Design of coded CPFSK modulation systems for bandwidth and energyefficiency

Consideration is given to the problems related to the design of M-ary continuous-phase frequency-shift keying (CPFSK) systems with modulation index h=J/M, combined with eternal rate r binary convolution encoders. The following questions are raised and answered: (1) how should different encoder-modulator systems be compared and how can comparable systems be recognized from the system parameters, i.e. M, h, and r?; (2) what are the limits on the information rate per unit bandwidth, versus signal-to-noise ratio, when reliable transmission is required?; (3) how does one choose the system parameters M, h, and r when the overall system has to achieve a specified performance?; and (4) how does one design the external rate r binary convolutional encoder to put in front of the M-ary CPFSK modulation system with h=J/M ? A simple approximation for the bandwidth of a CPFSK signal is given and shown to be sufficiently accurate for system design purposes. The design of the external convolutional encoder is carried out in a novel way that leads to fewer states in the combined encoder-modulator system and thus yields improved performance for a given demodulation-decoding complexity compared to previous approaches for the design of coded CPFSK systems     

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     

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     

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     

Performance analysis of RS-coded M-ary FSK forfrequency-hopping spread spectrum mobile radios

Decoding performance of Reed-Solomon (RS) coded M-ary FSK with noncoherent detection in a frequency-hopping spread spectrum mobile radio channel is theoretically analyzed. Exact formulas and an approximate one for evaluating word error rates (WERs) of error correction and error-and-erasure correction schemes on decoding the RS codes are derived. It is shown that with K symbol erasure and C symbol error detection, RS coded M-ary FSK achieves the equivalent diversity order of (K+1)(C+1)     

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     

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     

A differentially coherent receiver for minimum shift keying signal

The author extends to the case of minimum-shift-keying (MSK) modulation the differentially coherent reception theory established for phase-shift-keying modulation. A novel differentially coherent detector for MSK is thus derived. The receiver filter is equivalent to the cascade of a matched filter and an equalizer in order to suppress inherent intersymbol interference. It is shown that performance can be improved when the delay between signals, multiplied by the differential detector, is increased from one to M bit time intervals. This decreases the effect of noise correlation and, thus, the bit error probability. The bit error probability of the proposed receiver is calculated. It is found that almost all potential improvement due to the delay M is obtained with M=3     

On linear structure and phase rotation invariant properties ofblock M-PSK modulation codes

Two important structural properties of block M(=2^' )-ary PSK modulation codes, linear structure and phase symmetry, are investigated. An M-ary modulation code is first represented as a code with symbols from the integer group S_M-PSK=(0,1,2,---,M-1) under modulo-M addition. Then the linear structure of block M-PSK modulation codes over S_M-PSK with respect to modulo- M vector addition is defined, and conditions are derived under which a block M-PSK modulation code is linear. Once the linear structure is developed, the phase symmetry of block M-PSK modulation codes is studied. In particular, a necessary and sufficient condition for a block M-PSK modulation code that is linear as a binary code to be invariant under 2^h/180°M phase rotation, for 1⩽h⩽l is derived. Finally, a list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant     

Correlation detection and trellis decoding of CPFSK signals

It is well known that correlation detection and trellis decoding of continuous phase frequency shift keyed (CPFSK) signals yields superior performance in comparison to other coherent detection techniques. The authors show that an M-state trellis in the decoder can achieve almost all the performance gain that is guaranteed by the memory of the CPFSK modulation     

Asymptotic performance of M-ary orthogonal signals inworst case partial-band interference and Rayleigh fading

It is shown that for worst-case partial-band jamming, the error probability performance (for fixed E_b/N_I) becomes worse with increasing M for (M>16). The asymptotic probability-of-error is not zero for any E_b/N _I(>ln 2), but decreases inverse linearly with respect to it. In the fading case, the error-probability performance (for fixed E_b/N₀) improves with M for noncoherent detection, but worsens with M for coherent detection. For large E_b/N₀ the performance of the Rayleigh fading channel asymptotically approaches the same limit as the worst case partial-band jammed channel. However, for values of M at least up to 4096, the partial-band jammed channel does better. While it is unlikely that an M-ary orthogonal signal set with M>1024 will be used in a practical situation, these results suggest an important theoretical problem; namely, what signal set achieves reliable communication     

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     

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     

Dependence of the frequency shift of the optical-microwave doubleresonance signal in the Cs D2 line on the pumpingfrequency and power of a GaAs semiconductor laser

The OMDR (optical-microwave double resonance) effect in the Cs D₂ line was studied for realizing a gas-cell-type Cs atomic frequency standard. A glass cell containing Cs with buffer gases (Ar/N₂=1.26, total pressure=39 torr) was placed in a TE₀₁₂ mode microwave cavity at a temperature of 45°C and was pumped using a GaAs semiconductor laser frequency locked to an external interferometer tuned to the 6P_3/2 (F=2,3,4)←6 S_1/2(F=3) transition. The OMDR signal appearing at the resonance to the F=4←3 hyperfine transition of the 6S_1/2 state shifted with detuning of the laser frequency and with change of the laser and microwave powers. The dependence of the shift on these variables around an optimum operating condition was obtained as, Δν_MW[Hz]=-(0.31±0.02) {1+(0.44±0.15) (ΔP_L/P_L)} Δν_L [MHz]-10(ΔV_MW/V _MW)     

Nonredundant error correction analysis and evaluation ofdifferentially detected π/4-shift DQPSK systems in a combined CCI andAWGN environment

The application of the nonredundant error correction (NEC) technique to the North American and Japanese digital cellular modulation standard, π/4-shift differential quadrature phase shift keying (DQPSK), in a combined additive white Gaussian noise (AWGN) and cochannel interference (CCI) environment is proposed, analyzed, and theoretically evaluated. The performance for NEC receivers with single, double, and triple error correction capability is theoretically analyzed and evaluated. For the CCI, the general model, which includes M statistical independent interferers also employing the π/4-shift DQPSK modulation format, is adopted. The theoretical symbol error probability versus carrier-to-noise ratio have been obtained with M and the carrier-to-interference ratio (C/I) as parameters. The results indicate significant performance improvements over conventional differentially detected systems. Some of the results have been verified by computer simulation. The gains offered by the NEC receivers increase as C/I decreases and/or M increases. Significant error floor reductions have been observed     

Performance of packaged near-traveling-wave semiconductor laseramplifier with multilongitudinal mode input

The results for a packaged 1.30-μm InP/InGaAsP optical amplifier used to switch broadband multilongitudinal modes signals are presented. Despite the absence of optical isolators and even with the introduction of additional external reflections (R≈1.0%), the optical fiber-to-fiber gain is stable over a large temperature range at resonance (ΔG⩽0.35 dB ΔT=±0.75°C at G=5.76 dB). Although the amplifier is capable of higher levels of gain (G_max ≈13 dB), it is considered that stable gain, relative to variations in temperature and reflectivity is more critical to the overall system. It has been found that a multilongitudinal mode signal can be amplified by a resonant amplifier without system degradation caused by mode-partition noise, and that junction heating requires a thermal stabilization period up to ≈0.2 ms after the start of a current pulse     

Optimum system design for CPFSK heterodyne delay demodulationsystem with DFB LDs

An optimum system configuration for an optical continuous-phase frequency-shift-keying (CPFSK) heterodyne delay demodulation system with distributed feedback laser diodes (DFB LDs) is discussed. The optimum modulation index was determined by evaluating the LD phase noise effect and the IF noise effect. The IF noise effect was investigated in detail, considering the noise conversion effect through delay demodulation. In the case of 10-MHz IF beat spectral width, the modulation index m =1.5 is optimum for a 1.2-Gb/s system. With this optimum modulation index, a 204-km long-span transmission experiment, with -41.5 dBm receiver sensitivity, has been successfully performed. The feasibility of using stand-alone DFB LDs for a high-sensitivity CPFSK delay demodulation system has been confirmed through this experiment     

Combined coded/multi-h CPFSK signaling

A continuous-phase frequency-shift-keying (CPFSK) signaling technique is suggested that combines convolutional encoding and multi- h signaling. In contrast to regular multi-h signaling, this technique changes the modulation index in a preselected pattern in order to maximize the minimum Euclidean distance. A rate-1/2 convolutional encoder along with a 2-h quaternary CPFSK modulator which uses two fixed modulation indexes is considered. Minimum Euclidean distances are calculated corresponding to the best encoder/mapper combinations for different modulation index patterns at attractive pairs of modulation indexes. Numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum Euclidean distance of coded CPFSK signals can be significantly increased by combining with multi-h signaling. Modulation index patterns which perform significantly better than regular multi-h signals are determined. An error event analysis over the additive-white-Gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results