Chapter 2. Channel Measurement and Simulation
Ahmad Safaai-Jazi, Ahmed M. Attiya, and Sedki Riad
The development of channel models for UWB communication systems requires
In narrowband wireless communication systems, the information signal modulates a very high frequency sinusoidal carrier; thus, along each propagation
In this chapter, both measurement and simulation of UWB signal propagation are addressed. Section 2.2 surveys time domain and frequency domain measurement techniques. Important issues such as triggering, calibration, interference
2.2. Measurement Techniques
Measurements of UWB signal propagation can be carried out using a variety of
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
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
Figure 2.1. Schematic Diagram of the Time Domain Measurement Setup for UWB Channel Characterization.
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
Due to their
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
Figure 2.2. Calibration of Time Domain Measurement Setup.
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
. The scope generates a train of
sampling pulses to trigger its detection
Figure 2.3. Principle of Operation of Sampling Oscilloscope: Sampled Points Connected by Interpolation to Produce a Continuous Waveform.
2.2.2. Frequency Domain Measurement Techniques
Frequency domain characterization of UWB channels is based on measurements at different frequency points using a sweep
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.
Figure 2.4. Setup for UWB Channel Characterization Using Scalar Frequency Domain Method.
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
Figure 2.5. Calibration of Scalar Frequency Domain Measurement Setup.
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.
Figure 2.6. Measurement Setup for UWB Channel Characterization Using Vector Network Analyzer.
In conventional VNA language, measuring the channel transfer function is to perform a forward transmission complex scattering-matrix parameter
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
-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
Figure 2.7. Setup for Frequency Domain UWB Channel Characterization Using VNA in Conjunction with Electro-Optic System.
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
-parameters of small
A basic function of a VNA is to convert the measured signal to a lower fixed IF frequency, while
Figure 2.8. Block Diagram of S-Parameter Test Set.
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
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
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
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
represents the Fourier Transform of another signal that can
Thus, the complex spectrum of a causal analytic system can be expressed in terms of its magnitude. This gives
) = 1. It should be noted that the phase of this all-pass filter cannot be