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Showing papers in "IEEE Transactions on Vehicular Technology in 1973"


Journal ArticleDOI
David Cox1, D. Reudink
TL;DR: In this paper, a large-scale mobile radio system using dynamic channel reassignment switch the channels assigned to some of the calls in progress to maintain a nearly optimum separation between coverage areas simultaneously using the same channel.
Abstract: Large-scale mobile radio systems using dynamic channel REassignment switch the channels assigned to some of the calls in progress to maintain a nearly optimum separation between coverage areas simultaneously using the same channel. Dynamic channel REassignment produces a significant increase in channel occupancy. For example, in the systems studied, which have a uniform distribution of their fixed channels and were operated against a uniform spatial distribution of offered traffic, the channel occupancy was increased by 2/3 over a pure fixed channel assignment system at a blocking rate of one percent. This corresponds to a channel savings of about 40 percent for the same traffic carried at one percent blocking by the hybrid systems that were studied.

179 citations


Journal ArticleDOI
L.G. Anderson1
TL;DR: In this article, the authors investigated the increase in traffic capacity in a cellular high capacity mobile telecommunications system attainable with dynamic instead of fixed channel assignment and found that traffic capacity can be increased by approximately 25 percent with dynamic channel assignment.
Abstract: This paper reports the results of an investigation of the increase in traffic capacity in a cellular high capacity mobile telecommunications system attainable with dynamic instead of fixed channel assignment. Three dynamic channel assignment algorithms were studied by simulation using a 21-cell hexagonal array as a representative system layout. Detailed results for each algorithm are presented. For the particular system studied, traffic capacity can be increased by approximately 25 percent with dynamic channel assignment. A general upper bound on this increase has been found.

114 citations


Journal ArticleDOI
TL;DR: A simple device to simulate the Rayleigh distributed fast fading encountered in mobile radio is described and a design is given whose performance is shown to agree very closely with theory.
Abstract: A simple device to simulate the Rayleigh distributed fast fading encountered in mobile radio is described and evaluated. The Rayleigh envelope statistics are obtained by adding two independent Gaussian noise sources in quadrature. The theoretical spectrum of the received signal is approximated by shaping the spectrum of the noise sources with filters. A design is given whose performance is shown to agree very closely with theory.

102 citations


Journal ArticleDOI
TL;DR: This paper presents three algorithms which are in a certain minimax sense statistically optimum, and may be applied to any system that employs many servers, the use of some combinations of which is not allowed.
Abstract: Cellular mobile radio systems have been proposed that use many base stations to provide radio service over a large geographical area. In such systems, a stored-program processor assigns radio channels to base stations in real time, under certain interference constraints. The capacity and the queueing characteristics of the overall system are strongly dependent on the processor algorithms that are used. This paper presents three algorithms which are in a certain minimax sense statistically optimum. The procedures are quite general, and may be applied to any system that employs many servers, the use of some combinations of which is not allowed. The first algorithm provides for the preferential assignment of a "standard" channel. If all standard channels are busy, a "nonstandard" channel is selected in such a manner that the probability of blocking is minimized in that interferable facility most likely to suffer blocking. The second algorithm provides for the transfer of service from non-standard to standard channels whenever standard channels become free. The choice of the particular nonstandard channel to be freed is again made in a manner which minimizes the maximum probability of future blockage. The third algorithm provides for the rearrangement of channel assignments in those instances when all assignable channels, both standard and nonstandard, are busy. Such rearrangement can cause channels to become available under certain circumstances. If more than one rearrangement is possible, again the choice of what particular action should be taken is governed by the goal of minimizing the maximum probability of future blockage. All three algorithms attain short-term optimality by enumeration; that is, each candidate for assignment is considered in turn. Under the condition that the given candidate is selected, the conditional probability of future blocking in each of the server groups is calculated, and the maximum of these probabilities is associated with the candidate. After all candidates have been considered, that candidate which has the minimum associated probability is assigned. These algorithms produce, by definition, an instantaneous system state which is always optimum in the above minimax sense. In systems with large numbers of servers, the system changes state rapidly; thus, occasional short-term errors disappear rapidly, and short-term optimization tends to lead to peak performance in the long term as well.

100 citations


Journal ArticleDOI
William C. Y. Lee1
TL;DR: In this paper, the correlation between signals received by two mobile radio base station antennas is investigated to determine spacing requirements for space diversity, and an upper limit to the spacing of antennas used for diversity can be obtained and that it is within the achievable range.
Abstract: The correlation between signals received by two mobile radio base-station antennas is investigated to determine spacing requirements for space diversity. Measurements of the fading of UHF signals received by two base-station horn antennas oriented at different angles with respect to the incoming mobile radio signal were made for different antenna spacings. The experimental results are compared with an analytical expression derived in this paper; they agree fairly well. A further experiment was made after removing the possible local scatterers surrounding the base station. Comparing these two experimental results, we find that the following are true. 1) Propagation in the direction of a line connecting the two base-station antennas is the critical case and requires a large separation of 70 wavelengths. As soon as the incoming wave is 10° away from the in-line axis, the spacing requirement drops to 30 wavelengths. 2) Local scatterers at the base station tend to decrease the correlation between signals received at the two antennas. We conclude that an upper limit to the spacing of antennas used for diversity can be obtained and that it is within the achievable range.

48 citations


Journal ArticleDOI
David Cox1
TL;DR: From the measurements, it appears reasonable to model the urban mobile radio channel as a Gaussian quasi-wide-sense stationary uncorrelated scattering channel within a bandwidth of 10 MHz and for intervals along the street of up to 30 m.
Abstract: Small scale statistics of multipath propagation in a heavily built-up urban mobile radio environment are presented. The statistics cover vehicle travel distances on the order of 30 m along streets. Measuring equipment time delay resolution is about 0.1 µs. In some locations, paths with significant amplitudes are observed with excess delays of 9 to 10 µs. The delay spreads (√second central moment of power delay profile) in this environment are on the order of 2 µs. Often the signal at fixed delays has a Rayleigh-distributed amplitude but large departures from the Rayleigh distribution also occur. From the measurements it appears reasonable to model the urban mobile radio channel as a Gaussian quasi-wide-sense stationary uncorrelated scattering channel within a bandwidth of 10 MHz and for intervals along the street of up to 30 m.

42 citations


Journal ArticleDOI
TL;DR: The Automatic Route Control System enables a driver to operate efficiently over a complex route without reference to maps or lists and without prior knowledge of the route.
Abstract: The Automatic Route Control System (ARCS) is a self-contained on-board system that directs the operation of a conventional motor vehicle over predetermined routes and controls activities (such as the delivery or pickup of items) performed along the route. In effect, the system continuously measures the vehicle's location coordinates, compares these with the route coordinates, and then issues audio, visual, and/or printed instructions appropriate to the location. The system also detects driver errors and prescribes corrective action. The routes to be followed and the actions to be taken are defined on interchangeable magnetic tape cartridges, which may be updated daily or as required from a computerized central file. ARCS enables a driver to operate efficiently over a complex route without reference to maps or lists and without prior knowledge of the route. It also eliminates tedious manual report preparation because computer-ready data for route accounting can be acquired on a magnetic tape cartridge. Although applicable to most types of operations carried out over routes that can be defined in advance, the prototype application is for the delivery of newspapers. Installed in a van with paper throwers stationed at special windows on each side, the system signals each thrower with a tone through headphones at the proper time to throw papers to individual subscribers while driving through residential areas at 15-30 mi/h.

30 citations


Journal ArticleDOI
TL;DR: The control problems associated with the operation of a network of automatically controlled closely spaced high-speed vehicles are considered and a system operating concept based on the synchronous moving-cell approach to individual vehicle control is presented.
Abstract: The control problems associated with the operation of a network of automatically controlled closely spaced high-speed vehicles are considered. A system operating concept based on the synchronous moving-cell approach to individual vehicle control is presented. The need for a network traffic-management strategy is pointed out and one such strategy, called cycle preprogramming, is discussed. Finally, a study of the efficiency of the cycle preprogramming traffic-management strategy is described.

18 citations


Journal ArticleDOI
TL;DR: In this paper, a 10-GHz CW homodyne bistatic radar system has been developed to permit exploration of the feasibility of such an application and design and response to potential real and false-alarm targets and to the automotive environment.
Abstract: For effective protection of automobile occupants in high-speed collisions, passive restraints (such as airbags) must be actuated prior to impact. A 10-GHz CW homodyne bistatic radar system has been developed to permit exploration of the feasibility of such an application. System design and response to potential real and false-alarm targets and to the automotive environment are delineated. Possible elaborations on the basic system are described.

16 citations


Journal ArticleDOI
TL;DR: In this article, a theoretical and experimental comparison of performance between two types of predetection switching space diversity mobile radio systems was made at a frequency of 840 MHz using simulated Rayleigh fading for a vehicle speed of about 80 mi/h.
Abstract: A theoretical and experimental comparison of performance has been made between two types of predetection switching space diversity mobile radio systems. This comparison was made at a frequency of 840 MHz using simulated Rayleigh fading for a vehicle speed of about 80 mi/h. The switch diversity system was a conventional receiver antenna switching technique with two simulated physically separated receiving antennas and a single transmitting antenna. The feedback diversity system used a single receiving antenna with two simulated physically separated transmitting antennas. The transmitting antennas were switched remotely from the receiver. The difference in the performance of the two systems was shown to be primarily due to time delay inherent in the remote antenna switching technique.

11 citations


Journal ArticleDOI
S. Riter1
TL;DR: In this article, the effect of background noise on the performance of phase-trilateration urban vehicle-monitoring systems is discussed and an expression for the density function of the error as a function of such system parameters as carrier-to-noise ratio, frequency deviation, observation time, and bandwidth is derived.
Abstract: The effect of background noise on the performance of phase-trilateration urban vehicle-monitoring systems is discussed. An expression for the density function of the error as a function of such system parameters as carrier-to-noise ratio, frequency deviation, observation time, and bandwidth is derived.

Journal ArticleDOI
M.M. Peritsky1
TL;DR: In this paper, the authors consider the problem of estimating the population mean, given a sequence of independent samples, and derive an unbiased maximum-likelihood estimator, which is unique and is therefore "best" in the Blackwell-Rao sense of minimizing expected loss.
Abstract: A commonly used model for signal fading in many types of communication channels is that the amplitude of the received signal at a given time is a Rayleigh-distributed random variable. In this paper we show how classical statistical techniques may be applied to the problem of estimating the Rayleigh distribution parameter (i.e., the mean), given samples from the distribution. In particular, we first consider the problem of estimating the population mean, given a sequence of independent samples. We derive an unbiased maximum-likelihood estimator. We show that this estimator is unique, and since it is based on a sufficient statistic, it is therefore "best" in the Blackwell-Rao sense of minimizing expected loss. Using this estimator, we then develop confidence intervals whose length can be used as a guide in selecting the required sample size. We then consider the same estimation problem when the signal samples are obtained from the output of a logarithmic receiver. We derive an interval estimator which does not require taking the antilogs of the log samples, and which is not appreciably worse than the "best" estimator.

Journal ArticleDOI
TL;DR: In this paper, the authors define the service area of VHF/UHF land mobile and broadcast stations and demonstrate graphical and computer methods to determine and present such areas as a function of known equipment parameters and a propagation model derived from an extensive measurement program over irregular terrain.
Abstract: In this paper we define the service area of VHF/UHF land mobile and broadcast stations and demonstrate graphical and computer methods to determine and present such areas as a function of known equipment parameters and of a propagation model derived largely from an extensive measurement program over irregular terrain.

Journal ArticleDOI
J.S. Bitler1, C.O. Stevens
TL;DR: In this article, a UHF mobile telephone system using digital modulation is described, which uses on-off keying of an 836-MHz carrier, the code being supplied by an adaptive delta coder with a clock frequency of 50 kHz.
Abstract: A UHF mobile telephone system using digital modulation is described. The system uses on-off keying of an 836-MHz carrier, the code being supplied by an adaptive delta coder with a clock frequency of 50 kHz. The maximum audio baseband signal-to-noise ratio is approximately 30 dB. The mobile receiver employs space diversity in a maximal-ratio combiner. Due to the use of amplitude modulation of the carrier rather than exponential modulation, the diversity receiver is very simple. The system was tested in the laboratory and in the field. Field tests were made in suburban and urban areas. For the four-branch system, threshold occurred at an average IF signal-to-noise ratio of approximately 12 dB.

Journal ArticleDOI
R. Esposito1, R. Buck
TL;DR: In this paper, the authors describe the criteria for the design of a mobile laboratory for the characterization and measurement of man-made electromagnetic noise in the urban, suburban, and rural environment.
Abstract: This paper describes in detail the criteria for the design of a mobile laboratory for the characterization and measurement of man-made electromagnetic noise in the urban, suburban, and rural environment. A significant difference from previous similar measurements is the bandwidth of the receiving system, which is here of the order of 1 MHz. A simple model is proposed to describe the impulsive noise together with a series of experiments to validate the model and determine the significant necessary parameters. The detailed requirements for each of the subsystems of the mobile laboratory are discussed and some typical results obtained in trial runs are presented.

Journal ArticleDOI
Z.C. Fluhr1, E. Nussbaum
TL;DR: In this paper, the authors proposed a trunk-to-trunk switcher scheme for a 75MHz band to implement high capacity mobile telephone systems, which can be accomplished by means of an electronic switching system (ESS) with special data terminals and trunking arrangements.
Abstract: Federal Communication Commission Docket 18 262 allocated a 75-MHz band to the common carriers to implement high capacity mobile telephone systems. The Bell System has proposed a cellular arrangement of low-power transmitters/receivers that permits frequency reuse in a coverage area. This method of achieving spectrum efficiency will require extensive centralized coordination and control to properly administer channel assignments and to interconnect the mobiles with each other and with the direct distance dialing (DDD) network. This can be accomplished by means of an electronic switching system (ESS) with special data terminals and trunking arrangements, and a unique program. In the proposed plan the radio sites (base stations) act effectively as remote concentrators in the frequency domain under the control of ESS, which in turn acts primarily as a trunk-to-trunk switcher. In addition to the usual switching, signaling, and supervising functions, the switching office must also perform numerous special functions including paging of mobiles, location of mobiles (signal strength and ranging data analysis), channel reassignment of mobiles, and reswitching of mobiles to various base stations-these last three occurring while customers ate talking.

Journal ArticleDOI
TL;DR: In this article, the authors present a digest of the electrical system section of a report on the feasibility of using a hybrid heat engine/electrical propulsion system as a means of reducing exhaust emissions from street-operated vehicles.
Abstract: This paper is a digest of the electrical system section of a report [8] on the feasibility of using a hybrid heat engine/electrical propulsion system as a means of reducing exhaust emissions from street-operated vehicles. The electrical system is composed of an electric traction motor, a generator, control system, and batteries. Batteries are not covered in this paper, but the remainder of the items will be treated here. First, the electrical system parameters or characteristics that have the greatest impact on the total system are considered; next, details of the advantages and disadvantages of various approaches are summarized; and, finally, development efforts are recommended.

Journal ArticleDOI
TL;DR: In this paper, the authors argue that there is no shortage of radio spectrum, but rather, a shortage of new concepts in spectrum usage, and they challenge the technologists of this industry to come forward with innovative approaches based upon thorough, objective engineering analyses.
Abstract: The author alleges that there is no shortage of radio spectrum, but rather, a shortage of new concepts in spectrum usage. The recent reallocation of additional frequencies to land mobile radio uses (FCC Dockets 18 261 and 18 262) provides new opportunities for innovative approaches, approaches that are free of the constraints of existing rules and regulations, existing manufacturing and engineering processes and concepts. Intending to be provocative and to initiate action and dialogue, the author challenges the technologists of this industry to come forward with innovative approaches based upon thorough, objective engineering analyses. The FCC, he contends, sorely needs factual, objective data from industry technologists in order to make the best decisions possible.

Journal ArticleDOI
TL;DR: Quantitative results show that a worthwhile improvement in quality of reception can be obtained with small numbers of antennas, and there are advantages to be gained if, in future receiving systems, the diversity technique is incorporated directly into the receiver design.
Abstract: Diversity reception techniques can help to combat fast fading in urban areas, and this paper describes some predetection combining systems designed to be compatible with existing standard receivers. Quantitative results show that a worthwhile improvement in quality of reception can be Obtained with small numbers of antennas. There are advantages to be gained if, in future receiving systems, the diversity technique is incorporated directly into the receiver design.

Journal ArticleDOI
TL;DR: In this article, the authors showed that small-scale signal variations at 900 MHz should be more rapid and have amplitudes at least as great as those shown for 450 MHz, and that the improvements noted here may spur developments in circularly polarized antennas.
Abstract: Land mobile systems currently use vertically polarized antennas while trying to solve the problem of small sector signal variations, which are greater for vertical polarization than for either horizontal or circular polarization. This difference in small sector variations is shown from results of tests at 430 MHz. The variations at 900 MHz should be more rapid and have amplitudes at least as great as those shown for 450 MHz. At 900 MHz antennas can be made small for mobile service and the improvements noted here may spur developments in circularly polarized antennas.

Journal ArticleDOI
A.V. Gould1
TL;DR: The proximity type of automatic vehicle-monitoring system now being demonstrated by the Chicago Transit Authority, Chicago, Ill., will be described.
Abstract: The proximity type of automatic vehicle-monitoring system now being demonstrated by the Chicago Transit Authority, Chicago, Ill., will be described. Details of system configuration, communication links, and computer requirements will be described.

Journal ArticleDOI
TL;DR: In this paper, a variety of land mobile radio systems are compared by their spectral and economic efficiencies in providing various user services, such as mobile telephone service, dispatch service emergency, and dispatch service non-emergency.
Abstract: A variety of land mobile radio systems are compared by their spectral and economic efficiencies in providing various user services. System types covered are private one-channel, shared repeater one channel, controlled-access one-channel, trunked multi-channel, and cellular. Spectral efficiency is defined to be the number of mobile users that can be served per MHz of spectrum in a core urban area, while economic efficiency is the average system cost per mobile. Both efficiencies vary with the type of usage, hence they are calculated for three major usages-mobile telephone service, dispatch service emergency, and dispatch service nonemergency. Services are described via seven "service parameters," namely call holding time (average), tolerable average wait for channel access, peak busy hour utilization per mobile, audio quality (S/N), noise levels tolerable, and service range. Sensitivity of the basic results to variations in the service parameters are also computed and discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors used an omnidirectional antenna with vertical directivity, instead of the usual whip antenna, to increase average signal strength as a further improvement in the advantages of diversity reception.
Abstract: Field measurements of mobile radio signals have shown that signal arrival is concentrated in elevation angles lower than 16°. This suggests use of an omnidirectional antenna with vertical directivity, instead of the usual whip antenna, to increase average signal strength as a further improvement in the advantages of diversity reception.

Journal ArticleDOI
M.M. Peritsky1
TL;DR: If a server group carrying short-holding-time queued traffic at high blocking probability is combined with another server groupcarrying normal blocked-calls-cleared traffic at low blocking probability, the resulting mixed group will in many cases operate at an intermediate blocking probability.
Abstract: If a server group carrying short-holding-time queued traffic at high blocking probability is combined with another server group carrying normal blocked-calls-cleared traffic at low blocking probability, the resulting mixed group will in many cases operate at an intermediate blocking probability. Thus the mixed group provides better service to the queued traffic, while degrading the service of the cleared traffic. If the random arrival characteristics of the short-holding-time traffic are suitably modified by delaying calls an appropriate time before service, then the grades of service for both types of traffic may be engineered independently. An example of a possible use of this technique of induced delay, the combining of dispatch and mobile-telephone traffic on the same set of radio channels in the High-Capacity Mobile Telecommunications System, is discussed.

Journal ArticleDOI
G.A. Arredondo1
TL;DR: If the land lines are not equalized and the signaling tones are not exactly equal, the interference errors cannot be eliminated, but can be decreased by properly aligning the system.
Abstract: Many mobile telephone and personal paging systems require signaling simultaneously from multiple transmitters. This paper analyzes the factors that cause paging errors due to interference when the signaling format consists of audio tones sent simultaneously from two FM transmitters. The factors considered are: drift in carrier and modulation frequencies, and misequalization of land-line amplitude and audio delay. The following results are shown: 1) the interference errors are eliminated if the land lines are amplitude and phase equalized, 2)if the lines are not equalized but the modulation frequencies are equal, then the interference errors can be decreased by an order of magnitude if the transmitters are mistuned such that their difference carrier frequency is just greater than the modulation tone filter bandwidth in the receiver, and 3) if the modulation frequencies are slightly different, then the interference errors can be decreased somewhat by misequalizing the modulation indicies. It is then concluded that if the land lines are not equalized and the signaling tones are not exactly equal, the interference errors cannot be eliminated, but can be decreased by properly aligning the system.

Journal ArticleDOI
W.E. Shortall1
TL;DR: In this article, a low cost switched diversity receiving system was developed for use in UHF-FM mobile radio, where the input of a single receiver is switched back and forth between two antennas upon command from a signal level sensing logic circuit.
Abstract: A low cost switched diversity receiving system has been developed for use in UHF-FM mobile radio. The input of a single receiver is switched back and forth between two antennas upon command from a signal level sensing logic circuit. The system has been measured on simulated Rayleigh fading channels and has been found to give a significant improvement to both voice and data signals.

Journal ArticleDOI
TL;DR: Tests indicate that the statistics of the fading envelope at both the base and mobile stations closely agree with those predicted by theory for an equal gain combiner with correlation between the branches.
Abstract: This paper describes an adaptive retransmission system capable of providing a UHF (1 GHz) mobile radio channel with "two-way diversity." The system is unique in that all signal processing associated with the diversity combining is done at the base station. A two-branch prototype of the system, without modulation, was field tested to determine its adaptive retransmission performance. These tests indicate that the statistics of the fading envelope at both the base and mobile stations closely agree with those predicted by theory for an equal gain combiner with correlation between the branches.

Journal ArticleDOI
D.O. Reudink1, M.F. Wazowicz
TL;DR: In this paper, measurements of signal attenuation from a suburban hilltop base station to a mobile vehicle on several streets in the surrounding countryside were made simultaneously at frequencies of 836 MHz and 11.2 GHz and then repeated in the summer to determine the effects of foliage.
Abstract: Measurements of signal attenuation were made from a suburban hilltop base station to a mobile vehicle on several streets in the surrounding countryside. Measurements of signal strength were simultaneously made in the winter of 1971 at frequencies of 836 MHz and 11.2 GHz and then repeated in the summer to determine the effects of foliage. The presence of foliage reduced the received signal strength and the effect was more pronounced at X-band than at UHF. In cases where the shadowing obstacle was tree covered, signal levels at UHF might typically be 10 dB lower when the trees were in full leaf, whereas at X-band this additional loss could be as high as 20 dB. The experimental data was compared to values predicted by knife-edge diffraction and reasonable agreement was found.

Journal ArticleDOI
TL;DR: Several approaches to the operation of automated ground transport systems for urban use are presented and evaluated in this article, and six potential applications for automated transport systems are suggested, ranging from specialized single-link "horizontal elevators" to general-purpose wide area networks.
Abstract: Several approaches to the operation of automated ground transport systems for urban use are presented and evaluated. Such systems have been suggested principally in response to the problems of urban traffic congestian and are often proposed as solutions to such problems. Thus this paper, the first of a series of three, discusses the problems of urban transportation and their origins, identifying as the principal elements the institutional structure, urban geography, and design of facilities for urban automotive transport. Importantly, the origins of a significant portion of "the urban transportation problem" lie outside the transport sector. Six potential applications for automated transport systems are suggested, ranging from specialized single-link "horizontal elevators" to general-purpose wide-area networks.

Journal ArticleDOI
R.E. Langseth1
TL;DR: In this paper, the total bit-error probability using square-law detection of an on-off keyed carrier received through a fading medium is calculated, and it is shown that the use of diversity will recover much of the performance loss caused by the fading, provided that an optimum decision threshold is used.
Abstract: In this paper the total bit-error probability using square-law detection of an on-off keyed carrier received through a fading medium is calculated. It is shown that the use of diversity will recover much of the performance loss caused by the fading, provided that an optimum decision threshold is used. Consideration is given to the performance obtained with a fixed optimum threshold (depending only on the mean-square signal strength) and to that obtained with two forms of variable threshold, assumed to follow the instantaneous fading signal strength. Compared to the fixed optimum threshold, the best variable threshold results in a 5- or 2.5-dB reduction in the required rms SNR for a 10-4error rate with two- or four-branch diversity, respectively; as compared to the no fading case, use of the fixed threshold requires 3 dB more SNR for a 10-4error rate with four-branch diversity, and requires 32 dB more SNR if only a single branch is used. A calculation of the average fade duration of the diversity-combiner output-signal component shows that diversity reduces the average time that the signal component spends below the threshold according to N-1/2for N branches. This is true for both the fixed or the best variable threshold, but the average duration with the fixed threshold is larger by about [log (1+σ ρ 2)]1/2, where σ ρ 2is the mean-square SNR per branch.