Interleaved concatenated coding for the turbulent atmosphericdirect detection optical communication channel

The performance of two concatenated coding systems using a K =3, R=1/2 convolutional inner code and a Reed-Solomon (RS) (15, 9) or (15, 7) outer code was measured over a 5.76-km-long atmospheric direct detection optical communication channel. Inner code interleaving of 100 μs combined with outer code interleaving of 240 bits (60 RS symbols) was found to be sufficient to obtain a decoded BER of less than 10^-6 under conditions of moderate channel turbulence and an average of 6-10 detected photons per channel bit     

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     

Impact of finite frequency deviation on the performance ofdual-filter heterodyne FSK lightwave systems

A detailed theoretical analysis is given of the impact of finite frequency deviation on the sensitivity of dual-filter heterodyne frequency-shift-keying (FSK) lightwave systems. The analysis provides closed-form signal-to-noise ratio (SNR) results for estimating the bit-error-ratio (BER) performance of the system. These closed-form results provide an insight into the impact of finite frequency deviation 2Δf_d, laser linewidth Δν, bit rate R_b, and IF filter bandwidths on the system performance. Simulation results indicate that the accuracy of the approximate theory presented is within 1 dB for linewidths up to 22% when BER=10^-9. It is shown that there is a well-defined relationship between the choice of frequency deviation and the tolerable amount of laser phase noise. The sensitivity degradation can be very severe for a fixed linewidth as the frequency deviation gets smaller     

Performance analysis of optical heterodyne PSK receivers in thepresence of phase noise and adjacent channel interference

A phase-shift-keying (PSK) optical heterodyne receiver using synchronous detection by means of a Costas phase-locked loop (PLL) is investigated. Taking into account the laser phase noise and adjacent channel interference (ACI), an expression of the phase error variance is derived and error probability calculation is performed. Plots of the error probability versus the number of photons per bit are presented as a function of the optical domain channel spacing (D) and for several linewidth-to-bit-rate ratios (δf/R_b ). Relative sensitivity penalties, based on the performance with and without ACI, are evaluated for several combinations of D and δf/R_b. It is shown that, if lasers with larger linewidths are used, the frequency separation between optical carriers has to be increased in order to allow the same relative sensitivity penalty     

Combined effects of phase sweeping transmitter diversity andchannel coding

A novel transmitter diversity scheme that generates forced fading to improve the performance of channel coding is proposed and investigated. Since the required phase sweeping frequency is much smaller than the transmission bit rate, bandwidth expansion is negligible. A sinusoidal phase sweeping function ΔΘ sin(2πf_Ht) is employed in laboratory experiments using 32 kbit/s quarternary differential phase shift keying (QDPSK) with differential detection and BCH(23,12) code. It is shown that ΔΘ=200° and f_H=67 Hz can be used when m (interleaving depth)=10 b. Hence, excessively long interleaving is not required by the use of transmitter diversity. Under very slow Rayleigh fading (f_D=1 Hz), a measured improvement of 4.8 dB is obtained at a word error rate of 10^-2 without receiver diversity. Applications include paging systems that require very simple receivers     

Noise caused by semiconductor lasers in high-speed fiber-opticlinks

Theoretical and experimental results are presented for the signal-to-noise (S/N) ratio caused by mode partition noise, intensity noise, and reflection-induced noise in optical data links. Under given conditions an additional noise source with a S /N ratio of 20 dB will cause a power penalty of 1 dB in order to maintain a 10^-9 bit error rate. From numerical simulations the authors predict the maximum allowable dispersion in the presence of mode partition noise to be approximately 40% of a clock period. This figure is almost independent of bit rate and laser structure and agrees well with the measurements and with results of other workers. Numerical simulations of a buried-heterostructure and a TJS laser were carried out at four bit rates from 565 Mbit/s to 4.5 Gbit/s and the measurements were done at 2.2 Gbit/s using a TJS laser     

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p_e is considered. The value of p_e can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R₀, where R₀ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem     

New ternary line codes based on trellis structure

The trellis coding technique is applied to line-coded baseband digital transmission systems. For R=n/n+1(n=1,2,3) coding rates, a new codeword assignment model is proposed to accomplish basic requirements for line coding in which each length n binary data sequence is encoded into a length n+1 ternary (+,0,-) line codeword chosen among the code alphabet with 2ⁿ⁺² elements. Assuming Viterbi decoding, the system error performance is improved by increasing the free Euclidean distance between coded sequences. A new algorithm is given for the calculation of the free distance between line-coded sequences so obtained. For R=1/2 and R=3/4 rates, the analytical error performance upper bounds are derived. The power spectral densities of the new line codes are also calculated and compared with those of known line codes     

Experiments on postdetection diversity for narrowband digital FMmobile radio

Postdetection diversity, in which the demodulator outputs are weighted in proportion to the vth power of each demodulator input signal envelope when they are added, is described for GMSK signal reception using a frequency demodulator and a one-bit decision feedback equaliser. Experiments on a 16 kbit/s GMSK with a premodulation filter bandwidth-bit duration product of B_bT=0.25, show that using v=2 provides a diversity gain about 1-1.5 dB larger than selection combining, at an average bit error rate of 10^-2 in a Rayleigh fading environment     

Performance of time diversity/convolutional coding scheme

A rate R=1/3 coding scheme, comprising a time diversity delay line and an R=2/3 convolutional code, is investigated. The bit error rate performance of the scheme on a binary symmetric channel and a burst error channel is presented     

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     

Improved sphere bounds on the covering radius of codes

The sphere bound is a trivial lower bound on K(n,R), the minimal cardinality of any binary code of length n and with covering radius R. By simple arguments it is considerably improved, to K(n,1)⩾2 ⁿ/n for n even. A table of lower and upper bounds on K(n,R) for n⩽33, R ⩽10 is included     

Performance of π/4 SQAM in a hard-limited channel in thepresence of AWGN

A strategy that reduces the spectral spreading when an ideal hard-limiter is used as a first approximation to a fully saturated power amplifier is presented. This strategy combines superposed quadrature amplitude modulation (SQAM) filtering with the π/4-shift quadrature phase-shift keying (QPSK) digital transmission format adopted for the first generation of US digital cellular systems. Simulation results showed that this π/4 SQAM filtering strategy increased capacity by 35% in comparison to hard-limited π/4 QPSK. Using computer-aided design, a receive filter that would limit the degradation of E _b/N₀ to less than 1.4 dB at a bit error rate of P_e=10^-4 was selected     

Polysilicon emitter p-n-p transistors

In-situ boron-doped polysilicon has been used to form the emitter in p-n-p transistors. Various polysilicon deposition conditions, interface preparation treatments prior to deposition, and post-deposition anneals were investigated. Unannealed devices lacking a deliberately grown interfacial oxide gave effective emitter Gummel numbers G_E of 7-9×10^-12s cm^-4 combined with emitter resistances R_E of approximately 8 μΩcm². Introduction of a chemically grown interfacial oxide increased G_E to 2×10 ¹⁴s cm^-4, but also raised R_E by a factor of three. Annealing at 900°C following polysilicon deposition raised G_E values for transistors lacking deliberate interfacial oxide to approximately 6×10¹³s cm^-4, but had little effect of G_E for devices with interfacial oxide. Both types of annealed devices gave R_E values in the range 1-2 μΩcm²     

PLL propagation delay-time influence on linewidth requirements ofoptical PSK homodyne detection

Phase-locked loop (PLL) propagation delay-time influence on optical homodyne detection was investigated both theoretically and experimentally. Applying the Pade approximation, which is often used in the control system, to the calculation of the phase-error variance with the nonzero loop delay time, a high-accuracy analytic expression phase-error variance is obtained. The linewidth requirement with the nonnegligible loop delay time for phase-shift-keying (PSK) homodyne detection is obtained as δν=2.04×10^-3/τ where δν (hertz) is beat linewidth and τ (seconds) is the loop delay time. The linewidth requirement with small delay time approaches δν=6.2×10^-4 R_b where R_b (bits-per-second) is the system bit rate. Results were confirmed by a 10-GB/s optical PSK homodyne detection experiment using external cavity laser diodes. Receiver sensitivity degradations due to loop delay time and beat linewidth are in good agreement with theoretical results     

A low-noise K-Ka band oscillator AlGaAs/GaAsheterojunction bipolar transistors

The design considerations, fabrication process, and performance of the first K-Ka-band oscillator implemented using a self-aligned AlGaAs/GaAs heterojunction bipolar transistor (HBT) are described. A large-signal time-domain-based design approach has been used which applies a SPICE-F simulator for optimization of the oscillator circuit parameters for maximum output power. The oscillator employs a 2×10-μm² emitter AlGaAs/GaAs HBT that was fabricated using a pattern inversion technology. The HBT has a base current 1/f noise power density lower than 1×10^-20 A²/Hz at 1 kHz and lower than 1×10^-22 A/²/Hz at 100 kHz for a collector current of 1 mA. The oscillator, which is composed of only low-Q microstrip transmission lines, has a phase noise of -80 dBc/Hz at 100 kHz off carrier when operated at 26.6 GHz. These results indicate the applicability of the HBTs to low-phase-noise monolithic oscillators at microwave and millimeter-wave frequencies, where both Si bipolar transistors and GaAs FETs are absent     

Molecular-beam growth of homoepitaxial InSb photovoltaic detectors

Molecular-beam epitaxy has been used for the first time to fabricate np junctions in InSb grown onto p-type InSb (100) substrates. Diodes formed by the epitaxial growth of a silicon-doped layer on undoped homoepitaxial material exhibited a bulk generation-recombination-limited R₀A value of 10⁵ Ω cm² and D_λpk * of 3×10¹² cm Hz^1/2 W^-1 at liquid nitrogen temperature     

Bias in a stress-strength problem

The bias of the maximum likelihood estimator for R≠Pr{ X<Y} where X and Y are independent normal random variables with unknown parameters is discussed. The bias is an odd function with respect to δ=gauf^-1 (R), where gauf(·) is the Cdf of the standard normal distribution, so the study is restricted to R ⩾0.5, or equivalently, δ⩾0. There exists δ₀>0 such that the bias is positive in the interval 0<δ<δ₀. R has a positive bias at least in the interval 0.84<R<0.94     

Statistical inference under multiterminal rate restrictions: adifferential geometric approach

A statistical inference problem for a two-terminal information source emitting mutually correlated signals X and Y is treated. Let sequences Xⁿ and Yⁿ of n independent observations be encoded independently of each other into message sets M_X and M_Y at rates R₁ and R ₂ per letter, respectively. This compression causes a loss of the statistical information available for testing hypotheses concerning X and Y. The loss of statistical information is evaluated as a function of the amounts R₁ and R ₂ of the Shannon information. A complete solution is given in the case of asymptotically complete data compression, R₁, R₂→0 as n→∞. It is shown that the differential geometry of the manifold of all probability distributions plays a fundamental role in this type of multiterminal problem connecting Shannon information and statistical information. A brief introduction to the dually coupled e-affine and m-affine connections together with e -flatness and m-flatness is given     

Gohberg-Semencul type formulas via embedding of Lyapunov equations[signal processing]

The authors present a new way of deriving Gohberg-Semencul-type inversion formulas for Hermitian Toeplitz and quasi-Toeplitz matrices. The approach is based on a certain Σ-lossless embedding of Lyapunov equations. It has been shown that if a nonsingular matrix R has Toeplitz displacement inertia {p, q}, then R^-1 does not have the same Toeplitz displacement inertia. However, a para-Hermitian conjugate of R^-1 will have this property. It is also shown that the Gohberg-Semencul-type inversion formulas can be formed directly in terms of certain parameters of the embedding