There are various cases in physics and engineering sciences (especially communications) where one requires the envelope probability density function (PDF) of the sum of several random sinusoidal signals. According to the correspondence between a random sinusoidal signal and a random vector, the sum of random vectors can be considered as an abstract mathematical model for the above sum. Now it is desired to obtain the PDF of the length of the resulting vector. Considering the common and reasonable assumption of uniform distributions for the angles of the vectors, many researchers have obtained the PDF of the length of the resulting vector only for special cases. However in this paper, the PDF is obtained for the most general case in which the lengths of vectors are arbitrary dependent random variables. This PDF is in the form of a definite integral, which may be inappropriate for analytic manipulations and numerical computations. So an appropriate infinite Laguerre expansion is also derived. Finally, the results are applied to solve a typical example in computing the scattering cross section of random scatterers.

A set of measurements for indoor infrared channel are reported. These measurements have been performed to investigate the effects of rotation on the parameters of the indoor infrared channel. A large database containing more than 5000 frequency responses has been created. The measurements have been performed in rooms with different shapes and physical properties to address all kinds of operating environments. This paper addresses parts of the results obtained from these measurements. The channel path loss and its delay spread are two important channel parameters for indoor infrared channel. The effects of receiver rotation on these two parameters have been studied. It is shown that the delay spread of the channel and its path loss are linearly correlated on the log scale when the receiver is rotated. The correlation between these two variables in different rooms and also different transceiver configurations remains an almost constant value close to unity. Therefore, we conclude that in general, when the receiver rotates, the logarithm of the delay spread of the channel changes linearly with the log of the channel path loss.

Diffused infrared communication is a potential candidate for providing wireless service to portable computers inside buildings. The details of a model that estimates the impulse response and frequency response of the infrared channel in indoor environments of different shapes and sizes are described. An important feature of the model is inclusion of the effect of office furniture and people in the room on the channel's impulse response. The developed simulation package has been executed under diversified sets of conditions to obtain the impulse response of the IR channel in rooms of arbitrary shape, with and without furniture. The corresponding results have been compared with each other, and with some empirical data. The major conclusions are: (i) room furniture may have a great effect on the impulse response under certain conditions, (ii) there is general good match between the simulated and empirical frequency response functions of the channel.

The results of a multi-ray geometric model for estimating the signal coverage in line-of-sight (LOS) and non-line-of-sight (NLOS) microcellular environments are presented, some empirical propagation models are reviewed, and a simplified mathematical rule for estimating the received power for both LOS and NLOS topographies is suggested. The parameters of the proposed simplified model are: the distance between the base antenna and street intersection, distance between the intersection and mobile antenna, width of the street containing base antenna, and the width of the street containing the mobile antenna. Using this model base-mobile path losses for microcellular environments have been evaluated under diversified conditions and the results have been compared with the more sophisticated multi-ray geometric model, and with some empirical results reported in the literature. The fit is, in general, very good. The proposed model can be used in estimating the coverage for microcellular mobile radio communication systems. The computation time of this model is minimal compared to standard multi-ray models.

Performance and capacity of CDMA for mobile radio applications have been studied in detail by extensive computer simulation of large service area consisting of 19 hexagonal cells. Major results of the study are as follows: (i) interference initiating from the pilot tone reduces the 1st percentile of the speech channel's C/I, which offsets the improvements resulting from coherent combining capabilities; for the 10th percentile of C/I distribution, overall improvements resulting from the pilot transmission are 1 dB. (ii) With a pilot channel transmission in the forward link, the slope of the "C/I percentile" versus "number of active mobiles" curve is -2 dB/octave. (iii) The required dynamic range for 1st and 10th percentiles of the C/I distribution are, respectively, 10 dB and 5 dB. (iv) With a 2 dB standard deviation for power control, capacity reduces to 20% of its ideal value. (v) A dynamic range of 12 dB for the transmission power of the base is adequate. (vi) Capacity increases drastically by increasing path loss of transmission.

This paper reports the results of extensive measurements and analysis of the indoor radio propagation channel's temporal and spatial variations. The empirical database for the temporal variation analysis consists of 192 one-minute recordings of CW envelope fading waveforms with both antennas stationary. Measurements were carried out in an office environment at 1100 MHz with four transmitter-receiver antenna separations of 5, 10, 20, and 30 meters. Effects of controlled degrees of motion with 0, 1, 2, 3, or 4 individuals walking around the high antenna only, around the low antenna only, and around both antennas were investigated. The spatial variation analysis is based on 160 segments of 1.5-meter CW envelope fading data obtained from a wideband empirical database of 12000 impulse response functions. The measurements in this category were carried out at two different office environments with four antenna separations of 5, 10, 20, and 30 meters. The reported results include amplitude fading distributions, correlation properties, level crossing rates, duration of fades statistics, and spectrum widths of the frequency domain data.

Performance and capacity of CDMA for mobile radio applications have been studied in detail by extensive computer simulation of a large service area consisting of 19 hexagonal cells. The results for the reverse link (mobile-to-base) are reported in this paper. Using typical system parameters in the simulations the following major results were obtained: (i) capacity is very sensitive to interference from neighboring cells, (ii) any increase in path loss between mobile and base has noticeable effects in interference reductions and capacity improvements, (iii) transmitted power dynamic ranges as high as 60 dB are needed for successful implementation of power control, (iv) performance of power control based on C/I is better than performance based on received power, (v) imperfect power control has drastic effects in capacity reductions, (vi) for ideal power control and with typical system parameters capacity of cellular CDMA is about 15 times capacity of analog systems. Imperfect power control or decrease in transmission path loss may, however, reduce this number by a factor of 2 to 3.>

Multipath propagation in indoor environments results in distortions in signal amplitude and phase. Performance of digital communication systems is very sensitive to statistical properties of received signal's phase. To date, however, no empirically driven model for signal phase has been reported in literature. This is probably due to difficulties associated with measuring the phase of individual multipath components. In the present work two phase models, partly developed in Hashemi (1993), have been studied in great detail and their performance has been evaluated by means of extensive computer simulations. First and second order statistics of a narrowband CW fading signal obtained from a large empirical wideband impulse response data base for different choices of phase models have been investigated. It is shown that a deterministic phase model, that updates phase information using several scatterers for each multipath component, as well as a random phase model, which updates phase of each multipath with random increments, provide narrowband CW fading results consistent with those obtained in measurements.>

If indoor radio propagation channels are modeled as linear filters, they can be characterized by reporting the parameters of their equivalent impulse response functions. The measurement and modeling of estimates for such functions in two different office buildings are reported. The resulting data base consists of 12000 impulse response estimates of the channel that were obtained by inverse Fourier transforming of the channel's transfer functions. It is shown that the number of multipath components in each impulse response estimate is a normally-distributed random variable with a mean value that increases with increasing antenna separations; a modified Poisson distribution shows a good fit to the arrival time of the multipath components; amplitudes are lognormally distributed over both local and global areas, with a log-mean value that decreases almost linearly with increasing excess delay; for small displacements of the receiving antenna, the amplitude of the multipath components are correlated; the amplitudes of adjacent multipath components of the same impulse response function show negligible correlations; and the RMS delay spread over large areas is normally distributed with mean values that increase with increasing antenna separation.>

In this tutorial survey the principles of radio propagation in indoor environments are reviewed. The channel is modeled as a linear time-varying filter at each location in the three-dimensional space, and the properties of the filter's impulse response are described. Theoretical distributions of the sequences of arrival times, amplitudes and phases are presented. Other relevant concepts such as spatial and temporal variations of the channel, large-scale path losses, mean excess delay and RMS delay spread are explored. Propagation characteristics of the indoor and outdoor channels are compared and their major differences are outlined. Previous measurement and modeling efforts are surveyed, and areas for future research are suggested.>