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     

Pseudo-analog speech transmission in mobile radio communicationsystems

A low-complexity pseudo-analog speech transmission scheme is proposed for portable communications. It uses a speech coder based on adaptive differential pulse code modulation (ADPCM) in combination with a multilevel digital modulation technique such as M-ary DPSK or M-ary FSK and features low quantization noise, bandwidth efficiency, and robustness to transmission errors. A nonsymmetric M -ary DPSK scheme called skewed M-ary DPSK is proposed to enhance the noisy channel performance. Comparison to conventional analog FM and a digital speech transmission scheme using adaptive predictive coding and forward error correction (FEC) based on convolutional coding shows that the pseudo-analog system has the best objective signal-to-noise ratio performance under most channel conditions. Informal subjective evaluations rate the digital system superior to the pseudo-analog scheme for bad channels and conversely for good channels. It is concluded that the pseudo-analog system can be designed with low delay and high speech quality for good channels with high spectral efficiency     

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     

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     

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     

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     

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     

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     

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     

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     

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     

Upper bounds for small trellis codes

An upper bound on the minimum squared distance of trellis codes by packing Voronoi cells is derived and compared with previously known bounds. The authors focus on codes with small memory for modulation formats such as pulse amplitude modulation (PAM), m-ary quadrature amplitude modulation (QAM), and m-ary phase shift keying (PSK). The bound is tight to search results for coset codes with a small number of states     

On the use of repetition coding with binary digital modulations onmobile channels

Repetition, diversity, and single-error-correcting codes are examined for use with binary modulation techniques over a mobile communication fading channel. Both bit-error performance and bandwidth efficiency are considered for phase-shift keyed, differential phase-shift keyed, and frequency-shift keyed modulations. The error-correction capability of repetition coding is considered, and optimum repetition is found. M-tuple diversity with maximum-ratio-combining is then compared with repetition coding both with a single-error-correcting code and without coding. It is found that a minimum of a 10 dB signal-to-noise power ratio is required for an improved performance with repetition code or diversity. The repetition code is about 3 dB inferior to optimal diversity. An optimized design of moderate complexity and bandwidth expansion can be reached with twofold diversity and three repetitions as an inner layer of coding concatenated with an outer single-error-correcting code     

Multilevel trellis MPSK modulation codes for the Rayleigh fadingchannel

The multilevel coding technique is used for constructing multilevel trellis M-ary phase-shift-keying (MPSK) modulation codes for the Rayleigh fading channel. In the construction of a code, all the factors which affect the code performance and its decoding complexity are considered. The error performance of some of these codes based on both one-stage optimum decoding and multistage suboptimum decoding has been simulated. The simulation results show that these codes achieve good error performance with small decoding complexity     

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     

Signal sets matched to groups

Recently, linear codes over Z_M (the ring of integers mod M) have been presented that are matched to M -ary phase modulation. The general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes. A definition is given for the notion of matching. It is shown that any signal set in N-dimensional Euclidean space that is matched to an abstract group is essentially what D. Slepian (1968) called a group code for the Gaussian channel. If the group is commutative, this further implies that any such signal set is equivalent to coded phase modulation with linear codes over Z_M. Some further results on such signal sets are presented, and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed     

On the symbol error probability of maximum-selection diversityreception schemes over a Rayleigh fading channel

The symbol error probability of two selection schemes, namely, maximum signal-to-noise ratio (Mγ) selection and maximum output (MO) selection, for M-ary multidiversity reception over a Rayleigh fading channel are discussed. The symbol error probability of the MO scheme is lower than that of the Mγ scheme. The more diversity receptions that are used, the larger is the difference. A simple expression of crossover average signal-to-noise ratio (per bit) is presented as a guideline for increasing the number of diversity receptions     

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     

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)     

Identities and approximations for the weight distribution of q-ary codes

An explicit formula is derived that enumerates the complete weight distribution of an (n, k, d) linear code using a partially known weight distribution. An approximation formula for the weight distribution of q-ary linear (n, k , d) codes is also derived. It is shown that, for a given q-ary linear (n, k, d) code, the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q=q ^-(n-k) as u becomes large. The error term is a decreasing function of the minimum weight of the dual. The results are also valid for nonlinear (n, M, d) codes with the minimum weight of the dual replaced by the dual distance