Coherent Binary Phase Shift Keying Research Articles

Average BER analysis for binary signallings in decode-and-forward dissimilar cooperative diversity networks

In this letter, the average bit-error rate (BER) performance is analyzed for uncoded decode-and-forward (DF) cooperative diversity networks. We consider two typical networks: a single-relay cooperative network with the direct source destination link and a two-relay cooperative network with the direct source-destination link, under dissimilar network settings, i.e., the fading channels of different relay branches may have different variances. We first derive a closed-form approximate average BER expression of binary signallings including noncoherent binary frequency shift keying (BFSK), coherent BFSK, and coherent binary phase shift keying (BPSK), for the single relay network. We then generalize our analysis to the two-relay network, and a closed-form approximate average BER expression for binary signallings is derived. We also show that our BER expressions can be considered as generalizations of previously reported results in the literature. Throughout our analysis, only one approximation, so-called the piecewise-linear approximation, is made. Simulation results are in excellent agreement with the theoretical analysis, which validates our proposed BER expressions.

Diversity Combining and SNR Estimation for Turbo-Coded Frequency-Hopped Spread-Spectrum in Partial-Band Interference and Fading Channels

We compare different combinations of the repetition diversity order L and code rate R for turbo-coded Frequency-Hopped Spread-Spectrum (FH/SS) communication systems in the presence of fading and partial-band Gaussian interference. For a fixed overall channel code rate R/L we show that using the lowest code rate and no repetition diversity always performs better than using a higher code rate and some repetition for both coherent and non-coherent schemes. We then propose a simple maximum-likelihood-based method for signal-to-noise-ratio (SNR) estimation in Non-Coherent Binary Frequency Shift Keying (NCBFSK) without training symbols. Except for impractically small hop sizes of 8 bits or less we obtain performance virtually equal to that of perfect SNR knowledge but with much less complexity than iterative schemes previously proposed. For the case of Coherent Binary Phase Shift Keying (CBPSK) we derive the Expectation Maximization (EM) estimate of the SNR without training symbols and iteratively feed the estimator with the extrinsic information from the turbo decoder. The performance for CBPSK is near that of perfect SNR knowledge for hop sizes of 64 bits or more. Unlike previously proposed methods for CBPSK the EM estimate of SNR does not require knowledge of the noise and interference variance, received bit energy, or the fading channel model.

Explicit Analytical Expressions for Outage and Error Rate of Diversity Cellular Systems in the Presence of Multiple Interferers and Correlated Rayleigh Fading

The outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience Rayleigh fading and have the same correlation matrix. Two special cases, when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues, are considered for both the equal-power cochannel interference case and the unequal-power cochannel interference case. Further, the average bit-error rate of a coherent binary phase-shift keying (BPSK)-modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated Rayleigh fading is derived. The effects of the average signal-to-noise ratio (SNR) and the average signal-power-to-interference-power ratio on the system performance are examined.

Analysis of microdiversity and dual channel macrodiversity in shadowed fading channels using a compound fading model

Wireless channels are affected by short-term fading and long-term fading (shadowing). A compound fading model was proposed for the modeling of shadowed fading channels which resulted in a closed form solution for the probability density function (pdf) of the signal-to-noise ratio (SNR). This model is applied to a case where both micro- and macro-diversity schemes are implemented to mitigate short-term fading and shadowing, respectively. Using the compound fading model, it is shown that the pdf of the signal-to-noise ratio after the implementation of maximal ratio combining (MRC) at the micro level and selection combining (SC) at the macro level can be expressed in analytical form. Even when branch correlation exists, the pdf still can be expressed in analytical form. Thus, the compound pdf model offers significant improvement over approaches which use lognormal pdf for shadowing. The performance of a coherent binary phase shift keying (BPSK) modem is evaluated using this approach. The results demonstrate the simplicity and usefulness of the compound pdf in the performance analyses of shadowed fading channels even when branch correlation exists at the base station or correlation exists between base stations.

Error Rate of Quadrature Subbranch Hybrid Selection/ Maximal-Ratio Combining in Rayleigh Fading

The symbol-error rate (SER) of a quadrature subbranch hybrid selection/maximal-ratio combining (QBHS/MRC) scheme for 1-D modulations in Rayleigh fading is examined. At the receiver, N diversity branches are split into 2N in-phase and quadrature subbranches. Traditional hybrid selection/maximal-ratio combining (H-S/MRC) is then applied over the 2N subbranches. M-ary pulse amplitude modulation, including coherent binary phase-shift keying, with QBHS/MRC is studied. The SER performances of QBHS/MRC and H-S/MRC are compared. Results show that QBHS/MRC systems outperform traditional H-S/MRC systems

A non-correlator-based digital communication system using interleaved chaotic differential peaks keying (I-CDPK) modulation and chaotic synchronization

Abstract This paper presents a novel non-correlator-based digital communication system with the application of interleaved chaotic differential peaks keying (I-CDPK) modulation technique. The proposed communication system consists of four major modules: I-CDPK modulator (ICM), frequency modulation (FM) transmitter, FM receiver and I-CDPK demodulator (ICDM). In the ICM module, there are four components: a chaotic circuit to generate the chaotic signals, A/D converter, D/A converter and a digital processing mechanism to control all signal flows and performs I-CDPK modulation corresponding to the input digital bits. For interleaving every input digital bit set, every state of the chaotic system is used to represent one portion of it, but only a scalar state variable (i.e. the system output) is sent to the ICDM’s chaotic circuit through both FM transmitter and FM receiver. An observer-based chaotic synchronization scheme is designed to synchronize the chaotic circuits of the ICM and ICDM. Meanwhile, the bit detector in ICDM is devoted to recover the transmitted input digital bits. Some numerical simulations of an illustrative communication system are given to demonstrate its theoretical effectiveness. Furthermore, the performance of bit error rate of the proposed system is analyzed and compared with those of the correlator-based communication systems adopting coherent binary phase shift keying (BPSK) and coherent differential chaotic shift keying (DCSK) schemes.

Performance analysis of linear diversity-combining schemes on Rayleigh fading channels with binary signaling and Gaussian weighting errors

In this paper, we analyze the error probability performance of maximal-ratio combining (MRC), equal-gain combining (EGC), selection combining (SC), and generalized-selection combining (GSC) diversity schemes with coherent binary phase-shift keying (BPSK) signaling on Rayleigh fading channels with Gaussian channel-estimation errors. We first show that, with weighting errors, averaging the conditional probability of error with the density function of the instantaneous signal-to-noise ratio (SNR) at the output of the combiner yields a lower bound on the exact probability of error. Later, we derive the exact probability of error for MRC, EGC, SC, and GSC diversity schemes and show that, for the case of nonnegative values of the in-phase correlation coefficient between the actual and the estimated channel gains, the exact probability of error with weighting errors is the same as that of the case with perfect channel estimation, but with the average SNR per diversity branch /spl gamma/~, for the case of perfect channel estimation, replaced by the effective SNR /spl gamma/~/sub /spl rho//, due to weighting errors. The effective SNR is a function of both /spl gamma/~ and /spl rho/, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as /spl rho//spl rarr/0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity-combining rule.

Exact BER Analyses of Nakagami/Nakagami CCI BPSK and Nakagami/Rayleigh CCI QPSK Systems in Slow Fading

A recent letter presented an approximate bit error rate (BER) analysis of coherent binary phase-shift keying (BPSK) in cochannel interference with Nakagami faded desired and interfering signals. Here, the exact BER of coherent nonreturn-to-zero (NRZ) BPSK with cochannel interference in Nakagami fading is derived showing that the approximate analysis may be inaccurate. The exact BER of NRZ quaternary PSK (QPSK) with Nakagami faded desired user signal and Rayleigh faded interfering signals is also derived. Slow fading, asynchronous timing and independent fading gains are assumed.

Analysis of Performance of BPSK in an Additive Combination of Impulsive and Gaussian Noise

We analyze the bit error rate (BER) performance of a correlation receiver subject to impulsive plus Gaussian noise with coherent binary phase-shift keying (BPSK). The impulsive component of the noise is assumed to be due to random occurrences of impulses following a Poisson arrival process. Using the moments of the impulsive component, a series expression for the BER is derived by a Taylor's series approach. From this expression, approximate formulae for extreme values of signal-to-noise ratio (SNR) and impulse arrival rate (IAR) are obtained. Numerical results show that when the square root raised cosine pulse is used, (1) the BER performance improves with increase of the rolloff factor, but the improvement becomes more significant with decrease of the Gaussian-to-total noise ratio or increase of the IAR, (2) as the rolloff factor increases, a decrease of the IAR degrades the BER performance for low SNRs, but improves it for high SNRs.

Analyzing GPS signals to investigate path diversity effects of non‐geostationary orbit satellite communication systems

AbstractThe concept behind path diversity is that a user who can access several satellites simultaneously will be able to communicate more effectively than a user who could only access one. The success of this method depends on the environment, the satellite constellation, and diversity combining technology. This paper explores the path diversity effects of non‐geostationary orbit (NGO) satellite personal communication services, for different degrees of user mobility, under various scenarios, using the constellation of the global positioning system (GPS). Measurements are taken near downtown Taipei. Three types of mobilities (fixed‐point, pedestrian, and vehicular) are examined, and the switch diversity and maximum ratio combining method are applied to determine the path diversity gain and calculate bit error probability. The error probability performance of applying diversity schemes in coherent binary phase shift keying (BPSK) and non‐coherent differential phase shift keying (DPSK) modulations over Rician fading channels are also analysed and evaluated by using the characteristic function method. The results show that fading can be significantly reduced and diversity greatly increased. A significant diversity gain and improvement in bit error rate (BER) can be expected in all cases by simply applying switch diversity scheme. Besides, for the maximum ratio combining method, the results imply that summing two satellite signals suffices to increase diversity and improve the bit error rate performance. Copyright © 2002 John Wiley & Sons, Ltd.

Analysis of a two-branch maximal ratio and selection diversity system with unequal SNRs and correlated inputs for a Rayleigh fading channel

An analytical expression for the probability density function of the signal-to-noise ratio (SNR) at the output of a two-branch maximal ratio and selection diversity system is given. The two branches are assumed to be Rayleigh fading, correlated, as well as of unequal average SNRs. Measurements of the cumulative distribution functions after selection and maximal ratio combining were made in Rayleigh fading channels and compared with the analytical results. Also presented are the exact analytical average probabilities of symbol error for coherent binary phase-shift keying and coherent quaternary phase-shift keying before and after two-branch maximal ratio combining for a slow and flat fading correlated Rayleigh channel.

Selection and MRC Diversity for a DS/CDMA Mobile Radio System through Nakagami Fading Channel

Spatial diversity is an attractive technology for coping with the fading channels encountered in mobile communications. In this paper, the bit error rate (BER) is analyzed theoretically for diversity reception with a RAKE receiver in a Nakagami fading environment using either selection or maximal ratio combining. A coherent binary phase-shift keying (CBPSK) direct sequence code division multiple access (DS/CDMA) system is considered. An arbitrary branch correlation is also considered for any diversity order in the case of identical fading severity on the branches.

Performance of antenna array systems with optimum combining in a Rayleigh fading environment

The effect of cochannel interference on the performance of digital mobile radio systems in a Rayleigh fading environment is studied. The average bit error rate (BER) of an antenna array system with an optimum combining scheme that maximizes the output signal-to-interference-plus-noise ratio (SINR) is analyzed. BER expressions which are easy to evaluate numerically are derived for coherent binary phase shift keying (BPSK) schemes in an environment with cochannel interference and noise.

Performance analysis of optimum combining with multiple interferers in flat Rayleigh fading

This paper is a performance analysis of optimum combining in the presence of multiple equal power interferers and noise when the number of interferers is less than the number of antenna elements. Desired signal and interferers are subject to flat Rayleigh fading, and the propagation channels are independent. An approximate expression of the probability density function of the output signal-to-interference-plus-noise ratio (SINR) is derived analytically. It is then applied to obtain the cumulative distribution function of the SINR, and the bit-error rate (BER) of some binary modulations, including coherent binary phase-shift keying. In the case of a single interferer, an exact analysis is performed to prove the validity of the approximation. In the case of multiple interferers, the accuracy of the approximation is assessed through simulations. Although limited to equipower interferers, this analysis is a convenient way of assessing the performance of optimum combining in some typical situations and comparing it with that of maximal-ratio combining. The final results are remarkably simple and provide a useful complement to previous analyzes, especially in the region of reasonably high BERs which are of practical interest.

Performance analysis of cellular CDMA networks over frequency-selective fading channel

An effect of multipath fading on the performance of a cellular code-division multiple-access (CDMA) system is analyzed in this paper. A wide-sense stationary uncorrelated scattering (WSSUS) channel model and the coherent binary phase-shift keying (BPSK) with asynchronous direct-sequence (DS) spreading signal are assumed in the analysis. The average error probability for both the forward link and reverse link of a cellular CDMA system over a frequency-selective fading channel using a conventional correlation-type receiver and RAKE receiver are derived. The impact of imperfect power control and channel capacity of a cellular CDMA system is also investigated. The closed forms of average error probability derived in the paper can save a lot of computation time to analyze the performance and channel capacity of a cellular CDMA system. The analytical results show that the performance and maximum transmission rate of cellular CDMA systems degrade with an increase in the number of simultaneous users and the number of interfering cells. The signal-to-interface ratio (SIR) for the reverse link derived in this paper can directly describe the interrelationships among a number of paths, number of users, number of interfering cells, fading factors, and maximum variation of a received unfaded signal.

The use of coding and diversity combining for mitigating fading effects in a DS/CDMA system

Spatial diversity is an attractive technology to cope with the fading channel encountered in mobile communications. This paper presents novel closed analytical expressions of the bit-error rate (BER) achievable in a coherent binary phase-shift-keying (CBPSK) direct-sequence code-division multiple-access (DS/CDMA) system for any power delay profile and for either postdetection selection or maximal ratio combining (MRC). In particular, expressions for the cutoff rate R/sub o/ and for its related parameter D are also formulated in order to assess the system performance under the consideration of some channel coding schemes. Finally, an exemplary study is carried out in order to illustrate the behavior of a realistic space-diversity code-division multiple-access (CDMA) system according to the analytical expressions that have been derived.

Dual-Space Diversity over Land Mobile Satellite Channels Operating in the L and K Frequency Bands

Land mobile satellite communication systems at Ka/K band (30/20 GHz) are attracting more and more attention to researchers because of its frequency band availability and the possibility of using small earth stations and satellite antennas for the systems. However, the Ka/K-band communications also give significant challenges in the system design due to severe channel impairments expected from the satellite links. In this paper, K-band channel characteristics are studied and compared with those at L band. The channel is modeled as Rayleigh multipath fading with the line-of-sight (LOS) component following a lognormal distribution. The first and second-order statistics of the fading channel are studied. Dual-space diversity reception is investigated to combat the flat channel fading. The bit error rate performance of coherent binary phase shift keying (BPSK) with ideal bit and carrier phase synchronization over the fading channel at K band is evaluated theoretically and verified by computer simulations in the case with and without diversity reception.

Maximum-likelihood decoding and code combining for DS/SSMA slotted ALOHA

This paper considers the combination of multiple copies of a packet to improve the performance of a slotted direct-sequence spread-spectrum multiple-access (DS/SSMA) ALOHA packet radio system with coherent binary phase-shift keying (BPSK) modulation. Both slotted DS/SSMA ALOHA with and without forward error correction (FEC) are considered. For the case with FEC, maximum-likelihood decoding with code combining is used. Code combining allows for the combination of multiple copies of the same packet (which are typically discarded), to obtain a lower code rate for that specific packet, and therefore an improved probability of successful decoding. In both cases, combining multiple copies of the same packet results in a throughput which is an increasing function over a broad range of offered load, so that the system is more reliable from the point of view of stability. In addition, combining provides a higher throughput and a smaller time delay for packet transmission. This is illustrated by means of analytical and simulation results.

Suboptimum multiuser receivers for convolutionally coded asynchronous DS-CDMA systems

Motivated by the high complexity of the optimal sequence estimator for convolutionally coded asynchronous code-division multiple-access (CDMA) systems, developed by Giallorenzi and Wilson (see ibid., vol.44, no.8, p.997, 1996), and the potentially poor performance of the conventional receiver due to multiuser interference and the near-far problem, we examine relatively simple multiuser receivers which perform nearly as well as the optimal receiver. The multiuser receivers discussed are of two types. The first set of approaches are partitioned approaches that treat the multiuser interference equalization problem and the decoding problem separately. The second set of approaches are integrated approaches that perform both the equalization and decoding operations together. We study linear, decision feedback, and trellis/tree-based approaches in each category. The asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying (BPSK) receiver (termed asymptotic multiuser coding gain, or AMCG) is used as a performance criterion throughout. Also, computer simulations are used whenever the computation of the AMCG is not feasible. It is shown that a number of the approaches which are introduced achieve a high performance level with a moderate complexity.

Wideband indoor channel measurements and BER analysis of frequency selective multipath channels at 2.4, 4.75, and 11.5 GHz

Results from propagation measurements, conducted in an indoor office environment at 2.4, 4.75, and 11.5 GHz, are presented. The data were obtained in small clusters of six measurements, using a coherent wideband measurement system. The channel characteristics for the three frequencies are compared by evaluating path loss, rms delay spread, and coherence bandwidth. An analytical model for evaluation of the bit-error rate (BER) of the stationary frequency selective indoor channel is developed for a coherent binary phase shift keying (BPSK) receiver, based on the complex impulse response of the channel. Computational BER results are obtained for data rates up to 50 Mb/s, using the measured multipath channel impulse responses. The BER results for a number of clusters are presented and compared for the maximum reliable data rate as inferred by the measured rms delay spread of the channel.