires an overhead rate on the order of one bit per T1 frame, along with a delay of several frames. In an error-free channel, it introduces some errors, the rate of which is made acceptably low by using sufficient delay and overhead. In an errored channel, extension of errors is negligible. The second scheme, a sliding code scheme, requires an overhead rate on the order of a fraction of a bit per T1 frame, along with a delay of only several bit times. In an error-free channel, the rate of errors introduced is negligible. In an errored channel, approximately one out of every 2000 channel errors is extended into a burst, the length of which can be made acceptably low by using sufficient overhead     

Optimization of signal sets for partial-response channels. II.Asymptotic coding gain

For Pt. I see ibid., vol.37, no.5, p.1327-141 (1991). For a linear, time-invariant, discrete-time channel with a given transfer function H(f), and information rate R bits/ T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2^RK inputs of length K that maximizes the minimum l₂ distance between pairs of outputs. The author studies the minimum distance between outputs, or equivalently, the coding gain of optimal signal sets as K→∞. He shows how to estimate the coding gain, relative to single-step detection, of an optimal signal set length K when K is large     

Bounds on maximum throughput for digital communications withfinite-precision and amplitude constraints

The problem of finding the maximum achievable data rate over a linear time-invariant channel is considered under constraints different from those typically assumed. The limiting factor is taken to be the accuracy with which the receiver can measure the channel output. More precisely, the following problem is considered. Given a channel with known impulse response h(t), a transmitter with an output amplitude constraint, and a receiver that can distinguish between two signals only if they are separated in amplitude at some time t ₀ by at least some small positive constant d, what is the maximum number of messages, N_max, that can be transmitted in a given time interval [0,T]? Lower bounds on N_max can be easily computed by constructing a particular set of inputs to the channel. The main result is an upper bound on N_max for arbitrary h(t). The upper bound depends on the spread of h(t), which is the maximum range of values the channel output may take at some time t₀>0 given that the output takes on a particular value α at time t=0. Numerical results are shown for different impulse responses, including two simulated telephone subscriber loop impulse responses     

Use of a microwave cavity for sensing dielectric properties ofarbitrarily shaped biological objects

A rectangular waveguide resonator operating in the H₁₀₅ mode at 3.2 GHz is used in determining the change in resonant frequency, ΔF, and the Q factor of the cavity, ΔT , when measured with and without single corn kernels of various shapes and dimensions. By measuring those variables for a kernel oriented in two positions differing by a 90° rotation with respect to the maximum E-field vector, the average values of ΔF and ΔT are found to be independent of shape. The ratio ΔF/ΔT is independent of size and is a function of the material properties (ε'-1)/ε". This function is shown to be related to the material density, moisture content, or other characteristics when all other properties except the one selected remain unchanged