Error-correcting codes and nonlinear diversity combining againstworst case partial-band noise jamming of frequency-hopping MFSK systems

Error probability analyses are performed for a coded M-ary frequency-shift keying system (MFSK) using L hops per M-ary word frequency-hopping spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The bit error probabilities are obtained for a square-law adaptive gain control receiver with forward-error-control coding under conditions of worst-case partial-band noise jamming. Both thermal noise and jamming noise are included in the analyses. Performance curves are obtained for both block codes and convolutional codes with both binary and M-ary channel modulations. The results show that thermal noise cannot be neglected in the analysis if correct determinations of the optimum order of diversity and the worst-case jamming fraction are to be obtained. It is shown that the combination of nonlinear combining, M -ary modulation, and forward-error-control coding is effective against worst-case partial-band noise jamming     

A concatenated coded modulation scheme for error control

A concatenated coded modulation scheme is presented for error control in data communications. The scheme is achieved by concatenating a Reed-Solomon outer code and a bandwidth efficient block inner code for M-ary phase-shift keying (PSK) modulation. Error performance of the scheme is analyzed for an additive white Gaussian noise (AWGN) channel. It is shown that extremely high reliability can be attained by using a simple M-ary PSK modulation inner-code and a relatively powerful Reed-Solomon outer code. Furthermore, if an inner code of high effective rate is used, the bandwidth expansion required by the scheme due to coding will be greatly reduced. The scheme is particularly effective for high-speed satellite communications for large file transfer where high reliability is required. A simple method is also presented for constructing block codes for M-ary PSK modulation. Soome short M-ary PSK codes with good minimum squared Euclidean distance are constructed. These codes have trellis structure and hence can be decoded with a soft-decision Viterbi decoding algorithm. Furthermore, some of these codes are phase invariant under multiples of 45° rotation     

Offset DPSK with differential phase detector in satellite mobilechannel with narrow-band receiver filter

An expression is derived for the error probability of M-ary offset differential phase-shift keying (DPSK) with the differential phase detector and narrowband receiver filter in the satellite mobile (Rician) channel, which includes as special cases the Gaussian and land mobile (Rayleigh) channels. The error probability is computed as a function of various system parameters for M=2, 4, and 8 symbols and third-order Butterworth receiver filter. Both symmetric and conventional DPSK systems are considered. The optimal normalized bandwidth is close to 1.0. Symmetric and conventional DPSK differ significantly in error probability only for M=2 and in the lower range filter bandwidth. In most cases, symmetric DPSK outperforms conventional DPSK. This was particularly noted when the time delay between the specular and diffused signal components was taken into account     

An efficient modulation/coding scheme for MFSK systems on bandwidthconstrained channels

The performance of a bandwidth-efficient multiple-tone modulation scheme for M-ary frequency-shift keying (MFSK) is presented. The use of balanced incomplete block (BIB) designs is proposed to form the signaling frames. On each symbol interval the modulator selects a group of elements from a BIB design and divides its energy into the orthogonal waveforms corresponding to these elements. The multiple-tone FSK scheme based on these block designs is shown to increase greatly the bandwidth efficiency of a conventional M-ary FSK system. An implicit diversity is incorporated in the modulation scheme. Thus, a performance improvement comparable to that obtained by using time or frequency diversity is shown on a Rayleigh fading channel and also on an interference channel with partial-band Gaussian noise. The multiple-tone scheme based on this design is compared to a multiple-tone scheme based on Hadamard matrices suggested by J.F. Pieper et al. (1978). It is shown that similar performance is achieved on a fading channel, while an advantage close to 4 dB is obtained for the proposed scheme on an AWGN (additive white Gaussian noise) channel     

Frequency-hopped multiple access communications with coding andside information

The authors consider frequency-hopped spread-spectrum multiple-access communications using M-ary modulation and error-correction coding. The major concerns are multiple-access interference and the network capacity in terms of the number of users that can transmit simultaneously for a given level of codeword error probability. Block coding is studied in detail. The authors first consider the use of Q-ary Reed-Solomon (RS) codes in combination with M-ary modulation with mismatched alphabets so that Q>M. It is shown that the network capacity is drastically reduced in comparison with the system with matched alphabets. As a remedy, the use of matched M-ary BCH codes is proposed as an alternative to mismatched RS codes. It is shown that when the number of users in the system is large, a BCH code outperforms an RS code with a comparable code rate and decoding complexity. The authors consider the use of a robust technique for generation of reliable side information based on a radio-threshold test. They analyze its performance in conjunction with MFSK and error-erasure correction decoding. It is shown that this nonideal ratio-threshold method can increase the network capacity in comparison with the system with perfect side information     

Generalized cutoff rate of time- and frequency-selective fadingchannels

The generalized cutoff rate of time- and frequency-selective fading channels is evaluated for M-ary frequency-shift keying (MFSK) and M-ary differential phase-shift keying (MDPSK) modulation with soft decoding. The optimal signaling rate and code rate for dispersive channels are evaluated. The guard time effect, is used in multipath spread channels, is evaluated for frequency-selective channels, and the optimal combination of signaling rate, code rate, and guard time is presented. Special attention is given to CCIR (International Radio Consultative Committee) HF channel models     

Bit error rate performance of π/4-DQPSK in a frequency-selectivefast Rayleigh fading channel

The bit error rate (BER) performance of π/4-differential quadrature phase shift keying (DQPSK) modems in cellular mobile communication systems is derived and analyzed. The system is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). The probability density function of the phase difference between two consecutive symbols of M-ary differential phase shift keying (DPSK) signals is first derived. In M-ary DPSK systems, the information is completely contained in this phase difference. For π/4-DQPSK, the BER is derived in a closed form and calculated directly. Numerical results show that for the 24 kBd (48 kb/s) π/4-DQPSK operated at a carrier frequency of 850 MHz and C/I<20 dB, the BER will be dominated by CCI if the vehicular speed is below 100 mi/h. In this derivation, frequency-selective fading is modeled by two independent Rayleigh signal paths. Only one co-channel is assumed in this derivation. The results obtained are also shown to be valid for discriminator detection of M-ary DPSK signals     

Fully digital M-ary PSK and M-ary QAMdemodulators for land mobile satellite communications

A fully digital implementation of digital modems is the preferred option of system designers because high performance can be achieved at reasonable cost. The author explains the beneficial features inherent in fully digital demodulator implementations. Other features which are required for land mobile satellite communication systems are also discussed. Recently reported techniques for the synchronisation and detection of M-ary PSK and M-ary QAM modulation schemes are reviewed with emphasis placed on those which are well suited to digital implementation     

Shared time division duplexing: an approach to low-delayhigh-quality wireless digital speech communications

Various strategies to provide low-delay high-quality digital speech communications in a high-capacity wireless network are examined. Various multiple access schemes based on time-division and packet reservation are compared in terms of their statistical multiplexing capabilities, sensitivity to speech packet dropping, delay, robustness to lossy packet environments, and overhead efficiency. In particular, a low-delay multiple access scheme, called shared time-division duplexing (STDD) is proposed. This scheme allows both the uplink and downlink traffic to share a common channel, thereby achieving high statistical multiplexing gain even with a low population of simultaneous conversations. The authors also propose a choice of low delay, high quality speech coding and digital modulation systems based on adaptive DPCM, with QDPSK or pseudo-analog transmission (skewed DPSK), for use in conjunction with the STDD multiple access protocol. The choice of the alternative systems depends on required end-to-end delay, recovered speech quality and bandwidth efficiency. Typically, with a total capacity of 1 MBaud, 2 ms frame and 8 kBaud speech coding rate, low delay STDD is able to support 48 pairs of users compared to 38, 35, and 16 for TDMA with speech activity detection, basic TDMA and PRMA respectively. This corresponds to respective gains of 26%, 37% and 200%     

Semi-analytical performance evaluation in satellite digital linksin the presence of interference

A model for the semi-analytic performance evaluation of digital satellite radio links in the presence of interference on both the uplink and the downlink is presented. Error probability on the linear portion of the link is estimated using simulation to determine the moments of the interfering signal samples and analyzing the effect of an undetermined phase difference among carriers. The nonlinear portion of the link is modeled using a series expansion of the nonlinearity; the output terms are then separated, allowing construction of the conditional probability densities required in the error probability computation. Results are carried out for M-QAM (M-ary quadrature amplitude modulation) and M-PSK (M-ary phase-shift keying) modulation systems     

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     

A new method for the integration of modulation and channel codingin an ARQ protocol

A method for the integration of the modulation operation in an automatic-repeat-request (ARQ) scheme is described. This method uses a memory for the successive transmissions of a codeword and, through a suitable encoding operation, the Euclidean distances among the codewords are significantly increased with the number of transmissions. The application of the described method to some different modulation schemes, such as M-ary PSK with M>2 and continuous-phase frequency shift keying modulation, is described. The optimum combination of the modulation and channel coding operations for some short block codes is also presented. The results of the theoretical analysis show that the method described permits improving both the error probability and the throughput of an ARQ protocol with respect to similar schemes     

Defining, designing, and evaluating digital communication systems

The fundamental relationships in defining, designing, and evaluating digital communication system performance are reviewed. The concept of bandwidth-limited and power-limited systems and how such conditions influence the design when the choices are confined to M -ary phase-shift keying (MPSK) and M-ary frequency-shift keying (MFSK) modulation are examined. The definitions and computations involved in transforming from data bits to channel bits to symbols to chips are discussed. It is suggested that since most digital communication systems share these concepts, understanding them should enable one to evaluate other such systems in a similar way     

M-ary frequency shift keying withlimiter-discriminator-integrator detector in satellite mobile channelwith narrowband receiver filter

An expression is derived for the error probability of M-ary frequency shift keying with a limiter-discriminator-integrator detector and a narrowband receiver filter in the satellite mobile channel. This channel contains, as special cases, the Gaussian and Rayleigh (land mobile) channels. The error probability is computed as a function of various system parameters for M=2, 4, 8 symbols and a third-order Butterworth receiver filter     

Spread-spectrum multiple-access performance of orthogonal codes forindoor radio communications

Direct-sequence spread spectrum, with its inherent resistance to multipath, is a promising technique for indoor wireless communication. To allow multiple users within a limited bandwidth, code division multiple access (CDMA) is needed. The bandwidth efficiency of M-ary CDMA systems in fading multipath indoor radio channels is analyzed. It is shown that M-ary signaling improves the bandwidth efficiency significantly when compared to binary signaling     

Double differential MPSK on the fast Rician fading channel

An analysis of adjacent and nonadjacent double differential M -ary PSK (M-ary D²PSK) on the fast Rician fading channel is presented. The probability density function (PDF) of the first-order phase error (FOPE) and the probability density functions of the second-order phase error (SOPE) for both adjacent and nonadjacent D²PSK on a fading channel have been derived. Asymptotic approximations for these PDFs are proposed in the case of channels with weak fading (including the additive white Gaussian noise (AWGN) channel) and high signal-to-noise ratio. For nonadjacent D²PSK with independent FOPEs a simplified PDF of SOPE has been obtained. The derived PDFs allow calculation of error performance of D²PSK, as well as of DPSK, on the Rician channel including the AWGN channel and the Rayleigh channel and verification of some results reported in the literature earlier. It is shown that nonadjacent D²PSK can be optimized by choosing a proper separation between the first-order phase differences     

Spectral shaping and digital synthesis of an M-ary timeseries

The use of pulse shaping to control transmitted spectral density precisely is examined. A digital filter architecture is described that not only mitigates the traditional problems of lengthy development intervals and cost manufacturing methods, but offers the additional features of intrinsically coding high-speed binary (M=2) data into M-ary symbols while ensuring highly reproducible, baud-normalized, transmitter pulse shaping. A conceptual basis for the digital synthesis method is first described, including a functional circuit appropriate to the simplest filter realizations. Spectral effects internal to the filter are considered, and a simple method to obtain desired transmitted spectra is outlined. It is shown that even relatively short pulses used in high-level modulation systems lead to impractical memory storage demands; however, the simple expedient of segmenting the finite impulse function greatly reduced the individual memory requirements, though it necessitates intermediate adding operations. Experimental examples illustrate the design methodology for quaternary (M=4) data signals in a Nyquist communication channel and serve as points of reference for addressing performance and design flexibility     

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     

Performance of fast frequency hopped noncoherent MESK witha fixed hop rate under worst case jamming

The performance of fast-frequency-hopped M-ary frequency-shift keying with a fixed hop rate is evaluated, utilizing the Chernoff union bound method. The performance criterion used is a throughput measure i.e., an information rate sustained by a system for a given bit error rate, normalized by the hop rate. Both uncoded and coded systems are considered. It is shown using the cutoff rate argument that coding can provide a few dB gain in throughput. This is confirmed by the performance evaluation of various convolutional and block codes. Both partial-band noise jamming and multitone jamming with one tone per M -ary band are considered. Jamming parameters are assumed to be the worst case against the coding channel. Determination of the optimum M is also addressed     

Probability of error of M-ary PSK and DPSK on a Rayleighfading channel

M-ary phase-shift keying and differential phase-shift keying (DPSK) on a slow fading Rayleigh channel without diversity is investigated. Expressions for the distribution of the phase angle between a vector with Rayleigh amplitude distribution and a noiseless reference, and between two vectors both with Rayleigh amplitude distribution perturbed by Gaussian noise are obtained