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Chapter 8 Sounding, Sampling and Simulation 8.1 CHANNEL SOUNDING In the earlier chapters we discussed the characteristics of mobile radio channels in some detail. It emerged that there are certain parameters which provide an adequate description of the channel and it remains now to describe measuring equipment (channel sounders) that can be used to obtain experimental data from which these parameters can be derived. It is often of interest to make measurements which shed some light on the propagation mechanisms that exist in the radio channel but engineers are usually more interested in obtaining parameters that can be used to predict the performance, or the performance limits, of communication systems intended to operate in the channel. The choice of channel sounding technique will usually depend on the application foreseen for the propagation data. Basically, a choice has to be made between using narrowband or wideband transmissions and whether a time or frequency domain characterisation is required. In what follows we will brie¯y describe both narrowband and wideband systems and provide an indication of how relevant data can be extracted from measurements. We make only a brief reference to the data processing techniques, particularly in the case of wideband channels; for details the interested reader will need to consult the literature [1±4]. 8.2 NARROWBAND CHANNEL SOUNDING It is clear from the earlier discussion that when the mobile radio channel is excited by an unmodulated CW carrier (i.e. a single tone), large variations are observed in the amplitude and phase of the signal received by a moving antenna. These variations are apparent over quite small distances. A considerable number of mobile radio propagation studies have been undertaken by transmitting an unmodulated carrier from a ®xed base station, receiving the signal in a moving vehicle and recording the signal envelope. It is common to use a receiver which provides a DC output voltage proportional to the logarithm of the received signal amplitude, and a suitable receiver calibration therefore produces the signal strength in dBm or, if a calibrated antenna is used, the ®eld strength in dBmV/m. Figure 8.1 shows a simpli®ed block diagram of a generic receiving and recording system which has the basic features required. The signal envelope at the output of the The Mobile Radio Propagation Channel. Second Edition. J. D. Parsons Copyright & 2000 John Wiley & Sons Ltd Print ISBN 0-471-98857-X Online ISBN 0-470-84152-4 receiver is fed via a suitable interfacing circuit and an ADC into the memory (RAM) of a microcomputer. Distance pulses from a transducer are used to trigger the ADC so that samples are taken at an appropriate rate. Analysis of the stored data can either be carried out in suitable batches as ®eld trials proceed or the stored data can be retained for analysis later. It is not always convenient, or necessary, to initiate sampling using distance pulses and if the system is made portable for use within a room or building, for example, then time sampling is much more convenient. The phase of the received signal is sometimes of interest and can be measured, relative to a ®xed reference, if the signal is demodulated in two quadrature channels. Such receivers have been used by Bultitude [5] for indoor measurements and by Feeney [6] for small-cell measurements outdoors. To measure phase accurately it is essential that the local oscillators in the transmitter and receiver are phase-locked. In the majority of cases this is impracticable but the use of extremely stable sources, such as rubidium oscillators, can provide adequate coherence over quite long periods of time. In this manner, only those phase variations introduced by the propagation channel, and not those due to the transmitter/receiver combination, are measured. Of course, the phase information cannot realistically be studied at the carrier frequency. Translation of the quadrature information to a suitable lower frequency can be carried out by heterodyning to an intermediate frequency; two possibilities exist, either a conveniently low intermediate frequency or a direct conversion to zero-IF. In the ®rst type of receiver, care is needed in the choice of IF to avoid images, arising from the mixing process, from falling within the passband of the IF ®lter. This can be achieved using an initial frequency upconversion or by employing image rejection mixers. Two advantages exist for this architecture: the input frequency is not restricted to a narrow RF band and a suitable network analyser can be used to isolate sources of amplitude and phase unbalance in the various signal paths. The zero-IF (direct conversion) receiver requires mixers which have a suciently high operating frequency at the RF port, together with a DC-operating IF port. The operating frequency is restricted to a narrow range due to the constraint of maintaining quadrature in the various signal paths. High RF power levels are required to drive the mixers, so that an adequate dynamic range is achieved. These disadvantages are minimised if the design is limited to one carrier frequency. Other advantages also exist; for example, only one phase-locked stage is required 222 The Mobile Radio Propagation Channel Figure 8.1 Simpli®ed block diagram of a receiver and data logging system for use in the ®eld. and the single mixing process down to zero-IF provides an inherent detection function. Images are no longer a problem because they are well separated from the wanted information and are easily removed. Any imbalance in the amplitude or phase responses of the two channels can be reduced or eliminated through careful calibration or the use of digital correction techniques. Figure 8.2 shows the dual- channel receiver used by Feeney [6] for propagation and diversity experiments at 900 MHz. A dynamic range of 45 dB was achieved. 8.2.1 A practical narrowband channel sounder For characterising the channel in respect of its likely eect on narrowband systems it is usually adequate to transmit a CW carrier and to measure the variation in the envelope as the receiver is moved around within a given small area. Almost without exception, equipment designed for this purpose uses a ®xed transmitter and a mobile receiver. A data acquisition and analysis unit can easily be incorporated into the receiving system and designs can be tailored to meet any speci®c requirement, e.g. outdoors or indoors, or in con®ned spaces. The equipment described below was used by Davies [7] for indoor measurements but it is not restricted in any way and could easily ®nd other applications. A backpack system was preferred so that the operator could move around freely. This necessitated battery operation with a battery capacity adequate for several hours of operation. The system was speci®ed to have a dynamic range of 80 dB at 1.8 GHz, an automated attenuation control to allow the operator to walk into a room or area and conduct a test without any pretesting routine and a data acquisition system which stored not only the samples of signal strength, but also the setting of the attenuator control. Time sampling was used, the sampling rate being such that 4 or 5 samples per wavelength were taken at normal walking speed. The data acquisition system was designed to enable a large number of samples to be taken, subsequently averaged and the mean value stored. Sounding, Sampling and Simulation 223 Figure 8.2 Feeney's dual-branch, phase-locked direct conversion receiver. It was also designed to acquire the average signal level and CDF for a large number of locations. It was intended that the signal strength data should be analysed using a notebook computer, accessed via its printer port. Since it is not possible to insert a standard data acquisition card into such a computer, and since access via the printer port interface is slow, it was necessary for the data acquisition system to have on-board memory so that signal could be sampled and stored for downloading later. The notebook computer eectively controls the acquisition via a specially written program, and allows downloading from the on-board memory to the hard disk for permanent storage. The transmitter was of conventional design; it used a commercial frequency synthesiser as a signal source, the output being ampli®ed to provide an output power of 3 W, before being fed to a 5l/16 collinear antenna. A simpli®ed block diagram of the receiver, which is based on a single-conversion superheterodyne architecture, is shown in Figure 8.3. The receiving system is in two parts, a backpack unit and a handset similar in size to a modern cellphone, which incorporates the receiving antenna. In the receiver, the signal passes through an RF ampli®er and bandpass ®lter before being downconverted to a 10 MHz IF. Further ®ltering is provided by a crystal ®lter with very sharp roll-o characteristics and the signal is then fed to a logarithmic IF ampli®er/detector which has a dynamic range in excess of 80 dB. The input range of the receiver is controlled by the use of a programmable attenuator having a range of 128 dB in 1 dB steps. The control of this attenuator is automatic via the logging system and its setting is stored. The ecient logging of data is carried out by the data acquisition unit (DAU). Since it is only required that the mean signal level be recorded, a system was designed to enable the output of the receiver to be sampled and averaged in batches to produce a single value. A diagram of the DAU system is shown in Figure 8.4. The computer interface allows any recorded data to be downloaded to an IBM-compatible computer and stored for later analysis. If it is desired to have approximately 4±5 samples per wavelength at an average walking speed of 1.5 m/s, then the sampling frequency required is approximately 40 Hz at 1800 MHz (l % 17 cm). The microprocessor used for this application is the Texas Instruments TMS320-E15. This processor has the advantage that its program memory is contained in the on-chip EPROM of the device, so reprogramming is straightforward. The processor interfaces with several devices, namely an analogue-to-digital converter (ADC), a dynamic RAM, the programmable attenuator and a set of input switches and LCD display located in the handset. Interfacing with a notebook computer is performed by a parallel printer interface on the PC. The DAU can be in one of two modes, download or record. In record mode, the system `hangs' until the user wishes to sample. After initiating a measurement, 128 sample values are taken via the ADC at a sampling frequency of approximately 40 Hz. These 128 values are averaged to produce the mean signal level and if necessary an adjustment is made to the programmable attenuator. The change in attenuation is calculated automatically, using an algorithm which evaluates the mean signal strength, the dynamic range of the system and the current attenuation setting. A further 1024 samples are then taken at the constant sampling rate and the mean signal strength is calculated. Signal levels for the CDF of the collected data are also produced at probabilities of 1%, 50% and 99%. The calculated values are all displayed on the LCD and stored in the dynamic RAM, which also features a small backup battery to enable short-term storage of captured data. 224 The Mobile Radio Propagation Channel Sounding, Sampling and Simulation 225 Figure 8.3 Block diagram of the receiver. In download (or interface) mode, the user is allowed to interface the system with a computer or manually view the contents of the memory via the LCD on the handset. Using specially written software, full system calibration can also be undertaken. The software also provides testing of all the DAU elements; a useful feature which can be used before any ®eld measurements. The power source for the backpack signal strength measuring system is provided by a set of nickel±cadmium (NiCd) cells, producing an output voltage of approximately 13 volts. The total current consumption of the backpack is approximately 0.8 amps, so the battery pack will sustain the backpack for a period of up to 7 hours of continuous use. DC±DC converters are used to provide constant output voltages regardless of the ¯uctuations of the input power source. The complete receiver system including DAU is shown in Figure 8.5; it has a dynamic range of 80 dB and the noise ¯oor is at 7125 dBm. 8.3 SIGNAL SAMPLING Any record of signal strength has to be analysed in order to obtain the required parameters. The raw information, whether in linear or logarithmic units, has two components which represent the slow and fast fading; the mean value is in¯uenced by the distance from the transmitter. The analysis can be designed to obtain the mean or median value in a certain area and/or to derive information about the ®rst- and second-order statistics of the fading envelope. If it is desired to obtain information about the depth and duration of fades, it is necessary to sample the signal at a rate appropriate to the task. Expressions for the average level crossing rate and average fade duration of a Rayleigh fading signal have been obtained in eqns (5.43) and (5.47), and Table 5.1 gives values, in 226 The Mobile Radio Propagation Channel Figure 8.4 The data acquisition unit. wavelengths, with respect to the median value. For example, the average duration of a fade 30 dB below the median value is 0.01l, and at 900 MHz this value corresponds to a distance of 0.33 cm. Fairly rapid spatial sampling is therefore necessary to ensure such fades are not missed. In practice there is lognormal fading superimposed on the Rayleigh fading, and in order for results to be compared with theory it is necessary to separate the two fading processes by a technique of normalisation. Clarke's suggestion [8] of normalisation as a method of dealing with a signal in which the underlying process is Rayleigh was discussed in Chapter 5. It has become widely known as the running mean or moving average technique. The result is a new PDF p n r n 2r n exp Àr 2 n  whichisaRayleighprocesswiths 2  0:5 and an RMS value of unity. The question now arises as to what is a suitable distance for normalisation of experimental data? Parsons and Ibrahim [9] experimented with various windows having widths between 2l and 64l, coming to the conclusion that it was reasonable to treat the data as a stationary Rayleigh process for distances up to about 40 m at VHF and about 20 m at UHF. Davis and Bognor [10] investigated the eect of measurement length on the statistics of the estimated fast fading at 500 MHz and showed that as the distance was increased above about 25 m, variations in the local average values appeared. It seems therefore, from experimental evidence, that distances of up to 40 m are suitable at VHF, while there is danger in going above 25m at UHF. We have seen that rapid sampling is necessary to accurately obtain the second-order statistics of the signal; but following on from the above argument we might ask, in the context of extracting the local mean value, how many samples do we really need within the given measurement length and also, given those samples, with what accuracy and con®dence can we estimate the local mean? 8.4 SAMPLED DISTRIBUTIONS To answer the question about estimation of the local mean, we need to obtain some simple relationships that apply to sampled distributions. We can state quite generally Sounding, Sampling and Simulation 227 Figure 8.5 The complete receiving system. that if the probability density function of a random variable x is p(x) and if x 1 , x 2 , , x N are observed sample values of x, then any quantity derived from these samples will also be a random variable. For example, the mean value of x i can be expressed as  x  1 N X N i1 x i and this is an estimate of the true mean value Efxg;  x is a random variable and the probability density function p 1 (  x), which can be found provided p(x) is known, is called the sampled distribution. Generally the mean and variance of the sampled distribution can be written ^ m  Ef  xgE 1 N X N i1 x i ()  1 N E X N i1 x i ()  Efx i gm 8:1 and, assuming independent samples, ^ s 2  Ef  x À ^ m 2 gEf  x À m 2 g  E 1 N X N i1 x i À m ! 2 8 < : 9 = ;  1 N Efx i À m 2 g s 2 N 8:2 8.4.1 Sampling to obtain the local mean value Theoretical analyses have been published that deal with the question of signal sampling. Early work in this ®eld includes that of Peritsky [11] and Lee [12]. Peritsky investigated the statistical estimation of the local mean power assuming independent Rayleigh-distributed samples, and Lee presented an analysis concerned with estimating the local mean power using an averaging process with a lowpass ®lter. Their work was based on a statistical estimation of the RMS and mean signal strength in volts, i.e. they assumed a receiver with a linear response. Practical measurements, however, are often taken using a receiver with a logarithmic response; then the signal samples are expressed directly in decibels relative to some reference value and estimates can be made directly from them. If we consider the case of a Rayleigh fading signal, it is possible to determine the number of independent samples N necessary to estimate the mean or median value within a certain con®dence interval. The need for independent samples then enables us to relate N to the distance (length of travel) over which these samples should be obtained. Increasing the sample size can make the estimate more accurate through a knowledge of the eects that sampling rate and measurement length have on the standard deviation of the estimate, but some care is needed. Simply increasing the number of samples is not sucient since for a small measurement length they will not be independent and may be on an unrepresentative portion of the fading envelope. 228 The Mobile Radio Propagation Channel Similarly, a long measurement length and a sampling rate that is insucient to resolve the fading envelope would not adequately represent the local mean or median. It is necessary to have a suciently large sample size, and it is also necessary to take the samples over a measurement length that allows an accurate estimation of the required parameters. Additionally, in the real fading environment, slow fading also exists and this will have an in¯uence if the measurement distance is too large. It is necessary to take this into account in order to arrive at a compromise between measurement length and accuracy in practical measurements. 8.4.2 Sampling a Rayleigh-distributed variable The relationships between linear and logarithmic samples of a Rayleigh-distributed variable are derived in Appendix B. A widely used parameter is the median value r M of the logarithm of the signal strength. This can be obtained using (2k + 1) samples and ®nding the sample above and below which there are exactly k samples. Alternatively, the mean value of the logarithm of the signal strength can be found. This is given by the mean of the dB-record: Efr dB g 1 N X N i1 20 log 10 r 8:3 Note that Efr dB g depends on the values of all the samples of r. The relationship between this value and the value obtained from the mean of a linear receiver, i.e. Efrg, will be related through the statistics of the signal envelope (Rayleigh in this case) and in general this relationship will not be simple. This is not so for the median value, which is the same sample irrespective of whether the receiver response is logarithmic or linear. The median is widely used in mobile communications, ®rstly because it does not require a receiver with a characteristic that closely follows a predetermined law (say logarithmic or linear), merely one which can be calibrated with respect to any given reading. Secondly, the 50% cumulative distribution level is meaningful in estimating the quality of service in a given area. 8.5 MEAN SIGNAL STRENGTH For estimation of mean signal strength in decibels, the distribution of the estimate is not known. The estimate is obtained from the sum of independent samples, and if the number of samples is suciently large, the distribution can be approximated by a Gaussian distribution, using the central limit theorem, irrespective of the distribution of the individual samples. Let us write a standardised variable z, corresponding to a Gaussian variable x as z  x À m s The probability that z is less than a speci®ed value Z is then probz4ZPZ  Z ÀI 1  2p p exp À z 2 2  dz 8:4 P(Z) can be determined by reference to tables. Sounding, Sampling and Simulation 229 Now, in terms of the mean signal strength that we are trying to estimate,  z   x À ^ m ^ s which, using eqns. (8.1) and (8.2), can be written as  z   x À m s=  N p 8:5 Substituting this in eqn (8.4) we obtain PZprob  x4 Zs  N p  m  8:6 8.5.1 Con®dence interval We are seeking to establish the number of signal strength samples, N, that are necessary in order that we can assert, with a given degree of certainty (often expressed as a percentage), that the mean value of these samples lies within a given range of the true mean. This range is called the con®dence interval and can be found by con®rming that probÀZ 1 4z4  Z 1   Z 1 ÀZ 1 pzdz  2PZ 1  We can now extend eqn. (8.6) to obtain prob  x À Z 1 s  N p 4m4  x  Z 1 s  N p   2PZ 1 8:7 or alternatively prob À Z 1 s  N p 4m À  x4 Z 1 s  N p   2PZ 1 8:8 Table 8.1 has been compiled using Gaussian statistics and shows the range, in terms of s, within which a given percentage of values fall. For example, 68% of values fall within Æs. If we are dealing with samples taken from a receiver with a logarithmic characteristic then we know, from the relationships given in Appendix B, that 230 The Mobile Radio Propagation Channel Table 8.1 Values of P (Z 1 ) and con®dence intervals P (Z 1 ) Range 68% Æs 80% Æ1:28s 90% Æ1:65s 95.46% Æ2s 99% Æ2:58s [...]... bandwidth Several methods are possible 8.8.1 Periodic pulse sounding When a pseudo-impulse (i.e a short duration pulse) is used to excite the mobile propagation channel, the received signal represents the convolution of the sounding pulse with the channel impulse response In order to observe the time-varying behaviour of the channel, periodic pulse sounding must be employed The pulse repetition period... verify the models, either single-tone measurements have to be repeated at various frequencies over the band of interest, or an alternative sounding technique has to be used A primary limitation of the single-tone sounding technique is its inability to illustrate explicitly the frequency-selective behaviour of the channel In order to surmount this di culty, a spaced-tone sounding method can be used, in... repetition rate determines the maximum unambiguous time delay i.e the Figure 8.7 Periodic pulse sounding: T1 ˆ minimum echo-path resolution, T2 ˆ maximum unambiguous echo-path delay Sounding, Sampling and Simulation 235 maximum distance for which an echo contribution can be unambiguously resolved Periodic pulse sounding of the channel provides a series of `snapshots' of the multipath structure, with successive... asynchronous sounding technique and has many advantages in terms of cost and complexity In addition the system operates in real time because the output of the matched ®lter is a series of snapshots of the channel response and amounts to a one-to-one mapping of time delays in the time domain There are, however, several disadvantages which limit its appeal for channel sounding Firstly, the real-time information... time delays and Doppler shifts in multipath mobile radio channels Sounding, Sampling and Simulation 239 Figure 8.11 Channel sounder receiver as used by Cox There have been several further studies made, in the mobile radio [7,26±30] and microwave [31] ®elds, using the swept time-delay cross-correlator method The measuring equipment in all these studies was, in essence, a replica of the system used by... and receiver pass each other on a step-by-step basis rather than drifting slowly and continuously The earliest impulse response measurements of the mobile radio channel using a swept time-delay cross-correlation (STDCC) sounder were obtained by Cox [1] in New York City at 910 MHz In these experiments a 511-bit m-sequence, clocked at 10 MHz, was used to phase-reversal modulate a 70 MHz carrier This... [20], they have not yet been used extensively in studies of mobile radio channels 8.8 WIDEBAND SOUNDING TECHNIQUES Channel sounding using a number of narrowband measurements (simultaneously or sequentially) is attractive from the viewpoint of equipment complexity, but has clear limitations It is usually preferable to employ a genuine wideband sounding technique in which the transmitted signal occupies... This modulated signal was then translated to the sounding frequency by mixing with an 840 MHz local oscillator, and was ampli®ed to produce an average radiated power of 10 W The signal was radiated from an omnidirectional antenna mounted at a ®xed base 238 The Mobile Radio Propagation Channel Figure 8.10 Principle of pulse compression using a cross-correlation process station site All frequencies used... fading environment 232 The Mobile Radio Propagation Channel depends on how accurately we wish to estimate the local mean Since the con®dence interval decreases very slowly for large N, a smaller con®dence interval necessitates a very much larger number of samples and a correspondingly larger measurement distance If the mobile is close to the base station or is in a radial street where a strong direct... growth in private mobile radio schemes, particularly cellular radiotelephony, has increased the need for accurate methods of assessing, and/or predicting, the performance of these radio systems From a systems engineering standpoint, modulation schemes, data rates, diversity techniques, coding formats and equalisation techniques are of principal concern; from the standpoint of radio propagation modelling, . & Sons Ltd Print ISBN 0-4 7 1-9 8857-X Online ISBN 0-4 7 0-8 415 2-4 receiver is fed via a suitable interfacing circuit and an ADC into the memory (RAM) of a microcomputer. Distance pulses from a transducer. Chapter 8 Sounding, Sampling and Simulation 8.1 CHANNEL SOUNDING In the earlier chapters we discussed the characteristics of mobile radio channels in some detail. It emerged. Rayleigh-distributed variable The relationships between linear and logarithmic samples of a Rayleigh-distributed variable are derived in Appendix B. A widely used parameter is the median value