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     

Antijam performance of FFH/BFSK with noise-normalization combining in a Nakagami-m fading channel with partial-band interference

The bit error rate (BER) performance of a noncoherent fast frequency-hopped binary orthogonal frequency-shift-keying (FFH/BFSK) spread spectrum noise-normalization combining receiver is evaluated in the presence of partial-band interference (PBI) and additive white Gaussian noise (AWGN) over independent frequency-nonselective slowly Nakagami-m fading channels. It is shown from the analytical results, and verified by simulation, that a higher diversity level greatly improves the worst-case performance of the noise-normalization receivers over Rayleigh or more severe fading channels, while a lower diversity level is preferred for less severe fading channels. In the former case, a full band strategy is optimal for the interferer and a partial-band strategy is more disruptive in the latter case.     

Performance of Reed-Solomon Coded Frequency-Hop Spread-Spectrum Communications in Partial-Band Interference

This paper is concerned with the performance of a Communications system which utilizes frequency-hop spread spectrum, diversity transmission, Reed-Solomon coding, and parallel error-correction and erasure-correction decoding. Both binary signaling andM-ary orthogonal signaling are considered. The goals are twofold. First, it is desirable to provide good performance in partial-band Gaussian noise interference by use of coding and diversity with an efficient error-correction algorithm. Second, it is necessary to totally neutralize narrow-band interference (regardless of the power level or statistical distribution of the interference) in order to have an effective spread-spectrum system. Through an analysis of the effects of partial-band interference on a frequency-hop spread-spectrum system with diversity, it is shown that the use of ReedSolomon coding with a parallel errors and erasures decoding algorithm accomplishes these goals. The paper also investigates the accuracy of the Chernoff bound as an approximation to the true performance of a frequency-hop spreadspectrum communication system with diversity; side information,M-ary orthogonal signaling, and Reed-Solomon coding. The performance results presented in the paper are based on analysis and computer evaluation. Approximate results based on the Chernoff bound are also given. It is shown that the Chernoff bound forM-ary orthogonal signaling gives a very poor approximation for many cases of interest. This is largely due to the looseness of the union bound.     

Performance of a fast frequency-hopped noncoherent MFSK receiverwith nonideal adaptive gain control

An error probability analysis is performed for an orthogonal noncoherent M-ary frequency-shift keying (MFSK) communication system employing fast frequency-hopped (FFH) spread spectrum with diversity. The signal is assumed to be transmitted through a frequency-nonselective slowly fading channel with partial-band noise interference. The partial-band interference is modeled as a Gaussian process. Both the information signal and the partial-band noise interference signal are assumed to be affected by channel fading; it is assumed that the two fading processes are independent and that channel fading need not necessarily affect the information signal and the interference signal in the same way. Each diversity reception is assumed to fade independently according to a Rician process. Adaptive gain control is employed to minimize partial-band interference effects, and the effect of inaccurate noise measurement on the ability of the adaptive gain control receiver to reject partial-band interference is examined. The effect of thermal noise is included in the analysis     

Maximum-likelihood diversity combining in partial-band noise

Maximum-likelihood diversity combining is investigated for an FFH/MFSK spread spectrum system in partial-band noise (PBN). The structure of maximum-likelihood diversity reception in PBN plus white Gaussian noise is derived. It is shown that signal-to-noise ratio and the noise variance at each hop have to be known to implement this optimum diversity combiner. Several suboptimum diversity combining schemes are also considered. The performance of the optimum combining scheme is evaluated. It is shown that adaptive gain control diversity combining actually achieves the optimum performance when interference is not very weak     

Performance analysis of an FFH/BFSK receiver with ratio-statistic combining in a fading channel with multitone interference

The bit-error probability (BEP) is evaluated for a fast frequency-hopping/binary frequency-shift keying spread-spectrum communication system over a frequency-nonselective, slowly fading channel with worst-case band multitone jamming and additive white Gaussian noise. A diversity reception technique with ratio-statistic combining is applied at the receiver. Both square-law and envelope detectors are utilized and analyzed. Based on circularly symmetric signal theory, the paper obtains the closed-form expressions of probability density function and cumulative distribution function of the ratio-statistic output. It is shown from the analytical results, and verified by simulation, that the BEP performance of the ratio-statistic receiver is sensitive to the fading effect on the desired signal, but is insensitive to that on the jamming tones. It is also shown that the envelope detector provides better performance than the square-law detector.     

Performance of MFSK signals with postdetection square-law diversity combining in arbitrarily correlated Nakagami-m fading channels

This letter presents an analysis of the error probability for noncoherent orthogonal multiple frequency-shift keying (MFSK) signals with postdetection square-law combining (SLC) when the signals transmitted over additive white Gaussian noise (AWGN) and slow frequency-nonselective arbitrarily correlated Nakagami-m fading channels. New exact expressions in a onefold integral for the probability of error of MFSK signals with postdetection square-law diversity combining operating in AWGN channel as well as in arbitrarily correlated Nakagami-m fading channels are derived. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the L diversity channels are considered. The derived expressions can be easily computed, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems.     

Clipped Diversity Combining for Channels with Partial-Band Interference--Part I: Clipped-Linear Combining

Clipped-linear diversity combining is analyzed for receivers without side information. Communication systems with noncoherent demodulation, binary andM-ary orthogonal signaling, and diversity transmission are considered. The main source of interference is additive Gaussian partial-band interference, but a nonzero quiescent noise level is also included in the analysis to account for wide-band noise sources. Some of the results apply to general (non-Gaussian) interference. The numerical results demonstrate that clipped-linear combining can perform well in terms of both narrow-band interference rejection capability and maximum signal-to-interference ratio requirement. A practical disadvantage of clipped-linear combining is that it relies on measurements of the signal output voltage.     

Packet combining in frequency-hop spread-spectrum communicationsystems

The performance of frequency-hop spread-spectrum (FHSS) communication systems using hybrid automatic-repeat-request (ARQ) can be improved by combining current and prior transmissions at the receiver. Two methods for combining packets in systems that employ interleaving and Reed-Solomon (RS) coding are presented and analyzed for the partial-band interference channel. These methods use majority logic combining at the codeword level to make retransmission decisions. Bounded distance errors-and-erasures decoding and erasure generation by means of Viterbi's ratio threshold test (RTT) are incorporated in the analysis. Results of the analysis show that, with comparable packet error probabilities, the packet-combining schemes provide significant gains in throughput when compared with systems that do not employ combining     

Bayesian methods for erasure insertion in frequency-hopcommunication systems with partial-band interference

The erasure of unreliable symbols improves the performance of most types of error-control coding if a good method is used to decide which symbols should be erased. Bayesian decision theory is employed to obtain such a method for use in frequency-hop communications with Reed-Solomon coding and errors-and-erasures decoding. The performance of frequency-hop communications with Bayesian erasure insertion is analyzed for channels with both partial-band and wideband Gaussian noise. The Bayesian technique is compared with Viterbi's ratio-threshold test, and these are compared to receivers that do not erase and use errors-only decoding. Comparisons are also made with receivers that erase all the symbols that are affected by the partial-band interference. When interference is strong, large coding gains result from the Bayesian method, and error probabilities are reduced by several orders of magnitude     

On the application of the sum of generalized Gaussian random variables: maximal ratio combining

In most wireless communication systems, the additive noise is assumed to be Gaussian. However, there are many practical applications where non-Gaussian noise impairs the received signal. Examples include co-channel and adjacent channel interference in mobile cellular systems, impulsive noise in wireless and power-line communications, ultra-wide-band interference and multi-user interference in wireless systems, and spectrum sensing. To cover this issue, we consider in this paper the application of the sum of generalized Gaussian (GG) random variables (RVs). To this end, we consider single-input multiple-output (SIMO) systems that operate over Nakagami-m fading channels in the presence of an additive white generalized Gaussian noise (AWGGN). Specifically, we derive a closed-form expression for the bit error rate (BER) of several coherent digital modulation schemes using maximal ratio combining diversity in the Nakagami-m fading channels subject to an AWGGN. The derived expression is obtained based on the fact that the sum of L GG RVs can be approximated by a single GG RV with a suitable shaping parameter. In addition, the obtained BER expression is valid for integer and non-integer value of the fading parameter m. Analytical results are supported by Monte-Carlo simulations to validate the analysis.     

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 analysis of both hybrid and frequency-hoppedphase-coherent spread-spectrum systems. II. An FH system

For pt.I see ibid., vol.37, no.6, p.601-11 (1989). A pure phase-coherent frequency-hop (FH) system is described, and a digital receiver based on maximum-likelihood estimation of the phase of the frequency-hopped carrier is suggested. The theory developed in pt.I is used in the analysis of the receiver whose performance in the presence of both additive white Gaussian noise and partial-band interference is evaluated. By comparison to the bit error rate performance of noncoherent FSK systems, it is found that for channels without excessive phase distortion, an improvement is achievable with the coherent system, but at a price of a more complex transmitter and receiver     

Antenna diversity combining and finite-tap decision feedbackequalization for high-speed data transmission

The next-generation wireless communication systems are expected to support high-speed data transmission. Associated with high transmission rates, however, is the problem of multipath intersymbol interference (ISI) due to frequency-selective fading. Decision feedback equalization (DFE) and antenna diversity combining are two practical techniques for combating multipath ISI. Through simulations we investigate the performance of diversity combining, together with DFE, under various numbers of antenna branches and equalization taps, in a quasistationary frequency-selective fading environment with additive white Gaussian noise (AWGN) and cochannel interference (CCI). We consider joint optimization combining and power selection diversity combining. We simulate the combiner, using quaternary phase shift keying (QPSK) modulation with up to four antenna branches. Our results show that using antenna diversity and DFE with joint optimization combining provides performance improvement with lower computational complexity, as compared to that of using either DFE or diversity combining alone for combating ISI     

Symbol-error probability and bit-error probability for optimum combining with MPSK modulation

New expressions are derived for the exact symbol error probability and bit-error probability for optimum combining with multiple phase-shift keying. The expressions are for any numbers of equal-power cochannel interferers and receive branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to flat Rayleigh fading. The new expressions have low computational complexity, as they contain only a single integral form with finite limits and finite integrand.     

Exact closed-form performance analysis of optimum combining with multiple cochannel interferers and Rayleigh fading

A new closed-form expression is derived for the exact bit-error probability (BEP) for optimum combining with binary phase-shift keying. The exact BEP expression is for multiple, equal power, cochannel interferers and multiple reception branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to Rayleigh fading. The derivation starts by expressing the optimum combining decision statistic as a sum of quadratic forms of Gaussian random variables and it proceeds to average over the fading interference. The new BEP expression has low complexity as it contains only finite sums and products.     

Performance analysis of maximal ratio combining in the presence ofmultiple equal-power cochannel interferers in a Nakagami fading channel

The effect of cochannel interference on the performance of digital mobile radio systems in a Nakagami (1960) fading channel is studied. The performance of maximal ratio combining (MRC) diversity is analyzed in the presence of multiple equal-power cochannel interferers and additive white Gaussian noise. Closed-form expressions are derived for the average probability of error as well as outage probability of both coherent and noncoherent (differentially coherent) binary frequency-shift keying and binary phase-shift keying schemes in an environment with cochannel interference and noise. The results are expressed in terms of the confluent hypergeometric function of the second kind, a function that can be easily evaluated numerically. The analysis assumes an arbitrary number of independent and identically distributed Nakagami interferers     

Hermitian codes for frequency-hop spread-spectrum packet radio networks

Hermitian codes are an attractive alternative to Reed-Solomon codes for use in frequency-hop spread-spectrum packet radio networks. For a given alphabet size, a Hermitian code has a much longer block length than a Reed-Solomon code. This and other considerations suggest that Hermitian codes may be superior for certain applications. Analytical results are developed for the evaluation of the packet error probability for frequency-hop transmissions using Hermitian coding. We find there are several situations for which Hermitian codes provide much lower packet error probabilities than can be obtained with Reed-Solomon codes. In general, as the code rate decreases or the symbol alphabet size increases, the relative performance of Hermitian codes improves with respect to Reed-Solomon codes. Performance evaluations are presented for an additive white Gaussian noise channel and for certain partial-band interference channels, and the packet error probability is evaluated for both errors-only and errors-and-erasures decoding.     

Adaptive-rate coding for frequency-hop communications over Rayleighfading channels

Because of the variability of the channels in frequency-hop wireless systems and networks, the performance of error-control coding can be improved by adapting the rate of the code to the channel conditions. In this paper, adaptive-rate error-control coding is investigated for slow frequency-hop communications with Reed-Solomon coding. Two methods are investigated that use decoder side information as a means for selecting the code rate. These methods are based on counts of errors and erasures, which are provided by the demodulator and the decoder. The performance of the adaptive-rate coding system is evaluated for channels with Rayleigh fading, partial-band interference, and thermal noise     

Performance comparison of selection combining schemes for binary DPSK on nonselective Rayleigh-fading channels with interference

This paper is concerned with the error performance analysis of binary differential phase shift keying (DPSK) with differential detection over the nonselective Rayleigh-fading channel with selection diversity reception and with an additive, correlated, Gaussian interference process in each diversity channel. The fading process is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The selection schemes investigated are: 1) the selection combining (SC) scheme based on signal-to-noise power ratio (SNR); 2) the SC scheme based on signal-plus-noise (S+N); and 3) the SC scheme based on maximum output (MO). New, exact, closed-form bit-error probability (BEP) expressions are derived, and a performance comparison among the three SC schemes and combining diversity reception is given. The results obtained reduce to previously known results when the correlated interference process is absent, and when the fading process does not fluctuate over the duration of several symbol intervals. The results indicate that the performance of each scheme depends on the tradeoff between the number of diversity branches, the SNR, the interference level, and the correlation of the interference process. However, the SC-(S+N) scheme generally performs worse than the SC-SNR scheme, the SC-MO scheme and combining diversity reception scheme. The findings presented here are not only of fundamental theoretical value, but are also of practical interest to the designers of future mobile communication systems.