Error Probability Bounds and Approximations for DS Spread-Spectrum Communication Systems with Mutiple Tone or Multiple Access Interference

Upper and lower bounds on the average probability of error of direct sequence (DS) spread-spectrum communication systems operating in the presence of either multiple tone or multiple access interference are presented. The bounds are quite tight and can be used without the restriction that the peak level of the interference be less than the desired signal level. A simple method for evaluating approximations to the bounds for multiple access systems, in which the peak interference does indeed exceed the desired signal level, is presented as well. The tightness of both the bounds and the approximations are illustrated with numerical results.     

Signal detection in the presence of multiple-access noise

In this paper we address the mutual interference problems that arise as a result of many independent terminals simultaneously accessing a common channel. "Random code" bounds are used to show the existence of large signal sets for which any one signal can be reliably detected by matched filters despite the mutual interference. Two types of signal sets are considered: sets with a unique signature for every terminal and sets drawn from a small collection of distinct waveforms. The latter sets permit reductions in receiver complexity.     

Multiple-User Interference in FHMA-DPSK Spread-Spectrum Communications

In this paper, we investigate the performance of a nearoptimum receiver in a frequency-hopped multiple-access (FHMA) differential phase-shift-keyed (DPSK) spread-spectrum communication system. We obtain upper bounds on the bit error rates (BER's) for the chipsynchronous system and the chip-asynchronous system in the presence of a single interfering signal which interferes in one time-chip. We also obtain upper bounds on the BER for the chip-synchronous system with multiple-user interference, for the special case where each time-chip has at most one interfering signal of the same power as the desired signal. We find that, for the chip-synchronous system, the upper bound on the BER when one time-chip has two interfering signals is larger than the upper bound on the BER when each of the two time-chips has a single interfering signal. We also discuss system performance for a large number of simultaneous users, and examine the additive white Gaussian noise (AWGN) approximation for the multiple-user interference. Finally, results for the chip-synchronous system with single interference in one time-chip over a Rayleigh fading channel are presented.     

Moment space upper and lower error bounds for digital systems with intersymbol interference

A method for the evaluation of upper and lower bounds to the error probability of a linear pulse-amplitude modulation (PAM) system with bounded intersymbol interference and additive Gaussian noise is obtained via an isomorphism theorem from the theory of moment spaces. These upper and lower bounds are seen to be equivalent to upper and lower envelopes of some compact convex body generated from a set of kernel functions. Depending on the selection of these kernels and their corresponding moments, different classes of bounds are obtained. In this paper, upper and lower bounds that depend on the absolute moment of the intersymbol interference random variable, the second moment, the fourth moment, and an "exponential moment" are found by analytical, graphical, or iterative approaches. We study in detail the exponential moment case and obtain a family of new upper and a family of new lower bounds. Within each family, expressions for these bounds are given explicitly as a function of an arbitrary real-valued parameter. For two channels of interest, upper and lower bounds are evaluated and compared. Results indicate these bounds to be tight and useful.     

Sharp error bounds for intersymbol interference

Sharp upper and lower bounds of the Chebyshev type are established for the probability of error due to intersymbol interference and additive Gaussian noise in a digital communication system. The results are in relatively closed form, and the only statistical knowledge assumed about the interference is the peak eye opening and the variance. The bounds apply to correlated and uncorrelated signals and for any signal to noise ratio.     

Intersymbol Interference Performance of Systems with Correlated Digital Signals

For a digital system with correlated digital symbols, we derive upper and lower bounds on the probability of error when the system is subject to intersymbol interference and additive Gaussian noise. The bounds are expressed in terms of the error probability obtained with a finite number of intersymbol interference terms and some parameters associated with the remainder terms. We also show that the difference between the upper and lower bounds can be made arbitrarily small and that the error probability can be computed to any desired degree of accuracy. We give some examples to illustrate the method.     

On multiple interference error bounds

This letter presents upper and lower bounds for the error rate for (effectively) PAM signalling in the presence of thermal noise, cochannel interference, and intersymbol interference. To accomplish this, two known bounds and one new lower bound are used. For a class of examples from the literature, these simple bounds were found to provide an error-rate estimate accurate to 1 db in system SNR. Computational experiments indicate that this level of accuracy can be achieved when the system's eye is open by at least a factor of two.     

Performance of optimum transmitter power control in cellular radiosystems

Most cellular radio systems provide for the use of transmitter power control to reduce cochannel interference for a given channel allocation. Efficient interference management aims at achieving acceptable carrier-to-interference ratios in all active communication links in the system. Such schemes for the control of cochannel interference are investigated. The effect of adjacent channel interference is neglected. As a performance measure, the interference (outage) probability is used, i.e., the probability that a randomly chosen link is subject to excessive interference. In order to derive upper performance bounds for transmitter power control schemes, algorithms that are optimum in the sense that the interference probability is minimized are suggested. Numerical results indicate that these upper bounds exceed the performance of conventional systems by an order of magnitude regarding interference suppression and by a factor of 3 to 4 regarding the system capacity. The structure of the optimum algorithm shows that efficient power control and dynamic channel assignment algorithms are closely related     

Lower Bounds for Finite Intersymbol Interference Error Rates

Some simple lower bounds for the probability of error for band-restricted digital communication are presented. The bounds revolve two values of the complementary error function, the system SNR, the peak value, second moment, and sometimes, the fourth moment of the intersymbol interference. Contrary to other available lower bounds, no parameter searches or infinite series computations are required. The bounds hold when the system "eye" is open and in some cases when the source symbols are correlated.     

Gaussian Interference Networks: Sum Capacity in the Low-Interference Regime and New Outer Bounds on the Capacity Region

Establishing the capacity region of a Gaussian interference network is an open problem in information theory. Recent progress on this problem has led to the characterization of the capacity region of a general two-user Gaussian interference channel within one bit. In this paper, we develop new, improved outer bounds on the capacity region. Using these bounds, we show that treating interference as noise achieves the sum capacity of the two-user Gaussian interference channel in a low-interference regime, where the interference parameters are below certain thresholds. We then generalize our techniques and results to Gaussian interference networks with more than two users. In particular, we demonstrate that the total interference threshold, below which treating interference as noise achieves the sum capacity, increases with the number of users.     

Error Probability Performance of M-ary CPSK Systems With Intersymbol Interference

We derive upper and lower bounds on the probability of error ofM-ary CPSK systems subject to intersymbol interference and additive Gaussian noise. The bounds are expressed in terms of the error probability obtained with a finite pulse train and some parameters associated with the residual pulse train. Methods are given to compute the probability of error with a finite number of interference terms and it is shown that the difference between the upper and the lower bounds is a monotone decreasing function of the number of pulses in the finite pulse train. The applicability of the method to compute the probability of error with any desired degree of accuracy is illustrated by examples for quaternary and octonary systems.     

Outer bounds on the capacity of interference channels (Corresp.)

New outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and Gaussian interference channels. The bound for discrete channels coincides with the capacity region in special cases. The bound for Gaussian channels improves previous knowledge when the interference is of medium strength.     

Error Probability of Asynchronous Spread Spectrum Multiple Access Communication Systems

Several approaches for the evaluation of upper and lower bounds on error probability of asynchronous spread spectrum multiple access communication systems are presented. These bounds are obtained by utilizing an isomorphism theorem in the theory of moment spaces. From this theorem, we generate closed, compact, and convex bodies, where one of the coordinates represents error probability, while the other coordinate represents a generalized moment of the multiple access interference random variable. Derivations for the second moment, fourth moment, single exponential moment, and multiple exponential moment are given in terms of the partial cross correlations of the codes used in the system. Error bounds based on the use of these moments are obtained. By using a sufficient number of terms in the multiple exponential moment, upper and lower error bounds can be made arbitrarily tight. In that case, the error probability equals the multiple exponential moment of the multiple access interference random variable. An example using partial cross correlations based on codes generated from Gold's method is presented.     

Intersymbol-interference error bounds for hard-limited satellite channels

Upper and lower bounds on the probability of error for binary p.s.k. signals received over a hard-limited satellite channel in the presence of intersymbol interference are derived. Comparison with previously derived numerical results computed for a hard-limited channel containing a Chebyshev filter indicates that the bounds are reaionably tight.     

Outer bounds on the capacity of Gaussian interference channels

Two outer bounds on the capacity region of the two-user Gaussian interference channel (IFC) are derived. The idea of the first bound is to let a genie give each receiver just enough information to decode both messages. This bound unifies and improves the best known outer bounds of Sato and Carleial. Furthermore, the bound extends to discrete memoryless IFCs and is shown to be equivalent to another bound of Carleial. The second bound follows directly from existing results of Costa and Sato and possesses certain optimality properties for weak interference.     

Limiting performance of frequency-hop random access

The multiple-access capability of asynchronous frequency-hop packet-radio networks is analyzed. The only interference considered is multiple-access interference, and perfect side information is assumed. Bounds on the probability of error for unslotted systems are developed based on the distributions of the maximum and minimum interference levels over the duration of a given packet, and these are employed to develop corresponding bounds on the throughput. The idealized model makes possible the derivation of asymptotic results showing the convergence of these bounds for high traffic levels. The asymptotic performance of the system is seen to be the same as that of the corresponding slotted system. Results for the maximum asymptotic throughput are also obtained. These results show that the asymptotic sum capacity of the channel can be attained using Reed-Solomon coding. All these results are valid for either fixed or exponentially distributed packet lengths. The results indicate that the performance of frequency-hop networks is insensitive both to the distribution of packet lengths and to whether or not transmissions are slotted. It also demonstrates the efficacy of Reed-Solomon coding in combating multiple-access interference     

An efficient technique for evaluating direct-sequencespread-spectrum multiple-access communications

A technique is presented for obtaining bounds on the average probability of error for direct-sequence spread-spectrum multiple-access (DS/SSMA) communications. The technique is of interest because it yields arbitrarily right bounds, involves a small amount of computation, avoids numerical integrations, and applies to many types of detection. As an illustration, the technique is applied to binary DS/SSMA communications, an additive white Gaussian noise channel, and a coherent correlation receiver. It is assumed that all the signature sequences are deterministic. Each transmitter is assumed to have the same power, although the approach can accommodate the case of transmitters with unequal powers. Expressions are given for the density functions of the random variables that model the multiple-access interference. These expressions are used to obtain arbitrarily tight upper and lower bounds on the average probability of error without making a Gaussian approximation or performing numerical integrations to incorporate the effects of multiple-access interference     

Performance analysis of ultra‐dense networks with MRC reception and successive interference cancellation under rate‐limited backhaul

Ultra‐dense network (UDN) is one of candidate technologies for next generation cellular networks. In this paper, we explore performance limits of cooperative UDN with maximal ratio‐combining detection under limited‐capacity backhaul links. More concretely, based on the imperfect estimation, lower bounds of the average per‐user rate are derived for maximal ratio‐combining detection with and without successive interference cancellation scheme when the number of Base stations (BSs) in the network goes to infinite. Then we discuss how the average per‐user rate is impacted by the number of cooperative BSs and the backhaul capacity. Our results show that there is an optimal number of cooperative BSs in the UDN to achieve the best performance in low signal‐to‐noise‐ratio region. Simulations demonstrate that our asymptotic rate bounds are tight when the number of BSs is large. Copyright © 2016 John Wiley & Sons, Ltd.     

Performance Analysis on Two-Way Relay System with Co-Channel Interference

In this paper, we investigate the performance of two-way relay system with co-channel interference in a Rayleigh fading environment. Due to the mathematical intractability of original expression of signal-to-interference and noise ratio (SINR) induced by the bi-directional forwarding, a couple of effective bounds are derived for important performance metrics such as outage probability and average bit error rate of modulation, with application of diverse physical layer network coding (PNC) schemes of two time slot (2TS) and three time slot (3TS). Some asymptotic solutions are also proposed to intuitively exhibit the trends of performance in high SINR regime. We demonstrate that the performance bounds have practical meaning corresponding to different forwarding capability of the relay. Numeric simulations validate our analysis by showing that the theoretic bounds match well with simulation results. Additionally, the effect of distance between relay and sources is discussed in our interference scenario, as well as the impact of relay’s power allocation factor in 3TS PNC scheme.     

Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences

Frequency hopping (FH) sequences have found wide applications in various modern FH spread-spectrum communications and radar systems. In FH spread-spectrum communications, the interference occurs when two distinct transmitters use the same frequency simultaneously. In order to evaluate the goodness of FH sequence design, the Hamming correlation function is used as an important measure. In this correspondence, by considering separately the maximum Hamming autocorrelation sidelobe H/sub a/, and the maximum Hamming cross correlation H/sub c/, several new lower bounds on the size p of the frequency slot set F, the sequence length L, the family size M, and correlation properties are established. The new periodic bounds include the known Lempel-Greenberger bounds as special case when M=2, and are tighter than the Seay bounds under certain conditions when M>2. Furthermore, the new bounds disclose more information on the relationship between the maximum autocorrelation sidelobe and the maximum cross correlation compared with the Lempel-Greenberger bounds and Seay bounds. Besides, the aperiodic FH bounds which have not yet been previously reported are also presented and discussed in this correspondence.