Chapter2.Channel Measurement and Simulation

2.2. Measurement Techniques

Measurements of UWB signal propagation can be carried out using a variety of methods that may be broadly divided into two categories: time domain and frequency domain techniques. Both measurement techniques are discussed, and their advantages, disadvantages, limitations, and related important issues, such as triggering, noise, and calibration are addressed.

2.2.1. Time Domain Measurement Techniques

Time domain techniques can be used as a direct way to characterize UWB communication channels. Ideally, the impulse response provides complete characterization of a device or a system over the entire frequency band of use. However, it is not possible to directly measure the true impulse response of a device or a system since that requires the availability of an ideal dirac-delta excitation signal. In practice, very short duration pulses are used for the time domain characterization of UWB channels. The shorter the duration of the pulses used, the wider the bandwidth for which the UWB propagation characteristics can be measured. The basic idea of time domain measurements is to excite one end of the UWB channel with a periodic train of very short duration pulses separated by a sufficiently long quiet period so that all multipath components are received at the other end during the quiet period (prior to the next occurrence of the pulse). On the receiving side, the signal is detected using a wideband detector (typically, a digital sampling oscilloscope). In the following sections, we first discuss, in detail, the time domain measurement method used for characterizing UWB channels. Then, we examine the main sources of errors in the measurements, and the precautions needed to minimize these errors.

Time Domain Channel Measurement

The time domain measurement technique for UWB channel sounding, as shown in Figure 2.1, consists of a pulse generator, a digital sampling oscilloscope, a pair of transmitting and receiving antennas, and a triggering signal generator. The pulse generator represents the UWB signal source. This generator should be connected to the transmitting antenna through a low loss wideband cable to minimize signal degradation (attenuation and dispersion) prior to propagation through the antenna. When higher radiated powers are desired, a UWB power amplifier may be used at the feed point of the transmitting antenna. This amplifier should have a constant gain and a linear phase characteristic over the spectrum of the UWB signal in order to minimize signal distortion. The receiving antenna and the digital sampling oscilloscope constitute the receiver. To enhance the received signal power, a low noise amplifier may be used right at the output port of the receiving antenna. This amplifier should also have a constant gain and a linear phase characteristic over the spectrum of the UWB signal.

An important task in time domain measurements is the synchronization of both transmitting and receiving sides of the channel sounding system. To achieve this synchronization, a low jitter triggering signal should be maintained between the pulse generator and the digital sampling oscilloscope. A simple approach is to use a sample of the radiated pulse captured by means of a small antenna situated close to the transmitting antenna to trigger the sampling oscilloscope and thereby achieve synchronization. This method does not require an independent triggering generator, but the captured signal is typically weak and may not be strong enough to trigger the oscilloscope. Another disadvantage is that the captured signal is often cluttered by multiple reflections from the surrounding objects, and contains multiple triggering points, leading to false triggers. A more reliable triggering approach is to use a triggering generator with two outputs to synchronize the transmitter and the receiver. The triggering sequence is arranged such that a pretrigger signal is sent to the sampling oscilloscope, while a delayed trigger is sent to the transmitter. The time delay between the pretrigger and the delayed trigger signal should be adjusted to compensate for the time delay introduced by the triggering cables and propagation through the UWB channel being measured.

Due to their ultra wide bandwidths, UWB channel measurements are susceptible to interference and noise from various sources. Generally , two categories of noise, namely, narrowband noise and wideband noise, can be identified. Narrowband noise is usually due to electromagnetic interference from nearby narrowband systems. This type of noise usually takes the form of a sinusoidal waveform added to the received signal. To eliminate the narrowband noise, the received signal is first Fourier transformed to the frequency domain where it is bandpass filtered to remove the noise spectrum, and then the signal is converted back to time domain via the inverse Fourier Transform. The wideband noise, on the other hand, is typically in the form of random short pulses that are not repetitive. Averaging multiple acquisitions can significantly reduce this noise. Signal averaging is generally available as a built-in feature in sampling oscilloscopes.

Radiation from the electronic circuit of the pulse generator and leakage from the cable connecting the pulse generator to the transmitting antenna, where the signal level is high, may contribute significantly to the background noise level. This background noise level can be measured by replacing the transmitting antenna in Figure 2.1 with a matched termination while the pulse generator is on. This background noise level sets the minimum level below which received signals cannot be detected.

Another important issue is the calibration of the measurement setup. The purpose of calibration is to remove the influence of nonideal characteristics of the measurement equipment from the measured data. To measure the characteristics of a communication link consisting of the transmitting and receiving antennas and the propagation channel, the contribution of the measurement setup needs to be calibrated out. This requires measuring the response of the equipment while the link under measurement is replaced by a calibrated attenuator, as shown in Figure 2.2. This attenuator should have a fairly constant attenuation level, and a linear phase characteristic over the spectrum of the UWB signal. The attenuation of this attenuator is chosen to ensure the proper signal level at the sampling oscilloscope. The impulse response of the link can then be obtained by deconvolving the calibration measurement waveform from the corresponding measured waveform for the communication link.

Sampling and Triggering Issues

Sampling and triggering are two critical aspects in direct time domain measurements. Figure 2.3 illustrates the principle of operation of a sampling oscilloscope. The real time signal to be measured is assumed to be periodic with a period T . The scope generates a train of N sampling pulses to trigger its detection circuitry within a specified duration of the measured signal. The triggering signal required for generation of the sampling pulses should run at a slightly different period from that of the signal under measurement to ensure the acquisition of different sampled points on the waveform for the N sampling pulse train. The period of sampling pulses is thus T + ( T/N ). Each acquired sample corresponds to a point of the input waveform, so that the train of sampling pulses results in sequential sampled points of the measured waveform. The resulting sampled data represent the y -axis in the oscilloscope display. The corresponding x -axis is obtained via a ramp signal with a period of ( N + 1) T , which is triggered at the beginning of the sampling train and is reset at its end. This brief description of the principle of operation of the sampling oscilloscope highlights the importance of triggering and the problems that may arise due to false triggering and jitter. False triggering signals may arise from the dispersion by triggering cables, the mismatch between the triggering cable and the triggering input, defects in the triggering cable, or the ringing effect of the trigger signal generator. The spectrum of the triggering signal is usually concentrated at the lower frequencies. Thus, the dispersion of triggering cables is not generally a major cause of false triggering for high-quality commercial coaxial cables. The shielding of the triggering cable should help prevent electromagnetic interference from, or to, the propagation channel. The connectors should also be selected and attached to the cable carefully to prevent multiple reflections between them and the triggering cable. The trigger generator should be designed with the least amount of vertical (amplitude) jitter and horizontal (time) jitter to ensure stability and consistency of the triggering and sampling process, and hence the overall precision of the time domain measurement.

2.2.2. Frequency Domain Measurement Techniques

Frequency domain characterization of UWB channels is based on measurements at different frequency points using a sweep harmonic generator. The chief advantage of the frequency domain technique over the time domain method is the availability of a much larger dynamic range, resulting in improved measurement precision. Each measurement is represented by a complex transfer function value described by its magnitude and phase terms. The inverse Fourier transform of the channel transfer function yields the impulse response of the channel, which is the information sought for UWB channel characterization.

Transfer function measurements are typically performed using a vector network analyzer (VNA), which is capable of measuring the complex ratio between the response of a device network under test to its excitation. A scalar network analyzer (SNA) provides an alternative for measuring the transfer function magnitude only. Phase measurements in UWB communication channels involving long propagation distances should be dealt with very carefully, as the available vector network analyzers were not originally designed for this purpose. Both the scalar and vector network analyzer approaches to channel characterization are surveyed in the following sections. The difficulties associated with direct phase measurements in UWB channel sounding are addressed as well.

Scalar Frequency Domain Measurement

In the scalar frequency domain method, only the magnitude of the transfer function is measured. However, both magnitude and phase information are required to enable the conversion of the frequency domain data to the time domain impulse response. Hence, retrieving the phase information from the magnitude measurement, such as by using the Hilbert Transform, becomes an integral part of this approach. Figure 2.4 shows the setup for scalar frequency domain channel measurements using a scalar network analyzer. As shown in the figure, the synchronization between the source and the SNA is achieved by connecting the sweep output of the RF synthesizer to the sweep input of the SNA.

To calibrate the setup, a measurement without the UWB channel is performed. The calibration measurement is performed by connecting the line to the input of the transmitting antenna directly to the line at the output of the receiving antenna through a calibrated attenuator, as shown in Figure 2.5. The need for, and properties of, such an attenuator were discussed earlier in the time domain measurement section. The source calibration measurement is acquired and stored in the available SNA memory or that of an interfaced computer. Measurements on the UWB channel are then performed as shown in Figure 2.4, and the corresponding channel transfer function is obtained by subtracting the prestored source calibration data in dB from the channel measurement data, also expressed in dB.

As discussed in the time domain measurement section, the background noise level sets the minimum level below which the received signal cannot be detected. Again, the background noise for this setup can be measured while replacing the transmitting antenna in Figure 2.4 with a matched load with the transmitter operating.

Direct Measurement of Magnitude and Phase

In this approach, both magnitude and phase are measured directly. Figure 2.6 shows the schematic diagram of the measurement setup that can be used to obtain the complex frequency domain transfer function of the UWB channel. Here, the scalar network analyzer is replaced by a vector network analyzer in which the synchronization of all units is maintained internally, and no external synchronization is needed. The operation of the VNA is based on a superheterodyning mechanism rather than simple crystal detection or the thermocouple effect normally used in scalar measurements. Thus, the typical dynamic range of a VNA is much larger than that of a typical scalar network analyzer.

In conventional VNA language, measuring the channel transfer function is to perform a forward transmission complex scattering-matrix parameter S ₂₁ measurement. It can be seen from Figure 2.6 that measurements of channels with long propagation distances require long cables to connect the VNA's S -parameter test set ports to the transmitting and receiving antennas at the two ends of the channel. Such long cables present a major limiting factor in this measurement configuration. As the frequency increases , cable losses increase "exponentially," causing serious reduction in the measurement's dynamic range. To overcome this drawback, one can use an electro-optic transmission system to replace the transmission end cable while maintaining a short cable connection at the receiving end. In this approach, the microwave signal modulates the optical transmission in an optical fiber cable, with the needed length determined by the channel length. The optical signal is demodulated at the end of the fiber cable and connected to the input of the power amplifier that feeds the transmitting antenna, as shown in Figure 2.7. The main advantage of using the optical fiber cable is its very low loss compared with traditional coaxial cables. Another advantage of an electro-optic transmission system is its immunity to electromagnetic interference. One obvious disadvantage is the high cost of wideband electro- optic transmission systems.

The calibration of the direct magnitude and phase measurement system can be carried out in exactly the same manner as in the scalar measurement system, as depicted in Figure 2.5. One difference is that typically VNAs have built-in processors for data reduction, and direct display and acquisition of final calibrated results. However, correction for the use of the calibration attenuator would be performed manually.

Accuracy of Direct Phase Measurement with a VNA

In the previous section, we discussed the use of a VNA for direct measurements of magnitude and phase of the UWB channel. However, it should be noted that VNAs are generally designed for the measurement of complex S -parameters of small two-port networks rather than characterization of communication channels involving long propagation distances. Thus, it might be suspected that VNA-based measurements may not yield true characteristics of propagation channels, hence the need to understand and clarify the relationship between measured signals and true channel characteristics. In doing so, it is helpful to discuss briefly the principles of operation of a VNA, and to examine the effects of using long cables and long distances on UWB channel measurements.

A basic function of a VNA is to convert the measured signal to a lower fixed IF frequency, while preserving the magnitude and phase information during the conversion process. The phase can then be measured more easily at the IF frequency. Downconverters and a synchronized voltage tuned oscillator (VTO) are used to perform the frequency conversion. The input RF signal is divided in the S -parameter test set into two parts . For measuring S ₂₁ , the first part is used as a reference signal a ₁ , while the second part is used to feed port 1, as shown in Figure 2.8. The received signal b ₂ is collected at port 2, thus S ₂₁ = b ₂ /a ₁ . For calibration, ports 1 and 2 are connected directly, which corresponds to a transmission coefficient of unity magnitude and a phase shift equal to zero. If the two-port network under test is connected to the VNA ports via long cables, the calibration procedure should be performed using the same cables. However, in this case, the time delay of the reference path is much less than that of the effective two ports. To avoid errors in the phase measurements, the same time delay should be realized in the path of the reference signal. This can be done by replacing the extension B in the reference path in Figure 2.8 with another cable that has the same time delay as the cable used in the measurement of the two-port network.

If the VNA is operating in the sweep mode, another source of error in direct phase measurements may result. This error would be due to the difference between the measured frequency and the frequency of the received signal due to the propagation delay time through the channel. In the sweep mode, the VNA frequency changes linearly with the sweep time. Due to the long channel path, the frequency of the signal at the end of the channel would be different from that at the beginning, resulting in errors in both the magnitude and the phase measurements. Typically, the magnitude function does not experience steep variations with frequency while the phase function typically does; hence, noticeable phase errors are observed . Sweep mode errors can be estimated and appropriate correction can be applied if channel delay (between the transmitting and receiving antennas) is accurately known. However, determining this delay accurately is virtually impossible .

To circumvent the sweep mode errors, the use of frequency stepping instead of frequency sweeping is highly recommended. In the frequency stepping case, the time of the frequency step should be larger than the time delay between the transmitting and receiving antennas. However, it should be taken into consideration that the measured signal is that recorded at the end of the time step rather than the average of measured signals received during the time step. If this condition is clearly satisfied, the measured signal would correspond to the actual magnitude and phase values.

Phase Retrieval from Magnitude Measurements

With the difficulties associated with phase measurements, particularly when propagation distances between the transmitter and receiver are large, one appreciates the simplicity and ease with which magnitude measurements can be performed. However, the purpose of UWB channel sounding is to obtain the channel impulse response in the time domain, which requires full knowledge of the channel's complex transfer function in the frequency domain. This implies that knowledge of both the magnitude and phase of the transfer function is required. Here, we discuss how phase information can be derived from the magnitude data, which, as was discussed earlier, can be measured rather easily with a scalar network analyzer.

The phase retrieval method described in the following is based on using the Hilbert Transform, which requires that the impulse response of the UWB channel under test satisfies the causality and analyticity conditions. That is, the received signal cannot be detected any sooner than the corresponding free-space delay time, and for a finite energy pulse, the amplitude of the pulse decays to zero after a reasonable time period. Also, this method requires that the amplitude of each multipath component be smaller than the preceding one; that is, the amplitudes of multipath components decay successively. The latter requirement is satisfied for most line-of-sight scenarios and may not be satisfied in non-line-of-sight situations. For a causal analytic signal, the following Hilbert Transform relationship holds between the real and imaginary parts of its Fourier Transform

Equation 2.1

where H ( ) denotes the Hilbert Transform. Thus, for causal analytic signals, the real part of the Fourier Transform is sufficient to reconstruct the missing imaginary part. However, in scalar frequency domain measurements, the measurable quantity is the magnitude of the complex Fourier Transform of the signal and not the real part. This can be remedied by using the natural logarithm operator to state the magnitude and phase of the transfer function as the real and imaginary parts of the transformed response

Equation 2.2

The function represents the Fourier Transform of another signal that can satisfy causality and analyticity conditions if and only if all the poles and the zeros of R ( w ) lie inside the unit circle in the complex plane [13]. In this case, (2.1) can be applied directly to (2.2), resulting in

Equation 2.3

Thus, the complex spectrum of a causal analytic system can be expressed in terms of its magnitude. This gives

Equation 2.4

It is emphasized that the phase obtained from (2.3) represents the minimum phase of R ( w ). If all the poles and the zeros of R ( w ) do not lie inside the unit circle in the complex plane, a nonminimum phase contribution should be added to the minimum phase obtained by (2.3). This nonminimum phase contribution corresponds to the phase of an all-pass filter. Accordingly, (2.4) becomes

Equation 2.5

where G _all ( w ) = 1. It should be noted that the phase of this all-pass filter cannot be predicted by the Hilbert Transform because the logarithm of its magnitude is zero. The determination of the nonminimum phase contribution is the most complicated part of the phase retrieval process [3-5]. As far as the problem of UWB channel characterization is concerned , it has been found, by comparison with results obtained from time domain measurements, that the path loss exponent and time dispersion parameters for line-of-sight (LOS) scenarios when only the minimum phase contribution is considered do not differ too much from the actual results [6]. Thus, for LOS cases, (2.5) is used as the basis of analysis in scalar frequency domain measurements.