insertion of the cyclic prefix makes the waveform periodic, giving it the capability to tolerate small timing errors. That is, only a phase distortion is introduced to the useful symbol if the processing at reception starts earlier into the cyclic prefix (i.e. no fine synchronization is required). Furthermore, a multipath signal with a delay smaller than the cyclic prefix duration is merely a circularly shifted version of the original signal, which affects the symbol by a complex distortion, not as an ISI, which can be corrected by the channel estimation as mentioned earlier.
The above analysis illustrates the tolerance of OFDM to small sync errors and robustness against multipath, on the order of a half of the cyclic prefix duration. However, the OFDM modulation suffers from large to average power ratio (PAPR), which demands a high dynamic range, especially in the power amplifier (PA) of transmitters. Otherwise, the PA would enter saturation, causing nonlinear amplification of large‐amplitude signals. In addition, the guard bands are required in order to reduce possible inter‐band interference (IBI) such that the signal remains within its band in the presence of clock drift and Doppler frequency shift. The inter‐carrier (subcarrier) interference (ICI) can be avoided if the orthogonality of subcarriers is maintained, which places high demands on processing of OFDM baseband signals to cope with such issues as carrier frequency offset (CFO), carrier phase offset (CPO), sampling clock offset (SCO), symbol timing offset (STO), IQ imbalance and DC offset, and PA nonlinearity (constellation distortion and inter‐modulation distortion) [48].
Figure 40.7 shows the frame structure of DVB‐T signals [44]. The continuously transmitted DVB‐T signal stream is organized into frames, four frames making up a super frame. Each frame has 68 OFDM symbols. An OFDM symbol with duration TS is made of a symbol part with duration TU and a guard interval (cyclic prefix) with duration Δ. Continuous transmission of DVB‐T signals at a fixed rate enables accurate tracking of the signals for improved timing and positioning estimation as compared to intermittent transmission of packetized OFDM signals in Wi‐Fi and DSRC.
The DVB‐T standard specifies OFDM signals for 4, 5, 6, 7, and 8 MHz channels [44]. The parameters for an 8 MHz channel are shown in Figure 40.7. It has an elementary period T = 7/64 μs (the sampling period). The terrestrial transmission has two modes, namely, 2K and 8K. For the 8K mode, the FFT size (mode) is NFFT = 8192; the duration of useful symbol part is TU = NFFTT = 8192T = 896 μs; and the carrier spacing is 1/TU = 1116 Hz. The number of used carriers is K = 6817 so that the spacing between carriers Kmin = 0 and Kmax = 6816 is (K−1)/TU = 7.61 MHz, which is within the allocated channel bandwidth of 8 MHz. The difference between the allocated and used spectra is employed as the guard band; that is, the unused 1375 null subcarriers are split into 688 and 687 placed on the lower and upper edges of the transmission spectrum band, respectively. Several choices for the cyclic prefix duration Δ are listed in Figure 40.7. For Δ = 1/8TU, the cyclic prefix duration is Δ = 112 μs (or 1024T), and the resulting symbol duration is TS = TU + Δ = 1008 μs (or 9216T).
Figure 40.8 shows the process of generating an OFDM symbol for DVB‐T signals. The payload data are mapped into QAM after source coding and channel coding. Each OFDM frame also contains transmission parameter signaling (TPS) symbols, which are coded and assigned to specific carriers. For our purpose, we are interested in scattered pilot cells and continual pilot carriers. These pilots are intended for time synchronization, frequency synchronization, channel estimation, frame synchronization, transmission mode identification, and phase noise estimation among others, whose transmitted power is “boosted” by a factor of 4/3 relative to data and TPS carriers. We will use them for timing, ranging, and ultimately positioning.
Figure 40.7 Frame structure of DVB‐T signals.
Figure 40.8 Generation of an OFDM symbol for DVB‐T signals.
For each OFDM symbol, the continual pilots remain at the same carrier indexes, namely, k = (0, 48, 54 … 1491, 1683, 1704, 1752, 1758, 1791 … 6603, 6795, and 6816) [44]. The 2K mode stops at Kmax = 1704 (a total of 45 carriers) while the 8K mode continues until reaching Kmax = 6816 (a total of 177 carriers), as illustrated in Figure 40.9.
The scattered pilots are placed at the carrier indexes that belong to the subset {k: k = Kmin + 3×(l mod 4) + 12p ≤ Kmax for l = 0, 1, …, 67 and p ≥ 0}, a total of 142 and 568 carriers per symbol for the 2K and 8K modes, respectively. The placement pattern repeats every four OFDM symbols. As shown in Figure 40.9, the pilots are inserted once every 12 carriers with the starting index being 12, 3, 6, and 9 for symbol 0, 1, 2, and 3, and so on. Note that the scattered pilots may coincide with the continual pilot carriers (11 and 44 carriers in common per symbol for the 2K and 8K modes, respectively). Each continual pilot coincides with a scattered pilot once every fourth symbol. There are 17 and 68 carriers for TPS in the 2K and 8K modes, respectively. As a result, there are 1512 useful data carriers in the 2K mode and 6048 in the 8K mode, respectively.
Figure 40.9 Pilot organization for DVB‐T signals (not to scale).
Furthermore, the continual and scattered pilots are modulated according to the pseudorandom binary sequence (PRBS) specified by the polynomial generator GPRBS(x) = x11 + x9 + 1 with the all‐one initial condition. The PRBS is initialized such that the first output bit from the PRBS corresponds to the first active carrier, and a new value is generated by the PRBS on every used carrier of an OFDM symbol, whether it is a pilot or not.
Figure 40.10 shows the architecture of a software OFDM receiver for TOA estimation with DVB‐T signals. The top part of Figure 40.10 shows the typical processing steps employed by an OFDM communications receiver for the purpose of demodulating information data bits. The bottom part of Figure 40.10 shows the extra processing steps of three possible methods to extract refined TOA measurements for the purpose of ranging and positioning.
After passing through a fading channel h(τ) with L discrete multipath components, the transmitted signal s(t) arrives at the receiver as r(t), which is captured by the antenna, and down‐converted from RF to a suitable IF for sampling or resampling if necessary. The sampling rate fs is typically a multiple of the fundamental rate (1/T). Once in the digital domain, the first operation is to determine the start sample of an OFDM symbol, which is called coarse symbol synchronization. A popular method for coarse symbol sync is to find a match between
