When the range of single-hop wireless communication is limited by distance or harsh radio propagation conditions, relays can be used to extend the communication range through multihop relaying. This paper targets the need in certain scenarios for rapid deployment of these relays when little or nothing is known in advance about a given environment and its propagation characteristics. Applications include first responders entering a large building during an emergency, search and rescue robots maneuvering a disaster sight, and coal miners working underground. The common element motivatingthis work is the need to maintain communications in an environment where single-hop communication is typically inadequate. This paper investigates the feasibility of the automated deployment of a multihop network. A deployment procedure is proposed that employs real-time link measurements and takes into account the physical layer characteristics of a mobile multipath fading environment and the radio in use. A prototype system is implemented based on 900 MHz TinyOS motes supporting low-speed data applications including text messaging, sensor data and RFID-assisted localization. Results of deployments in a hi-rise office building are presented.

This paper presents the empirical results and analysis of a link variability study for an indoor, stationary 802.11 network subject to external interference. The objective is to characterize the relationships between the packet loss rate on a link and the transmitter-receiver distance, the SNR as reported by the 802.11 card, and time. Experimental results confirm that distance is not predictive of link reliability. Furthermore, attempting to estimate the packet loss rate by counting missing packets can lead to large estimation errors and latency for estimation parameters of practical interest. We find, however, that the SNR measurements reported by today's 802.11 cards can, under certain circumstances, be reliably predictive of the packet loss rate. These results suggest that SNR-based link assessment can provide for more rapid and accurate measurement of link reliability, but they point to the need for improved SNR measurements and models to adequately predict link quality in environments with significant external interference

New analytical results are given for the performance of the exponential backoff (EB) algorithm. Most available studies on EB focus on the stability of the algorithm and little attention has been paid to the performance analysis of EB. In this paper, we analyze EB and obtain saturation throughput and medium access delay of a packet for a given number of nodes N. The analysis considers the general case of EB with backoff factor r; binary exponential backoff (BEB) algorithm is the special case with r=2. We also derive the analytical performance of EB with maximum retry limit M (EB-M), a practical version of EB. The accuracy of the analysis is checked against simulation results.

We investigate the inherent scalability problem of ad hoc networks that originated from the nature of multi-hop networks. First, the expected packet traffic at the center of a network is analyzed. The result shows that the expected packet traffic at the center of a network is linearly related with the network size, that is, the expected packet traffic at the center of a network is O(k), where k is the radius of a network. From the result, the upper bound of the diameter of a network D = 2k, that guarantees the network is scalable, is obtained. The upper hound is given by C/r - 1, where C is the channel capacity available to each node and r is the packet arrival rate at each node.

New analytic results are given for the stability and performance of the exponential backoff (EB) algorithm. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were often used to make analysis more tractable. In this paper, care is taken to use a model for backoff that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput and the medium access delay of a packet for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. The accuracy of the analysis is checked against simulation results.

For a wireless LAN or a cluster of nodes in an ad hoc wireless network, multicast transmissions from a controlling station must be acknowledged by the nodes that are addressed. To ensure reliable reception at all the nodes, the multicast packet may be repeated on different transmissions, or on the same transmission as a form of diversity, or both. In this paper, policies for repeat transmissions of multicast packets are analyzed in terms of the average number of repeat transmissions required and the corresponding efficiency of the signaling on the multicast channel. The analytical results are parametric in packet/ACK error probability, the number of nodes, and the number of required ACKs. It is shown that a policy of accumulating ACKs and addressing only unacknowledged nodes on repeated non-diversity transmissions is more efficient than simply using a higher order of diversity on the multicast transmissions. Methods are shown for avoiding unnecessary repetitions in the case of a missing node.

Closed form bit-error rate (BER) expressions for differentially detected /spl pi//4-shifted differentially encoded quadrature phase-shift keying (QPSK) modulation (/spl pi//4 DQPSK) are derived for both additive white Gaussian noise (AWGN) and Rayleigh-fading channels. The derivations are carried out in an exact and most general manner in that in-phase (I) and quadrature (Q) channel bit-error probabilities P/sub cl/ and P/sub cQ/ are separately obtained in terms of the same-quadrature and cross-quadrature noise Correlation functions, including a measure of noise nonstationarity. We then specialize the general expressions for uncorrelated noise and equal noise powers in successive symbol periods to obtain a useful bit-error probability expression for the AWGN channel in the form P/sub e//spl ap/Q(/spl radic/(1.1716/spl middot/E/sub b//N/sub 0/)) where Q(/spl middot/) is the Gaussian distribution Q-function and E/sub b//N/sub 0/ is the bit energy-to-noise density ratio. Exact BER expressions for the Rayleigh-fading channel that involve the noise parameters are also given and are extended to the case of L-fold diversity combining.

The reliability of a CDMA cellular system reverse link is formulated as the probability that the link SNR is above the required threshold, accounting for multiple users, multipath receptions, signal and multipath fading, and Rake multipath diversity processing. Calculations of reliability show the gains obtained through RAKE processing, and the necessity of this processing when multipaths exist. It is shown that when multipath interference and link reliability requirements are accounted for, the number of CDMA users can be much smaller than that predicted using median SNR values.

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.>

An easily implemented matched filter scheme for acquiring hopping code synchronization of incoming frequency-hopping (FH) signals is analyzed, and its performance is evaluated for two types of jamming: partial-band noise jamming and partial-band multitone jamming. The system is designed to reduce jammer-induced false alarms. The system's matched filter output is compared to an adaptive threshold that is derived from a measurement of the number of acquisition channels being jammed. Example performance calculations are given for the frequency coverage of the jamming either fixed over the entire acquisition period or hopped, that is, changed for each acquisition pulse. It is shown that the jammer's optimum strategy (the worst case) is to maximize the false alarm probability without regard for the effect on detection probability, for both partial-band noise and multitone jamming. It is also shown that a significantly lower probability of false acquisition results from using an adaptive matched filter threshold, demonstrating that the strategy studied here is superior to conventional nonadaptive threshold schemes.>

Since a rectangular spectrum is unrealizable, more realistic spectra such as those where a jammer uses a bandpass filter before amplifying the jamming noise are considered. A Gaussian-shaped filter is used to represent a class of bandpass filters. This is a more realistic shape than the ideal rectangular shape. In addition, it can be easily analyzed by a reasonable approximation, i.e. a Gaussian-shaped spectrum that is constant over each hopped M-ary signaling band. Numerical results indicate that such a Gaussian-shaped partial-band noise jammer has nearly the same effects as an ideal rectangular-shaped partial-band noise jammer with an equivalent bandwidth.>

Error probability analyses are performed for a coded M-ary frequency-shift keying system (MFSK) using L hops per M-ary word frequency-hopping spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The bit error probabilities are obtained for a square-law adaptive gain control receiver with forward-error-control coding under conditions of worst-case partial-band noise jamming. Both thermal noise and jamming noise are included in the analyses. Performance curves are obtained for both block codes and convolutional codes with both binary and M-ary channel modulations. The results show that thermal noise cannot be neglected in the analysis if correct determinations of the optimum order of diversity and the worst-case jamming fraction are to be obtained. It is shown that the combination of nonlinear combining, M-ary modulation, and forward-error-control coding is effective against worst-case partial-band noise jamming.>

Linear and nonlinear diversity combining receivers for multihops-per-bit FH/BFSK waveforms in the partial-band noise jamming environment were studied in Parts I and II. It was shown that nonlinear combining receivers (Part II) can achieve a diversity gain for error rate improvement, while the linear combining receiver (Part I) cannot. The two types of nonlinear combining receivers treated in Part II required knowledge of system operational parameters for their optimum performance, such as measured noise power and the signal energy level at the receiver. In this paper, a self-normalizlng nonlinear combining receiver is shown to achieve a diversity gain without knowledge of signal or jamming levels, unlike the nonlinear schemes studied previously. The worst-case error probability performance of the self-normalizing receiver is obtained with and without system thermal noise. The numerical results are compared to those for the receivers studied earlier.

Frequency-hopping (FH)M-ary FSK (MFSK) spread-spectrum modulation is an effective choice for an electronic counter-countermeasures (ECCM) system. When the power efficient MFSK (M > 2) baseband orthogonal waveform is transmitted withL-fold diversity under constrained symbol energy, the resultant multiple (L) hops/symbol FH/ MFSK becomes a most viable low probability of intercept (LPI) waveform. In this paper, analyses are presented for the uncoded performance of such a waveform for two types of square-law nonlinear combining soft-decision receiver strategies under the assumption of worst-case partial-band noise jamming (countermeasures). The receivers employ, prior to combining, nonlinear weighting strategies of 1) adaptive gain control and 2) soft limiting (clipping) of the detector output of each channel of the dehopped waveform. The primary focus is on exact analytical results and, as such, the system's thermal noise is not neglected in the analyses. Numerical results of the error rates are graphically displayed as a function of signal-to-jamming power ratio withLandMas parameters under assumed values of signal-to-noise ratio. It is shown that. a diversity gain for error-rate improvement is realized for the nonlinear diversity combining receiver strategies. No attempt is made in this paper to compare the diversity performance to any error-control coding schemes.

In this paper, error probability analyses are performed for a binary frequency-shift-keying (BFSK) system employingLhop/bit frequency-hopping (FH) spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The error probabilities for theLhop/bit BFSK/FH systems are obtained as the performance measure of the square-law linear combining soft decision receiver under the assumption of the worst-case partial-band jamming. The receiver in our analysis assumes no knowledge of jamming state (side information). Both exact and approximate (multiple bound-parameter Chernoff bound) solutions are obtained under two separate assumptions: with and without the system's thermal noise in the analyses. Numerical results of the error rates are graphically displayed as a function of signal-to-jamming power ratio withLand signal-to-noise ratio as parameters. All of our results, exact and approximate, indicated that the higher number of hops per bit produced higher error probabilities as a result of increased combining losses when the square-law linear combining soft decision receiver is employed in demodulating the multihop-per-bit waveform.

In this paper, error probability analyses are performed for a binary frequency-shift-keying (BFSK) system employingLhop/bit frequency-hopping (FH) spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The performance results for two types of square-law nonlinear combining soft decision receivers under worst-case partial-band jamming are presented. The receivers employ, prior to combining, nonlinear weighting strategies of 1) adaptive gain control and 2) soft limiting (clipping) of the detector output of each channel of the dehopped waveform. Both thermal noise and jamming are included in the analyses. It is shown in the paper that a diversity gain for error rate improvement is realizable for nonlinear combining receivers provided that the noncoherent combining loss is less dominant than the jamming power reduction realized by the weighting strategy. Performance comparisons between linear and nonlinear combining receivers are presented.

This paper presents a complete analysis for the derivation of the probability of error for a hypothetical pure frequency-hopping (FH) spread-spectrum communication system, employing a binary differential phase-shift-keyed (DPSK) modulation and differentially coherent demodulation, in a partial-band jamming environment. The postulated DPSK/FH spread-spectrum system could be a practical system if the operational environment is multipath free. The optimum partial-band and wide-band jamming performance measures are obtained and compared under certain parametric conditions on the communicator's power levels. The present analysis is based on the application of the author's recent results on the derivation of the probability density functions (pdf) for the output of a cross correlator with arbitrary bandpass inputs of different power levels.

For general assumptions concerning bandpass signal and noise inputs, previous analyses of analog cross correlators have yielded very complicated expressions for the probability density function (pdf) of the correlator output. The inherent computational difficulties, therefore, limited the application of these pdf's almost exclusively to special cases of equal noise powers and noise spectrums symmetric about the signal's frequency. In this correspondence it is shown that for general bandpass inputs, the correlator output can always be expressed as the difference of two scaled independent noncentral chi-squared variables if a certain matrix transformation of variables is employed. The characteristic function method is then used to derive the pdf, which is as readily computed as for the case of special assumptions.

The detection performance of an FM correlator -the filtered product of two limiter-discriminator outputs-is assessed for a sinusoidal input signal with zero-mean Gaussian frequency modulation in Gaussian noise. Probabilities of detection and false alarm are obtained which depend upon carrier-to-noise ratio; modulation power; noise, modulation, and filter bandwidths; inter-channel delay; and observation time. Modulation and noise spectra are assumed Gaussian-shaped, and three filters are modelled: integrate-and-dump, RC integrator, and two-pole Butterworth.

Using the recently developed probability density function we obtain "directly" the error rate expressions for the binary differential phase-shift keyed (DPSK) systems when the noise values at the sampling instants in adjacent time slots are statistically dependent. Two cases are considered: One corresponding to equal SNR at each of the two sampling instants, and the other to unequal SNR's. The consideration of the former case, together with the assumption of unequal a priori symbol probabilities P0and P1results in an error rate expressionP_{E} =1/2[1 + (P_{0} - P_{1})\rho] \exp (-h^{2})where ρ is the noise correlation coefficient, and h2is the SNR. This expression shows clearly why PEis independent of noise correlation when the source symbols are equi-probable provided intersymbol interference is assumed absent. We then obtain the error probability expression in terms of unequal SNR's (at the two sampling instants) and the correlation coefficient ρ. Since intersymbol interference in a binary DPSK system gives rise to unequal SNR's, this expression provides a useful formula for estimating the system performance under such circumstances.

The probability density function (pdf) for the output of an analog cross-correlator with correlated bandpass inputs is derived. The pdf is derived by a "direct method" without resorting to the "characteristic function method," which usually requires contour integrations in a complex plane for inversion operations. The correlator consists of bandpass filters, a multiplier, and a zonal low-pass filter. We treat the general situation in which the two inputs are narrow-band signals of unequal power and of different phases. The bandpass input noises are assumed to be correlated and may have different powers. In the Appendix, another derivation for the pdf is given in the special case of equal power correlated noise. This derivation is based on the fact that the correlator output random variable is the difference of two independent noncentral chi-square variables of two degrees of freedom. We show that the two expressions for the pdf (one from the direct method and the other from the characteristic function method) are indeed equivalent. Finally, we discuss two major areas of application.