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     

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     

Error probabilities of fast frequency-hopped MFSK withnoise-normalization combining in a fading channel with partial-bandinterference

An error probability analysis performed for an M-ary orthogonal frequency-shift keying (MFSK) communication system employing fast frequency-hopped (FFH) spread-spectrum waveforms transmitted over a frequency-nonselective, slowly Rician fading channel with partial band interference is discussed. Diversity is obtained using multiple hops per data bit. Noise-normalization combining is employed by the system receiver to minimize partial-band interference effects. The partial-band interference is modeled as a Gaussian process. Thermal noise is also included in the analysis. Forward error correction coding is applied using convolutional codes and Reed-Solomon codes. Diversity is found to dramatically reduce the degradation of the noise-normalization receiver caused by partial-band interference regardless of the strength of the direct signal component. Diversity offers significant performance improvement when channel fading is strong, and performance improvement is obtained for high modulation orders (M>2). Receiver performance is improved when diversity, higher modulation orders, and coding are combined     

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     

Throughput analysis of a slotted frequency-hop multiple-accessnetwork

A link throughput analysis is presented for a slotted frequency-hop multiple-access (FHMA) packet radio network (PRN) operating in the presence of background noise, partial-band noise jamming, and partial-band tone jamming. The PRN consists of an arbitrary number of transceivers arranged in a paired-off topology. Forward error-correction coding is used for packet protection. M-ary FSK modulation is used with hard-decision decoding. Expressions are derived for the link throughput in terms of the channel cutoff rate and capacity. The dependency of the optimal processing gain, code rate, and jamming fraction on the population size, traffic intensity, bit energy to background noise ratio, and bit energy to jammer noise ratio is examined in detail. It is shown that a properly designed (optimized) PRN using random-access FHMA offers a significantly larger heavy-load throughput than a random-access frequency-division multiple-access PRN     

Capacity and cutoff rate of coded FH/MFSK communications withimperfect side information generators

When JSI (jamming state information) is imperfect due to thermal noise, the capacities and cutoff rates of the channels are calculated as a function of the signal-to-jamming-noise ratio for memoryless, noncoherent FH/MFSK (frequency-hopped M-ary frequency-shift-keying) systems under partial-band noise jamming (PBNJ). Both soft- and hard-decision metrics with perfect, imperfect, and no JSI are considered. The first of three imperfect JSI generator uses the maximum a posteriori (MAP) decision rule based on the energy from an FH tone frequency which is near the M-signaling FH tone frequencies. The second decision rule utilizes the MAP rule, but it is based on the total energy received at the M-signaling FH tone frequencies. The third generator has the same decision statistics as the second generator, but its decision rule is an easily implementable suboptimum rule. If hard decision are made and code rates are high, then the differences between the imperfect JSI generators and perfect JSI generator can be larger than 1 dB. If soft decisions are made, then the differences between the imperfect and perfect JSI cases are negligible     

Effect of worst case multiple partial-band noise and tone jammerson coded FH/SSMA systems

The author characterizes and evaluates the effect of simultaneous multiple partial-band noise or tone jammers and other user interference on a single communication link employing frequency-hopped spread-spectrum (FH/SS) signaling, M-ary frequency-shift keying (FSK) modulation with noncoherent demodulation, and Reed-Solomon coding. For the symbol error probability of these systems, the author derives exact expressions in the absence of multiple-access interference and tight upper bounds in the presence of other-user interference. Although the analytical methods are valid for any number of multiple jammers, the numerical study is restricted to the cases of two and three-partial-band noise and tone jammers. For fixed values of the spectral densities of noise jammers, or the energies per symbol of tone jammers, the worst-case fraction of the band that each jammer should use in order to maximize the error probability of the FH/SS or FH/SSMA system is evaluated. For the range of the signal-to-jammer power ratios examined, multiple-noise or multiple-tone jammers appear to have no advantage over single-tone jammers of equivalent spectral density or energy per symbol, but achieve approximately the same worst-case performance by jamming smaller fractions of the band     

Performance of fast frequency-hopped MFSK receivers with linear andself-normalization combining in a Rician fading channel withpartial-band interference

An error probability analysis is performed for both self-normalized and conventional M-ary orthogonal frequency-shift-keying (MFSK) noncoherent receivers using fast frequency-hopped (FFH) spread-spectrum waveforms transmitted over a Rician fading channel with partial-band interference. The self-normalization receiver uses a nonlinear combination procedure to minimize performance degradation due to partial-band interference. The performance of the conventional receiver is significantly degraded by worst-case partial-band interference regardless of the modulation order or number of hops per data symbol used, while the self-normalization receiver can provide a significant immunity to worst-case partial-band interference for many channel conditions when diversity is used, provided the signal-to-thermal-noise ratio is large enough to minimize degradation due to nonlinear combining losses. The improvement afforded by higher modulation orders is dependent on channel conditions     

Performance of robust metrics with convolutional coding anddiversity in FHSS systems under partial-band noise jamming

The performance of robust metrics (metrics that can be computed from the outputs of the matched filters only) with convolutional coding and diversity under worst-case partial-band noise jamming is analyzed. Both binary and dual-k convolutional codes employing these metrics with diversity are compared via Union-Chernoff bounds. The performances of metrics considered in the literature that assume perfect side-information are given for comparison purposes. It is found that there exist very good robust metrics that provide performance comparable to metrics using perfect side-information. Among the robust metrics considered, the self-normalized metric offers the best performance and achieves performance practically identical to that of the square-law-combining metric with perfect side-information for M=8     

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     

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     

Limiter-differential detection of a frequency-hopped CPFSKdiversity system in partial-band jamming

The error probability achieved by a differential detector with a bandpass limiter preceding the receiver is analyzed for a slow-frequency-hopped CPFSK diversity waveform transmitted over a partial-band noise jamming channel, and is compared to the system's performance without the bandpass limiter. The system's thermal noise is not neglected in the analysis. In principle, each bit is repeated on L different hops, and for the FH/CPFSK system analyzed, these repetitions are combined to yield a soft decision. The main result is that a diversity gain for error rate improvement in worst-case partial-band jamming is realized with the detector preceded by a limiter, but not without the limiter. This is shown by considering the error probability for L=2 in comparison with that for L=1     

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)     

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     

Performance of multitone FFH/MFSK systems in the presence ofjamming

A novel type of diversity signaling for an M-ary frequency-shift keyed modulation format involving the transmission of multiple tones on each diversity branch is considered. The properties of such a system are investigated, and its performance in the presence of tone jamming is analyzed. It is shown that significant gains can be realized with such a technique. The performance in the presence of worst-case partial band noise is briefly considered and shown to be worse than, though comparable to, that of the single-tone case     

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     

Diversity and coding for FH/MFSK systems with fading and jamming.II. Selective diversity

For pt.1 see ibid., vol.COM-35, p.1329-41 (1987). A performance evaluation is presented for selective diversity with feedback for frequency-hopping M-ary frequency-shift-keyed systems operating over Rayleigh faded channels in the presence of partial-band noise and partial-band tone jamming. The behavior of uncoded and coded systems is studied. For coded systems, the performance is evaluated for hard-decision receivers without channel state information and soft-decision receivers with perfect jammer state information. The results demonstrate that the performance of uncoded FH/MFSK with selective diversity is unacceptable. However, this diversity technique can offer definite improvements for coded FH/MFSK systems. Specifically, the effectiveness of selective diversity signaling depends on the provision of a feedback channel between the transmitter and receiver to provide the transmitter with the fading gains of the independently faded channels. To obtain an improvement from the selective diversity signaling scheme described here, there must be multiple independently faded channels between the transmitter and receiver. If not, the performance of the selective diversity signaling scheme will be identical to the performance of FH/MFSK without diversity     

Error probability of digital modulation in satellite mobile, landmobile, and Gaussian channels with narrow-band receiver filter

It is shown how to derive formulas for the error probability for M-ary differential phase shift keying with differential phase detection (DPD) and M-ary frequency shift keying with DPD, limiter-discriminator detection and limiter-discriminator-integrator detection in the satellite mobile channel (SMC) with narrowband receiver filter if such formulas are available for the Gaussian channel. The modification of the formulas involves only a redefinition of the noise power and autocorrelation function. Since the SMC contains as special cases the land mobile (Rayleigh) channel and the Gaussian channel, the derived formulas are valid for these channels as well. In fact the formula for the land mobile channel is in many cases reduced to a closed form, which does not contain an integral. The author computes the error probability for the four systems, and compares their performance assuming a third-order butterworth filter and M=2,4,8 symbols     

Convolutionally coded frequency-hopping communications withnonideal interleaving

The interleaving span of coded frequency-hopped (FH) systems is often constrained to be smaller than the decoder memory length, i.e. nonideal interleaving is performed. An upper bound on the performance of a Viterbi decoder of a convolutional code with nonideal interleaving is presented. A soft decision diversity combining technique is introduced, and the performance of combined convolutional and diversity coding subject to worst-case partial band noise jamming is investigated. Optimization of the FH system performance subject to constraints of allowed delay and synthesizer settling time provides the best combination of interleaving span and hopping rate. The FH system considered employs M-ary frequency-shift key (MFSK) modulation and noncoherent demodulation with 2-b soft decision based on Viterbi's ratio-threshold technique