OFDM Distance Measurement

Distance measurement using OFDM is based on the linear relationship between the slope of the phase shift of symbol subcarriers and propagation time. The measurement process will be described with reference to block diagrams Figures 5.23 and 5.24, and the timing diagram of Figure 5.25. The system consists of an interrogator and a responder. A packet of OFDM symbols originating in the interrogator terminal is transmitted to the responder. It begins with a preamble to facilitate frequency and symbol timing (not shown in Figure 5.25). In the interroga-tor of Figure 5.23, a subcarrier phase vecinterroga-tor is created as described in Section 5.7.1. Its components are forwarded in parallel to the IFFT block and to the resulting output is added the cyclic prefix. The sample clock times the output of a digital to analog converter that is upconverted in a modulator to the transmission frequency band. A symbol strobe, shown in Figure 5.23 as an input to the IFFT block, marks the beginning of each symbol.

In a distance measurement (DM) protocol, the DM symbols and their place in the packet are known to the responder. Referring now to the timing diagram, Figure 5.25, the interrogator aligns a periodic symbol strobe to the beginning of the first DM symbol, t_ssi, which continues at the symbol rate after the packet burst termination while the terminal changes from transmit to receive. A synchronized data strobe is produced at the end of the cyclic prefix, t_ds. The relationship between the clock and strobe pulses is shown in Figure 5.24. The number of sample clock pulses within a complete symbol period is indicated by M. The symbol period is the duration of the cyclic prefix, T_P, plus the time of the data symbol, T_D.

The responder downconverts the received signal and synchronizes its clock to the demodulated bits. It aligns an input symbol strobe to the beginning of the cyclic prefix at t_ssr (Figure 5.25) and proceeds to clock the signal into the buffer/store block of Figure 5.23, at the synchronized sample clock rate of the interrogator.

Subcarrier

phase vector IFFT Modulator RF out

Demodulator RF in

Figure 5.23 Interrogator and responder in OFDM distance measuring system.

Divide by M

Figure 5.24 Strobe and clock generation in OFDM distance measuring system.

When the entire DM symbol has been sampled and the samples stored in a memory register, the responder changes over from receive mode to transmit mode. After a period of time that is equal to an integer number, n, of symbol length times after the symbol strobe, that is, at t_ssi + nT_s in Figure 5.25, the responder clocks out the samples from the buffer/store unit and transmits them to the interrogator. The value of n takes into account the time required for the interrogator to complete transmitting the OFDM burst and change over to receive mode. In a distance measurement protocol, it should not be necessary to actually sample the incoming bits, just to mark the instant of the start of the cyclic prefix. The responder can know in advance the symbol that the interrogator will send it and to maintain a stored copy of the symbol sample sequence. Therefore, after detecting the beginning

T_P T_D

Figure 5.25 OFDM distance measurement timing diagram.

of the received symbol sequence, it does not have to sample that sequence and it transmits the stored copy of the sequence after a delay of an integral number of symbol periods as in the previous description. An advantage of using a stored symbol is that the retransmitted symbol will not be contaminated by noise or interference. However, it can be used only when the distance-measuring symbol is constant and is established in advance. A disadvantage in using the stored symbol is that the exact position of t_ssr must be determined, which is not the case when the incoming signal is buffered for later readout.

On the interrogator side, after sending the OFDM burst, the terminal changes over from transmit mode to receive mode while maintaining the data strobe clock uninterrupted. It receives the return OFDM burst retransmitted by the responder and clocks demodulated signal samples through an analog to digital converter, (A-D in Figure 5.23) to the FFT block. The FFT operation begins at a data strobe, T_ds + nTs(Figure 5.25), n symbol times plus the period of the cyclic prefix after the original symbol strobe of the interrogator at t_ssi. Symbol sampling is carried out for a duration of T_D. Due to the two-way propagation delay of the signal, the sample window for the FFT in the interrogator receiver commences before the start of the data portion of the symbol, that is, during the cyclic prefix. The value of this delay, T_PD, which equals the time from the beginning of the first sample to the end of the cyclic prefix, can be determined from the phase difference between the subcarriers that were transmitted from the interrogator to reception of the signal retransmitted from the responder. From the argument of each element, or subcarrier phase, of the output of the FFT is subtracted the argument of the corresponding element of the frequency domain data vector of the originally trans-mitted signal. This operation takes place in the phase slope analyzer block in Figure 5.23. The phase versus angular frequency slope of the resulting difference vector is the propagation delay, from which the distance between interrogator and responder can be calculated. Instead of measuring the phase slope directly, the time delay is preferably found by taking the IFFT of the phase difference vector, which

is expressed as complex elements. The ideal correspondence between the phase difference vector and the time delay resulting from the IFFT is shown in the Fourier transform shifting theorem, (5.42).

A plot of the IFFT of the phase difference vector can be examined and analyzed to separate the direct signal from multipath. The phase difference IFFT output of the interrogator receiver in an OFDM distance measurement system simulation is shown in Figure 5.26. A direct path and three echoes were used in the simulation.

The parameters of the returns are shown in Table 5.2. The same parameters were applied to both the forward and reflected transmission.

The following are the relevant parameters of the OFDM system:

• Data samples per symbol: 64;

• Active subcarriers: 52;

• Cyclic prefix: 16 samples;

• Sample rate: 20 Mbps.

In addition, the return signal at the interrogator receiver is oversampled by a factor of 4; that is, 256 samples per data period T_D.

It is necessary to determine what criteria to use to decide which peak is the true direct path. In Figure 5.26, the direct path is the largest peak. The two-way

00 1 2 3 4 5 6 7 8 9 10

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Samples

Figure 5.26 OFDM distance measurement simulation result.

Table 5.2 Multipath Parameters for OFDM Distance Measuring Simulation Example

Delay Rel Strength Phase Rotation

Path 1 T_D 0 dB 0°

Path 2 1.2 T_D −10 dB −10°

Path 3 1.3 T_D −6 dB −45°

Path 4 1.5 T_D −7 dB 20°

propagation delay between the interrogator and the responder is the sample number of the peak (N_sample) times the period of the sample clock (1/f_s), divided by the oversampling ratio. Thus, in this example, the true one-way range is given by the following expression:

range=c

2 ⭈N_sample ⭈ 1

f_s ⭈ 1

oversampling (5.43)

where c is the speed of light. In Figure 5.26, the direct peak occurs at N_sample = 44, and using (5.43) range= 82.5m.

Normally it cannot be presumed that the direct path is dominant and an algorithm that manipulates the phase difference IFFT output has to be developed to determine the propagation time of the earliest received multipath return in order to provide an estimate of the true range.

There are several basic differences between distance measurement on frequency hopping channels and OFDM. In OFDM, the distance measurement data is taken from modulated waveforms whereas in the case of frequency hopping the carriers are unmodulated during the measurement time. In the frequency hopping method, accuracy may be increased by reducing the I/Q low pass filter bandwidth—decreas-ing signal bandwidth. The most straightforward means for increasbandwidth—decreas-ing OFDM DM accuracy is to increase the sampling rate in the interrogator receiver. When the sampling rate is increased without increasing the number of subcarriers the band-width remains the same but resolution is improved.