Multiple Frequency Shift Keying Research Articles

Multiple-symbol trellis-coded modulation applied to noncoherent continuous-phase frequency shift keying

This paper considers a maximum-likelihood (ML) noncoherent detection scheme for multiple full response continuous-phase frequency shift keying (CPFSK) waveforms and introduces a trellis-coded modulation (TCM) scheme for this noncoherent modulation. By utilizing a Gaussian approximation for Rician random variables, we express the pairwise error probability as a function of the equivalent normalized squared distance (ENSD). ENSD plays the same role as normalized squared Euclidean distance when evaluating error probability performance for coherent detection. We derive an analytical approximation on the bit-error probability by employing ENSD for both the coded system and the uncoded system. For the uncoded system we show that the bit-error probability of noncoherent detection approaches that of coherent symbol-by-symbol detection in the limit as the multiplicity of the symbol goes to infinity for large signal-to-noise ratio (SNR), We determine specific optimal trellis encoders for binary and 4-ary CPFSK with modulation index 1/2 and 1/4, respectively, by application of Ungerboeck's (1982) set partitioning approach.

Mfsk signal detection using acousto‐optic joint transform correlator

AbstractA multichannel acousto‐optic joint transform correlator is presented. On‐plane acousto‐optic (AO) cells and a square‐law converter are employed. The AO cells are driven by frequency multiplexed temporal signals to produce spatially modulated signals. The joint transform power spectrum is generated with a square‐law converter. By inverse Fourier transformation with a coherent readout, the cross correlation of input signals can be obtained. Since the architecture can process wideband signals, it may be applied to detect multiple frequency shift keying (MFSK) signals.

Multiple tone interferers in an FH-MFSK spread spectrum communication system

An analysis of the effect of multiple tone interferers on the bit error rate (BER) in a frequency-hopped multiple frequency shift keying (FH-MFSK) spread spectrum communication is given. A constant insertion rate detection strategy has been considered and a matched tuned filtering used in the receiver. We have obtained results in the 20 MHz (one-way) bandwidth with a data rate of 32 kbit/s and a Rayleigh fading channel. The results show that adequate performance can be achieved even when 40 tone interferers are present with a signal to interference ratio of -10 dB and a signal-to-noise ratio of 25 dB.

Correction to "Frequency Hopping with Multiple Frequency-Shift Keying and Hard Decisions"

Correction to "Frequency Hopping with Multiple Frequency-Shift Keying and Hard Decisions"

Frequency Hopping with Multiple Frequency-Shift Keying and Hard Decisions

The performance of frequency-hopping systems with multiple frequency-shift keying and hard decisions is determined for operation against optimal partial-band jamming. A receiver that eliminates the potential advantage of optimally placed jamming tones is proposed. The effects of Reed-Solomon, binary block, and convolutional codes are analyzed. Concatenated codes with hard and soft decisions available to the outer decoder are examined. Continuous-phase frequency-shift keying with limiter-discriminator demodulation is shown to offer potentially improved performance in frequency-hopping systems.

Performance of Frequency-Hopping Multiple-Access Multilevel FSK Systems with Hard-Limited and Linear Combining

In comparing two proposed frequency-hopping mobile radio systems for digitized speech, Goodman et al. have observed that the system employing multiple-frequency-shift-keying (MFSK) can accommodate many more users than the ones with differential-phaseshift-keying (DPSK). Besides the difference in modulation methods, the MFSK system uses hard-limited combining while the DPSK one uses linear combining. In this paper, we show that using linear combining in the MFSK system causes the performance to degrade considerably.

Hard-limited versus linear combining for frequency-hopping multiple-access systems in a Rayleigh fading environment

In comparing two proposed frequency-hopping mobile radio systems for digitized speech, Goodman et al. have observed that the system employing multiple frequency-shift keying (MFSK) can accommodate many more users than the one with differential phase-shift keying (DPSK). Besides the difference in modulation methods, the MFSK system uses hard-limited combining while the DPSK one uses linear combining. Upper bounds are obtained on the probability of error for DPSK systems with hard-limited combining and linear combining. These bounds suggest that the DPSK system with hard limiters can support about twice as many users as the original one.

Improved Decoding Scheme for Frequency-Hopped Multilevel FSK System

We have recently examined, for possible application to digital mobile radio telephony, a digital spread-spectrum technique employing multiple frequency-shift keying (MFSK) modulation with code-division-multiple access (CDMA) by frequency-hopping over a common bandwidth. The system uses the cellular approach where all mobiles within a cell communicate with a fixed base station in the cell. An analysis of base-to-mobile transmission shows that mutual interference limits the number of users which the system can accommodate at a given error rate. This paper describes a new decoding scheme to reduce mutual interference which makes use of the well-defined algebraic structure of the users' addresses. Analysis of the new decoder at high signal to noise (s/n) ratio shows it to outperform conventional decoding, allowing a 50 to 60 percent increase in the number of users who can simultaneously share the system at a given error rate. We describe a simple implementation of the decoder using shift registers.

Optimum Reception of Coded Multiple Frequency Keying in Presence of Random Variable Phases

Wide-band multiple frequency-shift keying is perturbed by random phases in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M \geq 2</tex> frequency slots. We consider a coded digital system, where the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> phases can be treated as mutually dependent random variables. If their joint distribution is known, the optimum (maximum-likelihood) receiver is shown to be in general very complicated. We show that there are a few phase distributions and signal-to-noise-ratio extremes for which the optimum receiver and its performance can be simply described. If the joint phase distribution is not known, we give an appropriate minimax receiver with a guaranteed performance. This performance is evaluted for orthogonal coding, white Gaussian noise, and nonfading signals. It is valid for all joint phase distributions.

Theoretical Diversity Improvement in Multiple Frequency Shift Keying

Multiple frequency shift keying (MFSK) is a modulation suitable for transmitting digital data under fading conditions. A quantitative analysis of MFSK-with-diversity is presented. The MFSK signals on the several diversity channels are presumed to be perturbed independently by Rayleigh fading and additive white Gaussian noise. Also, it is assumed that fading is slow and that envelope, cross-correlation (matched filter) detection is used. The diversity combining method is chosen so that the receiver performs a likelihood-ratio test in deciding which one of K frequencies was transmitted. This optimum comibining method is to square and add the detected outputs of corresponding filters from each diversity channel. Theoretical error probability as a function of signal-energy-per-bit received is derived, and curves are plotted for two-, four-, and eight-frequency MFSK-with-diversity. Bandwidth requirements, as a function of type and order of diversity, are determined. Eight-frequency MFSK with triple diversity has a 21.8-db advantage over simple FSK for transmitting 6-bit characters with a 0.001 error probability.