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The DVB‐T signals [44] share the same traits for use as SOOP for PNT as the ATSC‐8VSB signals discussed in Section 40.2.1. However, there are two major differences worth noting as far as PNT is concerned. First, the ATSC‐8VSB broadcasting can be viewed as a frequency division multiple access (FDMA) system with pulse amplitude modulation (PAM), wherein each DTV station transmits in its own frequency band which a receiver needs to tune to. In general, the ATSC‐8VSB stations are asynchronous, mostly operating on their own frequency and clock. From time to time, the DTV stations broadcast common network programming and may synchronize to the GPS time. In contrast, the DVB‐T can be used in a SFN in which all transmitters in the same SFN cell operate on the same frequency (efficient use of the spectrum) and are synchronized to the GPS time, thus being a synchronous network. A receiver therefore can receive signals originating from different transmitters on the same frequency band.

Second, the DVB‐T standard utilizes orthogonal frequency division multiplexing (OFDM) modulation as its air interface. The OFDM modulation has been adopted by many modern wireless communication systems such as Wi‐Fi 802.11 [45], 4G/LTE [46], and ultra‐wideband radar [47]. It offers high spectral efficiency due to the use of orthogonal subcarriers, which overlap but do not interfere, with properly chosen subcarrier spacing and pulse shaping. Since its bandwidth is small compared to the coherent bandwidth of the channel, each subcarrier is distorted by flat fading, which can be easily corrected using simple channel estimation techniques (e.g. one parameter). More importantly, a guard interval is inserted between successive OFDM symbols to avoid inter‐symbol interference (ISI); that is, there is no ISI if the maximum delayed version of a preceding symbol (multipath) does not cross over the guard interval into the subsequent symbol. In OFDM, the guard interval is used to transmit an exact copy of the end portion of an OFDM symbol waveform ahead of the whole symbol, called the cyclic prefix. The 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 T_S is made of a symbol part with duration T_U 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 N_FFT = 8192; the duration of useful symbol part is T_U = N_FFTT = 8192T = 896 μs; and the carrier spacing is 1/T_U = 1116 Hz. The number of used carriers is K = 6817 so that the spacing between carriers K_min = 0 and K_max = 6816 is (K−1)/T_U = 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 = 1/8T_U, the cyclic prefix duration is Δ = 112 μs (or 1024T), and the resulting symbol duration is T_S = T_U + 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 K_max = 1704 (a total of 45 carriers) while the 8K mode continues until reaching K_max = 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 = K_min + 3×(l mod 4) + 12p ≤ K_max 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 G_PRBS(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 f_s 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 two blocks of samples that are a symbol apart (i.e., the cyclic prefix) by searching through the samples sequentially. A match is found when a first block of N_CP = Δ/T samples (over the cyclic prefix) correlates with a second block that is N_FFT samples later (over the symbol end). The peak location of the complex correlation points to the start of an OFDM symbol, used as an estimate of the integer STO, while the phase of the complex correlation provides a coarse estimate of the fractional CFO because the phase is only measured within ±π. The fractional CFO thus estimated is then removed from the samples by phase rotation (multiplying the samples by a complex exponential of the CFO estimate).

Since the coarse estimate of the symbol start via cyclic prefix matching may be off by ±50 samples, to ensure that the FFT window starts within a safe zone of cyclic prefix, the FFT window is purposely adjusted ahead of the peak location by a certain number of samples. This adjustment introduces an extra phase due to the circular shift property of cyclic prefix, which is readily absorbed into the channel model together with a fractional STO. They are ultimately removed in channel equalization, and thus data demodulation is not affected. Note that the start sample of each sliding FFT window, plus the number of advanced samples, and the fractional STO together constitute the TOA estimate (the start of an OFDM symbol) in the receiver’s local time. However, the TOA estimates are coarse and are typically not tracked over time in a wireless communications receiver. It is one of the reasons a refined TOA estimation and tracking process is needed for PNT.

FFT is applied to the samples within the sliding window, yielding a frequency‐domain representation of an OFDM symbol. After the fractional CFO correction, the spectrum (the received frequency‐domain signal) may still be subject to a shift by a number of frequency bins (subcarriers) equal to an integer CFO if present. Since the continual pilots are shifted by the same amount, the integer CFO can be estimated by determining where the continual pilots reside in the spectrum. Correlation between the continual pilot subcarriers of two consecutive symbols reaches the maximum value when the nominal continual pilot indexes are adjusted up or down by an amount equal to the integer CFO. Furthermore, the phase of the correlation peak between the continual pilots of two consecutive symbols can be used to estimate the residual fractional CFO and the SCO. The integer CFO is then easily corrected by spectrum shift (re‐indexing).

Figure 40.10 Architecture of a DVB‐T OFDM signal processor with TOA tracking.

There are four insertion patterns of scattered pilots in successive symbols, and each pattern therefore repeats once every four symbols. The particular insertion pattern of a received symbol can be determined by correlating its scattered pilot subcarriers with those at the indexes of four possible patterns. Four correlations are therefore calculated, one for each possible insertion pattern, and the one that produces the maximum correlation value is the pattern present in the current symbol.

Once the pattern of scattered pilots is found for the current symbol, the scattered pilots together with continual pilots extracted from the current symbol (as received) are scaled by those from a local replica (as transmitted) to afford an estimate of the channel frequency response (transfer function) at the pilot subcarrier frequencies. As shown in Figure 40.9, the spacing is 12 subcarriers between scattered pilots. As a result, a linear frequency interpolation can be applied to extend the estimated frequency response from the pilot subcarriers to the full used OFDM subcarriers.

At this point, a communications receiver goes on with channel equalization, which scales the received symbol frequency response with the inverse of the estimated channel frequency response at all data OFDM subcarriers to obtain the equalized symbol subcarriers, from which information data bits are demodulated after de‐mapping, de‐interleaving, and decoding, among other necessary steps. On the other hand, a PNT receiver can apply a suitable method to obtain TOA measurements for ranging and positioning as described below.

An open‐loop TOA estimation scheme consists of applying the inverse FFT (IFFT) to the estimated frequency response at all data OFDM subcarriers, zero‐padded to cover the guard bands, to produce the channel impulse response (CIR), which describes the multipath signals in terms of their strength and delay relative to the start of the sliding window. The peak location of either the earliest arrival (above a detection threshold) or the strongest arrival can be taken for coarse TOA estimation through interpolation via a quadratic or sinc‐function curve fitting to within a fractional of a sample (about 0.11 μs for the 8K mode or 30 m) [49].

A more elaborate method to estimate the multipath signal parameters is to apply the matching pursuit (MP) algorithm [50] to the CIR [9, 10, 51, 52] in the time domain or the order‐recursive least‐square matching pursuit algorithm [53] to the channel transfer function [54] in the frequency domain. The estimated multipath signal parameters are then used to initialize a number of DLLs to track the delay of dominant signals for multipath resolution and refined TOA estimation [9, 10, 51, 52, 54]. Similar methods are used for 4G LTE signals [55, 56] and GNSS signals [57–59].

Although individual OFDM symbols are generated and processed almost independently, the signal stream is continuous in a framed OFDM system. As a result, the TOA of OFDM symbols can be tracked from symbol to symbol over time, which can be implemented either based on the pilot component or on the full symbol. In pilot‐carriers‐based delay tracking for refined TOA estimation (the lower‐middle part of Figure 40.10), the received pilot carriers are correlated with early, prompt, and late versions of the locally generated pilots. The normalized early minus late (EML) correlation power serves as the delay error discriminator, which drives a low‐pass loop filter. The filtered delay error is then used to correct the received pilot components so as to align up with the locally generated ones, thus closing the tracking loop [51, 52, 54].

In decision‐directed delay tracking for refined TOA estimation (the lower‐left part of Figure 40.10), the correlation is made between the received full OFDM symbol and the one reconstructed from the demodulated data (the signal path to @ in the right part of Figure 40.10) [60, 61]. However, the latency in decoding and de‐interleaving may degrade the tracking performance. A simpler method is to use hard data decisions on equalized symbols (the signal path in the dashed line to @ in Figure 40.10). Decision‐directed delay tracking offers two advantages. First, the use of full OFDM symbols in correlation involves more subcarriers, particularly high‐frequency components, which tend to sharpen the correlation peak while lowering the side lobes. Second, it allows for a time‐domain implementation of tracking in addition to the frequency‐domain implementation (the dashed line from the frequency‐domain OFDM symbols) similar to the above‐described pilot‐carriers‐based delay tracking. In the time domain, a joint time and frequency tracking loop can be implemented, operating on the time samples independent of the communications receiver except for data bits.

Sample results of processing in‐the‐air DVB‐T signals are presented below. The correlation functions of various components of an OFDM symbol are shown in Figure 40.11. In Figure 40.11(a), the correlation function for the scattered pilots of an OFDM symbol is shown. Since the scattered pilots are inserted once every 12 carriers, their time‐domain waveform has a periodicity of N_FFT/12, and so does their correlation function. The details of the correlation peak are shown in Figure 40.11(b). As long as the initial STO is less than 1/12th of a symbol duration, there is no ambiguity in determining the peak.

Figure 40.11 Ideal correlation functions for various components of an OFDM symbol.

When the correlation functions of scattered pilots in four consecutive symbols are coherently summed, the resulting function has a periodicity of N_FFT/3 as shown in Figure 40.11(c), which is because the pattern of aggregated scattered pilots has a spacing of three carriers. The correlation peak maintains the same shape, but the unambiguous interval increases by a factor of 4.

The difference between continual pilot carrier indexes is shown in Figure 40.11(d), which exhibits repetition in frequency. The correlation function of continual pilots of an OFDM symbol is shown in Figure 40.11(e), which has the same periodicity as in Figure 40.11(c) but with a raised level of cross‐correlation due to spectral leakage of its irregular subcarrier placement. It is one reason why only scattered pilots are used in correlation tracking for refined TOA estimation.

The correlation function of a full OFDM symbol with all subcarriers is shown in Figure 40.11(f), where the continual and scattered pilots have an amplitude factor of 4/3 while data subcarriers of unity amplitude are drawn randomly from a QPSK constellation of z = (1/)(±1 ± j). The resulting correlation peak is similar to Figure 40.11(b), but the periodic peaks are significantly suppressed (below the fourth sidelobe). The full OFDM correlation can be used for decision‐directed tracking for refined TOA estimation as illustrated in Figure 40.10.

A field test for tracking DVB‐T signals was run in Marseille, France [54]. The spectrum of an ideal DVB‐T signal in the 8K mode is compared to that of sampled signals as shown in the top and bottom plots of Figure 40.12(a), respectively. Within the effective bandwidth of 8 MHz, the null margins used to avoid out‐of‐band emissions and pilot subcarriers with boosted power are clearly visible. The cross‐correlation of the cyclic prefix in the guard interval with that at the end of the symbol useful part, averaged over four OFDM symbols, is shown in Figure 40.12(b), where the correlation peak is located at the 1564th sample (the top plot), and the factional CFO is estimated to be 0.00012 rads/s from the corresponding differential phase (the bottom plot).

After cyclic prefix removal, the FFT is applied to the samples in the useful part. The continual pilot pattern is used to estimate the integer CFO over two consecutive OFDM symbols, while the scattered pilot pattern for each OFDM symbol is detected after CFO correction. Figure 40.12(c) shows the CIR (the blue curve) estimated from an OFDM symbol as a snapshot of multipath acquisition. The threshold (the black dash line) is set as 80% of the total power within the acquisition region to detect possible paths (the red circled line). The first path is declared among all acquired paths according to their rate of occurrence. In this particular case, the paths arriving at 1564.5, 1565.5, and 1566.5 in samples are the three most frequently detected ones with their occurrence probability equal to 1, and the earliest arrival is at the 1564.5th sample. This path is then used to initiate the DLL tracking with the 20 s tracking results shown in Figure 40.12(d). As shown, the 95% accuracy is within 0.95 m with an estimated C/N₀ of 57.97 dB‐Hz.

In general, the carrier phase of OFDM signals is not tracked for at least two reasons. First, the dc component of most baseband OFDM symbols is a null subcarrier to avoid the effect of dc bias at reception. Second, generation and transmission of OFDM symbols are independent from one symbol to the next. As a result, no phase continuity is required to be maintained at any subcarriers. As analyzed earlier, for communications, demodulation of OFDM symbols with cyclic prefix is tolerant to small timing errors and depends on the relative phase at data subcarriers, which can be easily calibrated with the help of pilot subcarriers. However, the OFDM signaling adopted by DVB‐T retains the dc component. Besides, the cyclic prefix duration is specified in such a way that a whole number of cycles is ensured for the middle carrier [44]. It happens in DVB‐T that the middle carrier is assigned as a continual pilot subcarrier, which has a constant value across OFDM symbols. As a result, the baseband center frequency (dc component) has no phase discontinuity, which gives rise to the opportunity for carrier phase tracking. Carrier phase tracking has the potential to provide more accurate timing for ranging and ultimately for positioning than cross‐correlation of cyclic prefix and pilot subcarriers currently used for coarse and fine TOA estimation, respectively. The possibility of carrier phase tracking for DVB‐T signals was recently shown in [62] with in‐the‐air DVB‐T signals collected in experimental tests.