On the error probability of coded frequency-hopped spread-spectrummultiple-access systems

A simple, exact calculation is presented of the probability distribution of the number of hits in a block of n symbols in a frequency-hopped, spread-spectrum, multiple-access communication system. While the sequence of hits is not Markovian, there is an underlying Markovian structure that allows the probability distribution of the number of hits to be calculated in a recursive fashion. Knowing the probability distribution of the number of hits makes it possible to calculate the probability of error for a system employing error correcting codes for several different types of receivers, including receivers with both errors and erasures. The numerical results show that both the approximation obtained by assuming the actual sequence of hits is Markovian and the approximation obtained by assuming the hits are independent are very good. When the number of frequency slots is not too small (less than five), calculations show that assuming the independence of hits gives an error probability accurate to within 1% of the actual error probability. Assuming the hits are Markovian gives error probabilities which are accurate to within 0.001%     

Probability of error for noncoherent M-ary orthogonal FSK with postdetection switched combining

The paper extends the notion of postdetection switched combining introduced by the authors to M-ary orthogonal modulation (Alouini and Simon, ibid., p.1591-1602, 2003) and proceeds to analyze and evaluate its average bit-error rate performance for the dual-branch case. The particular variation chosen for the switching strategy uses a different model than that previously used for the binary case and although it results in a slightly poorer performance, it nevertheless outperforms conventional (predetection) switched combining for all values of M. Results are obtained for a variety of popular channel models including Rayleigh, Rician, and Nakagami-m fading. Because of its relative simplicity of implementation, the proposed scheme once again offers a very attractive low-complexity solution for mitigating the deleterious effects of multipath fading.     

Performance of noncoherent maximum-likelihood sequence detection for differential OFDM systems with diversity reception

For the single-carrier M-ary differential phase-shift keying (MDPSK), the multiple-symbol differential detector, or the noncoherent maximum-likelihood sequence detector (NSD), and its three special cases, namely, the noncoherent one-shot detector, the linearly predictive decision-feedback (DF) detector, and the linearly predictive Viterbi receiver are reviewed based on a hierarchical interpretation. For the multicarrier transmission, the differential orthogonal frequency division multiplexing (OFDM) systems with diversity reception are discussed. It is well known that there are two types of differential OFDM systems, namely, the time domain differential OFDM (TD-OFDM) and the frequency domain differential OFDM (FD-OFDM). In this paper, the NSD and its special cases are incorporated to the differential OFDM systems. Furthermore, we provide a simple closed-form bit-error-rate (BER) expression for the differential OFDM systems utilizing the noncoherent one-shot detector with diversity reception in the time-varying multipath Rayleigh fading channels. Numerical results have revealed that, with multi-antenna diversity reception, the performance of the noncoherent one-shot detector is improved significantly. However, when only one or two receive antennas are available, the implementation of the linearly predictive DF detector or the linearly predictive Viterbi receiver is necessary for achieving better and satisfactory performance.     

Probability of error analysis of digital partial responsecontinuous phase modulation with noncoherent detection in mobile radiochannels

An analysis is presented of noncoherent detection of constant-envelope digital partial-response continuous-phase modulation (PRCPM) in fast Rayleigh fading that characterizes land mobile radio channels. Closed-form expressions for the probability of error are derived for limiter discriminator detection, and both 1- and 2-bit differential detection. Numerical results are presented for cases of practical interest to researchers and designers of land mobile radio systems. The expressions derived for the probability of error are general and can be used for all PRCPM schemes     

Generalized correlation-delay-shift-keying scheme for noncoherent chaos-based communication systems

In this paper, we propose a generalized correlation-delay-shift-keying (GCDSK) scheme for noncoherent chaos-based communications. In the proposed scheme, several delayed versions of a chaotic signal are first produced. Some of them will be modulated by the binary data to be transmitted. The delayed signals will then be added to the original chaotic signal and transmitted. At the receiver, a simple correlator-type detector is employed to decode the binary symbols. The approximate bit error rate (BER) of the GCDSK scheme is derived analytically based on Gaussian approximation. Simulations are performed and compared with the noncoherent correlation-delay-shift-keying (CDSK) and differential chaos-shift-keying (DCSK) modulation schemes. The effects of the spreading factor, length of delay, and the number of delay units on the BER are fully studied. It is found that GCDSK can achieve better BER performance than DCSK under reasonable bit-energy-to-noise-power-spectral-density ratios.     

Probability of error in digital communication systems with intersymbol interference and dependent symbols (Corresp.)

An upper and lower bound to the probability of error is presented for a digital communication system with dependent symbols affected by additive noise and intersymbol interference. Explicitly considered are two systems in which independent binary symbols are encoded into ternary dependent symbols, i.e., a bipolar code and a dicode. The bounds practically coincide under a proper choice of certain integers; hence the true value of probability of error can be computed as a function of signal to noise ratio.     

Probability of error under conditions of optimum and suboptimum incoherent diversity reception in a dispersive communication channel with fading and time spread

Expressions are derived for estimating the probability of error under conditions of optimum and suboptimum incoherent diversity reception of signals with an arbitrary structure in a dispersive communication channel with fading and time spread. Effects of intersymbol interference are taken into account. Results of calculations are presented.     

Coded modulation for noncoherent reception with application to OFDM

Power- and bandwidth-efficient differentially encoded transmission over slowly time-varying fading channels with noncoherent reception and without channel state information is considered. For high bandwidth efficiencies, combined phase and amplitude modulation is used. For increased power efficiency, channel coding and multiple-symbol differential detection are applied, i.e., interleaving and detection are based on blocks of N>2 consecutive symbols. The presented concepts are directly applicable to transmission over flat fading channels. However, concentrating on the situation of frequency-selective channels, we consider their application to multicarrier transmission using orthogonal frequency-division multiplexing (OFDM). When coding across subcarriers, OFDM transforms the actual frequency-selective channel into a slowly time-varying frequency-nonselective fading channel. This paper presents a design for multilevel coding schemes to approach theoretical limits for power- and bandwidth-efficient noncoherent transmission over the equivalent fading channel. It is shown that bit-interleaved coded modulation, which relies on Gray labeling, is competitive only in the case of conventional differential detection with N=2. The theoretic considerations are well approved by simulation results, where turbo codes are applied as component codes     

Probability of error calculation of OFDM systems with frequencyoffset

Orthogonal frequency-division multiplexing (OFDM) is sensitive to the carrier frequency offset (CFO), which destroys orthogonality and causes intercarrier interference (ICI), Previously, two methods were available for the analysis of the resultant degradation in performance. Firstly, the statistical average of the ICI could be used as a performance measure. Secondly, the bit error rate (BER) caused by CFO could be approximated by assuming the ICI to be Gaussian. However, a more precise analysis of the performance (i.e., BER or SER) degradation is desirable. In this letter, we propose a precise numerical technique for calculating the effect of the CFO on the BER or symbol error in an OFDM system. The subcarriers can be modulated with binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), or 16-ary quadrature amplitude modulation (16-QAM), used in many OFDM applications. The BPSK case is solved using a series due to Beaulieu (1990). For the QPSK and 16-QAM cases, we use an infinite series expression for the error function in order to express the average probability of error in terms of the two-dimensional characteristic function of the ICI     

On the error probability of coded frequency-hopped spread-spectrummultiple-access systems with more than one code symbol per dwellinterval

The multiple-access capability of an asynchronous, frequency-hopped spread-spectrum (FH-SS) communication system employing error correcting codes is reviewed. Many current FH-SS systems employ error correcting codes with more than one code symbol per dwell interval. A method of computing the codeword error probability induced in such spread-spectrum systems is presented. The codeword error probabilities induced in spread-spectrum systems utilizing more than one versus one code symbol per dwell interval are compared. It is concluded that FH-SS systems with one code symbol per dwell interval are more efficient in combating multiple-access interference than FH-SS systems with more than one code symbol per dwell interval     

Random-access communication with multiple reception

Communication over a random multiple-access (RMA) broadcast channel with multiple reception capability is considered. Multiple reception refers to the assumption that a collision is defined as the simultaneous transmission of more than d packets, where d ⩾2. In most previous studies of RMA channels, it was assumed that d=1, that is, whenever more than one source tries to use the same slot, a collision occurs, and all the messages involved must be retransmitted. In practice, however, it might be possible to construct RMA systems where simultaneous transmission of d or fewer packets, where d⩾2, is successful. In this work, the author presents conflict resolution algorithms and determine lower bounds to the capacity of such RMA channels for many different feedback models. It is shown that the packet transmission rates (throughput) reported previously can be achieved under much less restricted feedback models     

Efficient evaluation of the error probabilities of spread-spectrummultiple-access communications

We consider the performance of code-division multiple-access (CDMA) communications. In particular, we illustrate the use of a semianalytical approach which is combined with importance sampling for the efficient evaluation of the average bit-error rates (BERs) of asynchronous direct-sequence (DS) based CDMA systems employing binary phase shift keying (BPSK) modulation along with specific signature sequences for a variety of system parameters     

Capacity of frequency-hop spread-spectrum multiple-accesscommunication systems

The information theoretic capacity is considered. In order to account for independent encoding and decoding and private (to the sender and receiver) hopping patterns, an interference channel model is adopted with K sender-receiver pairs with the ith receiver only interested in the message transmitted by the ith sender. Both synchronous and asynchronous hopping patterns are investigated. Although the channel exhibits memory in the latter case, it is possible to compute the capacity region. The asymptotic normalized sum capacity is also computed     

Probability of error in PAM systems with intersymbol interference and additive noise

The effect of intersymbol interference and additive noise on the performance of a digital data transmission system is considered. The data sequence is assumed to be independent and equiprobable. The additive noise is independent of the signal but is not restricted to be Gaussian. A simple lower bound, an upper bound, and a simple approximation to the upper bound, on the probability of error are derived. The approximation to the upper bound is twice the lower bound; hence, either can be taken as an approximation to the actual error probability.     

FSO通信系统接收性能的仿真研究

通过对自由空间光通信(FSO)系统组成原理的分析,利用OptiSystem光通信软件设计了FSO光传输链路仿真模型.在IM/DD调制方式下,结合眼图分析仪和误码率分析仪,对光链路接收性能进行分析,得到了很低的误码率,验证了无线光信号在较为恶劣天气下传输具有切实可行性.     

Use of error patterns in coded communication systems

In digital communication systems, receivers often have trouble in deriving the correct bit synchronisation from transitionless received signals. The letter shows that transitionless signals can come from four sources, and that this problem can be easily eliminated by injecting a detectable error pattern into the transmitted coded signal.     

The performance of optical fiber direct-sequence spread-spectrummultiple-access communications systems

Because of the random nature of the photodetection process and the multiple-user interference, an exact analysis of avalanche photodiode (APD)-based optical code division multiple-access (CDMA) communications systems is intractable and quite often, Monte Carlo (MC) simulations which yield exact estimates of system performance in terms of bit error rates (BERs) require a prohibitive computational burden. A quick and accurate MC method for simulating APD-based optical CDMA systems is presented. In particular, a performance analysis of optical CDMA systems employing optical orthogonal and prime sequence codes is undertaken     

Probability of error for digital systems with inaccurately known interference (Corresp.)

The "moment bound theory" is known to provide a useful technique to evaluate error probabilities for digital communication systems in the presence of additive noise and random interference. In this correspondence this theory is extended to the case where the moments of the interference are known only within certain intervals, and upper and lower bounds to the error probabilities are sought. A situation like this can occur in several applications. For example, the exact statistics of the interference may not be known, and only estimates of the first moments may be available. Another example arises when the signal is disturbed by intersymbol interference generated by a channel impulse response whose samples are known only in a certain interval--either because they have been measured with finite accuracy, or because we want to estimate the error probability for a class of channel impulse responses. Several numerical examples are provided which show the range of applicability of this technique.     

Compact formulas for the average error performance of noncoherent m-ary orthogonal signals over generalized rician, nakagami-m, and nakagami-q fading channels with diversity reception

This paper derives exact expressions for the average error performance of M-ary orthogonal signals with noncoherent equal-gain diversity combining over nonidentical generalized Rician, Nakagami-m, Nakagami-g, and implicitly Rayleigh fading channels. The assumption of generalized distributed fading envelopes implies that the received average signal-to-noise ratios (SNRs) and/or the fading parameters can have arbitrary nonidentical values. The derived expressions are precisely given in terms of either one-fold integral or rapidly convergent infinite series, which can be readily evaluated numerically. In addition, they can be usefully used to study the impact of arbitrary correlation among diversity branches on the system average error performance.     

New super-orthogonal space-time trellis codes using differential M-PSK for noncoherent mobile communication systems with two transmit antennas

In this paper, we develop super-orthogonal space-time trellis codes (SOSTTCs) using differential binary phase-shift keying, quadriphase-shift keying and eight-phase shift keying for noncoherent communication systems with two transmit antennas without channel state information at the receiver. Based on a differential encoding scheme proposed by Tarokh and Jafarkhani, we propose a new decoding algorithm with reduced decoding complexity. To evaluate the performance of the SOSTTCs by way of computer simulations, a geometric two-ring channel model is employed throughout. The simulation results show that the new decoding algorithm has the same decoding performance compared with the traditional decoding strategy, while it reduces significantly the overall computing complexity. As expected the system performance depends greatly on the antenna spacing and on the angular spread of the incoming waves. For fair comparison, we also design SOSTTCs for coherent detection of the same complexity as those demonstrated for the noncoherent case. As in the case of classical single antenna transmission systems, the coherent scheme outperforms the differential one by approximately 3 dB for SOSTTCs as well.