GB2536487A - Coherent method for signalling and ranging using unsynchronized digital radio transceivers - Google Patents

Abstract

A method for determining the range between two points comprising transmitting a downlink radio signal from a base station at a first location to a transponder at a second location, transmitting an uplink radio signal from the transponder to the base station in response to receiving the downlink signal and the base station computing the distance between the two locations by measuring the time delay between the transmission of the downlink signal and the reception of the uplink signal. At least one of the signals comprises Hyperbolic Frequency Modulated (HFM) chirps of a known bandwidth whose phase varies as a logarithmic function of time. The base station and transponder each comprise a single reference oscillator for generating the radio signals and digital clock frequencies. The reference oscillators are not synchronised with each other.

Description

description

1.1 Title Coherent method for signalling and ranging using unsynchronized digital radio transceivers.

1.2 Background

The central problem which the present invention addresses is that of determining the distance in meters from a main radio unit (the "base-station") to a subsidiary radio unit (the "transponder"). The transponder is envisaged as a small lightweight battery-powered device which is easily carried around whereas the base-station can be a larger piece of equipment with e.g. multiple antennae for direction finding. Presuming that angle-of-arrival can be found using standard techniques (e.g. the MUSIC algorithm), then range information can usefully locate the transponder on a map using polar coordinates.

An example use-case is tracking and locating assets accurately over a range of several hundred metres to several miles, for example high value goods in transit like cash. This highlights several difficult engineering challenges which are addressed by the present invention.

* The radio physical link is highly asymmetric. It presumes a larger mobile base-station ranging to a smaller battery-powered transponder which has a very limited transmit power.

A single mobile base-station unit is desired, outputting a position estimate, as opposed to the minimum of three receivers required for time-difference-of-arrival trilateration in a plane. The latter technique is also sensitive to poorly conditioned geometry (and thus large error amplification) in real deployment scenarios.

* The transponder preferably exploits software radio techniques which facilitates flexible, high-performance signal processing with low development cost. The penalty is variable latency for the offline processing required by the software. The present invention accounts for this variable latency in the range estimation algorithm.

The system operates as follows. The base-station transmits a signal to the transponder on the "downlink", providing it with a time reference and then the transponder transmits a signal on the "uplink" back to the base-station. The base-station can then determine range by comparing the transmit and receive times of respectively, the downlink and uplink signal. Figure 1 illustrates the strict sequence of operation and Figure 2 expresses the measured quantities and formulae for determining range.

Range accuracy is inversely proportional to the bandwidth of the transmitted signals. Typically, these signals are pseudo-random or chirp sequences with good autocorrelation (pulse compression) properties which deliver a sharp peak in time in the receiver correlators. For instance, a 1MHz bandwidth signal theoretically delivers a correlator peak of (c.'/bandwidth) = 300 metres between the -3dB points where c=speed of light (3x108ms-1). Hence, there is a desire to use large bandwidth signals for measuring range.

As the transponder is battery-powered, has a small form-factor, and may be in a location where transmit radiation is compromised, the uplink signal has very low power. The only way to overcome this is by transmitting a very long signal (e.g. >100ms) on the uplink so that the transmit energy can be integrated at the receiver with sufficient Signal to Noise Ratio (SNR). The optimum method to do this is matched filtering which coherently integrates all of the received signal energy. Non-coherent methods (e.g. differential correlators) rarely have sufficient gain and do not operate typically if SNR«OdB.

The central problem with matched filtering of long sequences is that the transmitted signal must be an exact replica (up to amplitude and phase) of the signal with which it is correlated at the receiver.

However, the base-station and transponder will be driven by quartz crystals which have a residual frequency error (measured in parts per million -ppm). In a modern digital radio transceiver, this error causes a frequency shift and stretching or shrinking of the signal length in time as illustrated in Figure 4. Such a sequence disparity can cause a severe reduction in the coherent processing gain provided by a matched filter to the point where the system does not work.

For mitigation, the base-station can potentially use a 1 PPS GPS input for precise timing, but the transponder could be subject to large temperature variation, battery voltage droop etc. causing short-term unpredictable variations in error of many ppm.

Prior art solutions which impinge on the scenario addressed by the present invention are listed below Hyperbolic frequency modulation of waveforms has been used to render measurements insensitive to errors such as Doppler effects as per Reference 1 and Reference 2 for object detection.

a The transponder enters a frequency and time acquisition loop. Typically, the transponder achieves frequency synchronization by searching for a known frequency tone sent in a periodic beacon from the base-station (e.g. via the FFT algorithm). The error in frequency of the tone gives the transponder frequency correction information and allows it to tune precisely to a channel in order to receive a spread-spectrum timing synchronisation signal. Given this information, it can alter its own processing so that transmit signals are launched at the correct local time and frequency. This process is analogous to the acquisition stages of e.g. a GSM modem. There are two main problems with the process for a low-complexity transponder.

-- Increased complexity / power drain in the transponder requiring tracking loops to track crystal error drift.

--- Vulnerability to narrowband interference during acquisition of the narrowband beacon a Instead of having a strict 'base-station' and 'transponder', it is possible to have two of the same radio units ('A' and 'B') and estimate the round-trip delay with errors from A to B (using the approach in Figure 2) and then the round-trip delay with errors from B to A. The two measurements from the two units can then be combined cancelling the errors. This requires the two units to exchange a data message (to exchange timing information) via a modem every time a ranging measurement is needed. A product using this technology is given in Reference 3. Though this is appropriate in ranging applications where symmetric radios are permitted by the link budget, it does not fit the highly asymmetric scenario addressed by the present invention.

1.3 Statement of invention

The present invention allows high performance ranging and signalling in the presence of significant crystal error between base-station and transponder. It implements full coherent matched filtering in both receivers and therefore maximises receiver SNR.

The central feature of modern digital radio transceivers that is exploited is illustrated in Figure 3 where a single crystal drives both the Radio Frequency (RF) synthesisers and also provides the clock signal to the data converters. Errors in the crystal result in a specific affine transformation A on the Time-Frequency (TF) plane as illustrated in Figure 4. The zero-error TF block is transformed into a modified block by A. On transmit, A provides the transformed TF block of the actual transmit signal. On receive, A provides the actual TF window 'seen' by the receiver.

The present invention uses Hyperbolic Frequency Modulated (HFM) chirps as the primary broadband signal to be transmitted and received. HFM chirps are well known in acoustic and submarine ranging for their immunity to Doppler shifts from a moving target.

An extreme example of an HFM chirp trajectory, for clarity, is illustrated in Figure 5. Crucially, the frequency trajectory of HFM chirps is invariant under transformation A which means one can be transmitted with crystal error X and received with crystal error Y and still be recovered as a coherent correlation peak in the matched filter. The crystal errors, however, are manifest as a shift in time of the correlation peak meaning that, of itself, a single HFM chirp does not provide range. This is illustrated in Figure 5 where a number of A-transformed TF windows can be seen to map precisely on to the chirp trajectory at different time positions. (Note that practical HFM chirps are finite in length and so relative crystal error causes slight discrepancy at the extremities of the transmitted and receive correlator sequences, and hence a slight reduction in correlation quality i.e. peak height).

This unknown crystal error problem is solved by the transponder sending a pair of HFM chirps, one ascending in frequency, the other descending. The base station has two correlators, one for the ascending chirp, the other for the descending chirp. If the crystal errors were zero at both ends of the link, the correlation peaks would be separated in time by a known amount. Given a non-zero crystal error at the transponder, the shift in peak time at the output of correlator 1 (ascending chirp) is the opposite sign to the shift in the peak time at correlator 2 (descending chirp). The difference in the times of the correlator peaks can be converted back to an estimate of the crystal error.

For an improved estimate with full matched filtering of the concatenated chirps, a fine-grained but highly-localised Maximum Likelihood (ML) search (in terms of sample index and a) can recover the extra 3dB going from a single chirp to the concatenated pair. This provides the final correlator peak (for receive timing estimation) and a estimate.

Two technological factors make this feasible * The reducing cost of very large FFTs for performing fast convolution matched filtering (latency is not considered to be a significant constraint in the envisaged asset-tracking application).

* Short term quartz crystal stability (coherence) over periods up to several seconds.

The preferred embodiment of a complete ranging architecture is thus * The base-station transmits an HFM chirp at a pre-scheduled time * Transponder correlates on the downlink HFM chirp transmitted from the base-station in a time window coarsely aligned with the expected signal from the base station.

a Starting from the downlink correlator peak time, the transponder counts precisely M samples according to its crystal before triggering an uplink HFM chirp pair.

* The base-station receives the HFM chirp pair, correlates against both chirps in the pair and estimates tx.mob,",der and the receive time.

* With the estimate of the ti"ansix,"d" the timing errors in the transponder can now be compensated for at the base station and a range estimate is generated from the round-trip time.

In practice, Doppler shift due to relative base-station / transponder velocity causes an unavoidable time-offset error on the downlink chirp correlation in the transponder. This results in a potentially large ranging error at the base-station. The solution for the preferred embodiment is to alternate up and down HFM chirps on the downlink and for the base-station to average out the alternating range bias. This keeps transponder signal processing to a minimum. A perfect solution would be to implement the concatenated chirp pairs used for the uplink on the downlink, but the signal processing overhead is much higher. This is matter is discussed in more detail in section 1.6.7.

A parallel claim is that it is also possible to utilise very long HFM chirps to send data, for instance, using up and down chirps as respectively 0 and 1 symbols. This could be useful in situations where a modem has to operate open-loop with very long sequences to overcome transmit power limitations or severe link attenuation e.g. magnetic communications down oil-wells. The transmitter and receiver are un-synchronized, but the benefit of direct fully coherent signal demodulation is afforded. The spread-spectrum nature of the signal beneficially overcomes problems with narrowband interference.

1.4 Advantages * The system is fully coherent and, particularly, allows the use of long sequences to overcome link budget constraints in the transponder transmitter.

^ The base-station and transponder can be un-synchronized and the clocks can be allowed to drift.

a In terms of receive correlators, one unit is required in the transponder, and two units in the base-station (there is no parallel search in frequency).

^ Transponder clock error is computed as an instantaneous by-product of estimating one round-trip delay. It is an open loop architecture where clock error can vary from frame to frame.

* The transponder functionality is pared back to a bare minimum of (1) correlate a receive sequence (2) estimate the peak timing (3) count M samples and (4) transmit the uplink signal.

This is in tune with minimising processing and maximising battery life.

^ There is no narrowband frequency acquisition stage: this is vulnerable to tonal interference and also makes the base-station readily visible to a malicious eavesdropper with a radio scanner.

* All signals are HFM chirps making the system covert and highly immune to interferers, particularly tones. Optionally, the envisaged FFT processing can zero narrowband interferers during the fast convolution stage of matched filtering.

* An enhancement to FFT matched filtering in the presence of noise and interferers is to employ noise floor estimation for the purpose of pre-whitening the signal before correlation. This approaches the theoretical performance of a Maximum Likelihood detector.

1.5 Introduction to Drawings

Figure 1 -A "ping-pong" sequence diagram annotated with the sequence of events in a single base-station to transponder ranging frame. It is assumed that the transponder has coarsely synchronized with the downlink periodic beacon after a beacon search phase. The operations are thus 1. The base-station initiates a downlink beacon transmission (alternating from frame to frame between mirror-image down and up chirps) and starts a ranging timer.

2. The downlink beacon is transmitted. (This should be a broadband signal and is an HFM chirp in the preferred embodiment for the reasons set out earlier in this document) 3. The downlink beacon propagates through space 4. The transponder (coarsely synchronized to the beacon) pre-emptively opens a receive window where baseband IQ samples are stored in a memory buffer.

5. The downlink beacon is streamed into the memory buffer, including small guard periods before and after.

6. A correlation process determines the time-offset (in the receive window) of the received downlink beacon.

7. After a predetermined period (measured in a fixed number of quartz oscillator clock cycles) from the downlink correlation time-offset, the transponder initiates a response signal on the uplink. This period, the turnaround time Tthinawk,,,e, allows the transponder software to process the correlation.

8. The uplink response is transmitted. (This should be a broadband signal and is an HFM chirp in the preferred embodiment for the reasons set out earlier in this document).

9. The uplink response propagates through space.

10. The base-station pre-emptively opens a receive window where baseband IQ samples are stored in a memory buffer. This occurs at a fixed time-offset after the downlink beacon has been sent, and is dominated by the allowance for TI",,,,ourid.

11. The uplink response is streamed into the memory buffer, including small guard periods before and after.

12. A correlation process determines the time-offset (in the receive window) of the uplink response and stops the ranging timer which records the total ranging time 7 -total. Range can now be estimated from Twial and Tthrnaiou"d.

13. The base-station processes the range estimates resulting from the alternating down and up chirps (across pairs of frames) on the downlink in order to minimise Doppler error as discussed in section 1.6.7.

Figure 2 -A supplementary depiction of one ranging frame comprising transmission of a downlink signal from the base-station, reception and processing by the transponder and transmission of an uplink signal back to the base-station. In particular it shows how range is estimated from Tr",", and laarnaround * Figure 3 -The fundamental logical architecture of a modern digital radio transceiver with a single quartz crystal driving both the RF synthesisers and data converters.

Figure 4 -A view of the Time-Frequency (TF) plane depicting a block of N samples transmitted or received from baseband. Also shown is the affine transformation matrix A due to clock error which modifies the location of the reference TF block.

Figure 5 -An example Hyperbolic Frequency Modulated (HFM) chirp with a number of A-matrix transformed TF blocks (due to crystal error) shown to map back on to the HFM chirp trajectory exactly at different time offsets. The generator parameters aref,=1kHz,/2=2kHz,f=1.5kHz, 7=10 seconds.

Figure 6 -The baseband phase trajectory of the HFM chirp illustrated in Figure 5 showing it to be a very smooth curve (sum of straight line and logarithm function as expressed in Equation 6). This means that HFM chirps are trivially easy to A-matrix transform in phase-domain when performing the final coherent matching (i.e. fine search in a) of concatenated up/down chirps on the uplink at the base-station receiver. The complex baseband signal is then just created by cos(e) and sin(0) lookup tables.

Figure 7 -Comparison of the correlation peak strength of HFM and Linearly Frequency Modulated (LFM) chirps for generator parameters offi=h-500kHz,f2=fc+500kHz,f=750Mhz, T=1 second as a function of transmitter crystal error in ppm. The HFM chirp is seen to have an almost constant strength (with slight roll-off caused by start/stop truncation of the HFM chirp trajectory) while the LFM chirp correlation strength collapses away from Oppm error. Note that the parameters are illustrative of those which a real radio ranging system (subject to emission regulation) may use.

Figure 8 -A comparison of the correlation peak structure for HFM and LFM chirps using the parameters from Figure 6 at a transmit crystal error of +5ppm. Though the LFM chirp has appreciable gain, the sharpness of the peak is highly degraded, smearing out the ranging information. This is because the LFM chirp is no longer coherently matched-filtered. The HFM chirp still has near-optimal pulse compression because it is still coherently matched filtered due to the properties of affine transform A. Figure 9 -DSP dataflow in the transponder showing correlation and peak detection of the downlink signal, and generation of the uplink signal (nominally) 1;",",,,,""d seconds later. The correlator uses a state machine which is synchronized to the envisaged alternation of up and down chirps on the downlink as described in section 1.6.7.

Figure 10 -DSP dataflow in the base-station receiver showing two parallel correlation and peak detection paths for chirp #1 and chirp #2 in the concatenated pair sent on the uplink. These are combined to compute the coarse time offset and clock error of the whole signal. A fine estimate is then generated efficiently by the algorithm proposed in section 1.6.10.

Figure 11 -An example image showing the intensity of chirp (#1,#2) uplink correlations as a function of sample index offset and fine candidate a values in the form of matrix C as discussed in section 1.6.10. This is the final stage of base-station uplink processing in order to recover an optimal estimate of a and correlation timing. Conceptually, the chirp #1 correlation 'crosses over' the opposite-going chirp #2 correlation giving the distinctive X-shaped plot: the meeting point is the optimal solution.

Figure 12 -Illustration of chirp-rate diversity comprising multiple uplink HFM chirp pairs with different lengths. The purpose is to allow some trade-off between robustness to short channel coherence time (favoured by short chirp pairs) and coherent gain (favoured by longer chirp pairs).

1.6 Detailed description

1.6.1 The advantages of chirps for ranging Range accuracy is inversely proportional to the bandwidth of the transmitted signals and thus accurate range means using broadband signals. A highly effective method for generating broadband signals is to sweep a pure carrier frequency between J;, the start frequency, and f,, the end frequency over a defined time window of T seconds. The bandwidth of the signal is roughly (117/2).

The primary advantage is transmitter efficiency; there is no amplitude information and the power amplifier can operate at its optimal operating point. This is very important in the transponder where battery energy is at an absolute premium. The correlation properties of the signal are good and represent a time-resolution which is commensurate with the signal bandwidth.

Therefore we only consider chirp signals in the present invention.

1.6.2 Properties of a single-crystal digital radio transceiver The central feature of modern digital radio transceivers that is exploited is illustrated in Figure 2 where a single crystal drives both the Radio Frequency (RF) synthesisers and also provides the clock signal to the data converters; the Analogue-to-Digital (ADC) and Digital-to-Analogue (DAC) converters. The architecture converts between a channel-filtered baseband digitally-sampled complex signal and a radio frequency analogue signal. (Note that the actual circuitry may be more complex, with IF stages, but the simplified logical architecture is still generally valid). The circuit is parameterised with the nominal data converter sample rate'', and radio carrier frequency_[.

The clock error factor a is defined in Equation 1 as the ratio of the measured crystal frequency and the expected frequency and is also defined in terms of the standard "parts per million" ppm value. The clock error modulates the actual RF frequency and also the sample rate. This modulation can be represented as an affine transformation A on the Time-Frequency (TF) plane as specified in Equation 2.

a = -1 + fmeasured ppm expected Equat Lt;,1 = A [fj where A. [10a 01 Equation 2 1.6.3 Hyperbolic FM chirps definition The following formulae provide the phase 0(r) in radians of a baseband hyperbolic chirp which has the following parameters: z T seconds long * Starts and ends at, respectively, frequencies ji and fj (Hz) * Carrier frequencyfc (Hz) Given a computed from Equation 3 we can generate the required baseband hyperbolic chirp frequency trajectory via Equation 4 which makes it clear that f(t) is a section from a rectangular hyperbola. The phase is then created by integratingOgiving Equation 5; note that the phase due to HFM has a simple logarithmic form.

For the example parameters ji=1000,./2=2000,X=1500,A=1000 and T=10 seconds, we get the frequency trajectory illustrated in Figure 4 and the (baseband) phase trajectory in Figure 5. 1 (fi

a = -T f-1) Equation 3 f f -+ at Equation 4 0(0 = 27 (-alm(1 + at) -fet) Equation The fundamental desired property which is exploited in the present invention is that HFM chirps are invariant under affine transformation A in Equation 2. This means that they can be transmitted and received with respective clock errors utz and a, and still be matched-filtered with optimal pulse compression for range determination.

1.6.4 Comparison of FIRM and LFM chirps for ranging Linearly Frequency Modulated (LFM) chirps are a commonly used broadband signal. They are characterised by a straight-line frequency trajectory between f and]; and consequently a quadratic phase trajectory. One attraction is that they are very simple to generate in analogue and digital circuitry by using integrators / ramp generators. This is why they are commonly used.

However, given the capability of up-converting baseband digital signals using the digital radio architecture in Figure 2, arbitrary sampled waveforms are possible, such as HFM chirps which preserve the constant amplitude property. A clear demonstration of the superiority of HFM chirps compared to (LFM) chirps for ranging with unsynchronized transceivers is given by Figure 6 and Figure 7.

1,6,5 Crystal error becomes time correlation error Given a from Equation 1 and a from Equation 3 (which defines the specific HFM chirp segment from jj, f, and "/), the relative time shift of a transmit/receive window with respect to a perfect chirp (a=0) is given by Equation 6. For illustration, Figure 5 illustrates a number of time-shifted windows corresponding to possible positions of transmit chirps or receive correlation windows on the time-frequency plane. (Note that for clarity, this model is a mathematical abstraction which does not consider fixed receive correlator latency etc.). The time difference between a receive event and a transmit event is therefore given by Equation 7 which shows that the transmitter and receiver can both have crystal error.

twindow = 1/a _ Equati 6 -1 -1 - tx ttxto_rx a Equation 7 1,6,6 Super-resolution peak-finding All timing references are generated by detecting the position of peaks from receiver correlators. These discrete-time signals theoretically satisfy the Nyquist criterion and can be reconstructed back to continuous time to discover the true position of the underlying peak. However, as these signals have a low oversampling factor for efficiency (say in the range of 1 to 2 at best) sophisticated processing is needed to recover the true peak.

There are a number of efficient ways to implement this in DSP * Interpolate the signal peak using a sufficiently long resampling filter to provide a reasonable number of reconstructed samples around the peak value (e.g. x8 oversampled). Then a polynomial fit (usually a quadratic fit) is applied to the highest magnitude sample triplet to estimate the true peak position by solving algebraically for the maximum.

* Apply a successive approximation (binary search) algorithm with dynamically recomputed (sufficiently long e.g. ±32 samples) resampling windows which converges on the true underlying peak position. The search algorithm first tries delays of ±1/4 samples from the highest peak, records the highest position, and then tries delays of ±1/8, ±1/16, ±1/32 etc. until sufficient resolution is reached.

1.63 Doppler effect and compensation on the downlink Based on a linearised model of the downlink HFM frequency trajectory (with "chirp rate" (17/0/2' measured in Hz/s) the range modulation effect (A,. metres excess error) of relative velocity v (ms-1) between transponder and base-station at carrier frequency/ (Hz) is given by Equation 8. Note that a linearised model is sufficiently accurate when the bandwidth (f2ili) is very small with respect to the carrier frequencyf=V2-Fjp/2 as is envisaged for wireless applications.

T of

[J2 -J'1 Equation By alternating up and down HFM chirps (with the same T and alternating values off, and h) from the base-station (such that the transponder can synchronize and predict the alternation), then consecutive values of Arfor the same velocity v (ms') should sum nearly to zero and be effectively cancelled. It is anticipated that this is performed in a higher level of processing within the base-station 1.6.8 Paired up/down hyperbolic chirps to determine transponder crystal error On the envisaged uplink, a consecutive pair of frequency-symmetric HFM chirps of equal length T seconds are envisaged. Chirp #1 goes from f; to fj and chirp #2 goes from J2 to At baseband in the time-domain, chirp #2 is a time-reversed, conjugated version of chirp #1 placed immediately after the latter. From Equation 6, the receive correlation event at t, (seconds) of chirp #1 is given by Equation 9. Likewise the receive correlation event at t, (seconds) of chirp #2 is given by Equation 10, taking into account the time-stretching of the preceding chirp #1 caused by transponder clock error abi. The absolute time difference in the receive correlation peaks:CF,ti is therefore given by Equation 11. Rearranging terms, a", is therefore directly computed from the observed Tthif using Equation 12.

Figure 10 illustrates the DSP needed in the base-station receiver to effect this function. 1 a

Note that ar,(the base-station receive clock error) must be determined via an accurate frequency standard e.g. a GPS 1 PPS calibration input when available: if it is known to a sufficient accuracy, then any residual error will have a negligible impact on range calculation (for illustration, a 1 ppm error equates to -300metres error over a ranging turnaround time of 1 second).

1 t" a _ 1/1a 1 f a t, = r" where al = T - ), f2 tit /ate Varx + T 1 (f2 t2 where a2 = -T f-1-1) a2 a," Equation 10 Ilatx yarx 1/atx _ 1/a T (1 1)1 (1 1) 1 Tdiff = t2 tl = rx T -----az al atx (a2 al atx al az arx Equation 11 1 1 1 1 1 a, = (---+ T) I (Tim' a2 a2) arx) Etinanati 1.6.9 Precise timing control of transponder uplink transmission during turnaround A critical part of the proposed ranging architecture is that the transponder counts exactly M samples between the time-position (in samples) of the downlink correlation peak time reference and before starting the uplink signal. This time reference is real-valued and includes a fractional sample delay recovered by super-resolution peak-finding. The time-reference is rounded to the nearest sample leaving a residual fractional delay in the range (-0.5, +0.5) samples In order to generate a transmit signal which is delayed by an arbitrary fractional amount, two viable techniques emerge which are easily implemented in software and/or digital circuitry: s Store a 'polyphase' table of complex baseband uplink signals as a matrix where numerous rows provide delays ranging between -0.5 and +0.5 samples. The row nearest to the desired delay is transmitted. This technique uses lots of memory and results in rounding error on the delay. However, the economics of modern flash memory may make this technique attractive. Store the transmitted signal as a baseband phase trajectory (as in Figure 6) and generate the fractional delay by two-point linear interpolation. The complex baseband signal to be transmitted is then generated by sin(e) and cos(e) lookups of the interpolated phase. This technique has negligible error and a much smaller memory footprint, but requires two table look-ups per sample. Therefore, it is the preferable technique.

It is crucial that there are no significant errors in this M-sample-counting turnaround period, beyond the unavoidable errors caused by downlink correlation noise and RF variations in the group delay through the analogue transmit chain. It is envisaged that the bulk of RF imperfections can be characterised and calibrated out during manufacturing testing.

Figure 9 illustrates the DSP needed in the transponder to effect this function.

1.6.10 Efficient fine correlation search phase using resampled phase-domain chirp In low-SNR conditions, the a, (transponder transmit clock error) estimate from Equation 12 will have some residual error on it which can be improved by additional processing. The next stage of processing is to access the full correlation of concatenated chirps #1 and #2 in order to get an extra 6dB of gain and thus a 3dB of SNR improvement against noise. This is implemented using a localised two-dimensional grid search by bracketing around the a estimate on the "y" axis and correlator start indices on the "x" axis. This forms a matrix C where rows correspond to different candidate values of CL.

The estimate we already have of ar, gives us an initial start index on the "y" axis. Substituting the at, estimate from Equation 12 into Equation 9 provides an estimate oft,, the time shift in the correlation peak due to at, and an. This gives us a starting point for the search on the "x" axis.

The bracketing of (X values is dependent onA and T. A good range is given by Equation 13 which brackets the correlation between ot values which cause a complete collapse in correlation (caused by the receive sequence 'rotating' completely in the dot-product and hence summing to theoretically zero). By analogy, this is equivalent to covering the mainlobe of the sin(x)/x function in e.g. an FFT bin between first zeros. 1.

asearch range = aesilmate ± 2T Equation For each candidate value of a (row of C), an A-matrix transformed chirp pair must be synthesised. As explained earlier, this is very simple to achieve by linear-interpolation on the chirp phase-domain trajectory, followed by good sin(e) and cos(0) approximations to generate the complex signal (pre-conjugation is necessary for correlation). The columns of C are generated by direct dot products with the receive sample buffer at the different start indices. This processing can exploit parallelism, if possible, as the correlations are all independent.

Final interpretation of the output is to find the row and column coordinates of the biggest peak. This provides the final a estimate and also the correlation timing estimate by super-resolution as discussed in section 1.6.6.

An example C matrix output as an intensity image of correlation magnitude is shown in Figure 9.

1.6.11 Chirp-rate diversity using multiple sequences with different lengths Real-world ranging scenarios with moving transponders mean that the propagation channel suffers from multipath, changing Doppler shifts and Rayleigh/Rice fast-fading with a finite time over which the channel is approximately stationary (the "coherence time"). This time governs the length of sequence which can be coherently matched filtered.

From the single default of one chirp pair as discussed in section 1.6.8, it is logical to consider multiple chirps as illustrated in Figure 10 varying from short pairs to longer pairs i.e. "chirp-rate diversity". The purpose is to trade coherent gain in the matched filters with the coherence time of the channel because it is not feasible to exploit the coherent gain of long sequences when the channel is fast-fading. Short chirp pairs would be optimal at close range (because of reduced transmitted energy) and faster-fading channels (short coherence time). Longer chirp pairs would be optimal at longer ranges (because of increased transmitted energy) and slower-fading channels (long coherence time). The envelope which trades off the increasing lower bound on channel coherence time with increasing range capability is then a product of uplink transmit power which is dictated by the overall system link budget.

Note that on the downlink, the chirp rate is assumed to be much higher because the beacon is much shorter as it has the advantage of being a higher power base-station transmission (i.e. it has more immunity to fast fading channel coherence time). Additionally, the transponder has very limited capability for processing chirp-rate diversity on the downlink. This means that chirp-rate diversity is not considered to be a desirable option for the downlink.

1.6.12 Software mitigation for multipath Multipath in the receiver is manifest as the impulse response of the channel rays convolved with the autocorrelation of the HFM chirp signal (due to transmit and receive HFM chirp filters). It is a critical obstacle for all ranging systems because the desired output comes from the direct path (shortest distance) rather than the longer paths of reflected rays. These reflected rays can often be stronger than the direct path, particularly in dense urban "canyon" environments, leading to erroneous range reports of greater distance than is physically the case (when the highest power ray is selected as the time reference).

To re-iterate, the present invention permits long-sequence spread-spectrum ranging with near-optimal pulse compression in the presence of considerable crystal error (e.g. tens of ppm) at either end of the link. The requirement for long sequences is created by the link budget e.g. a range of several kilometres with low transponder antenna gain and transmit power. A conventional prior-art system would also require similarly long sequences with the extra overhead of needing complex crystal error acquisition and tracking loops.

For mitigating multipath, achieving the desired goal of good pulse compression via the present invention provides tightly defined pulse mainlobes in time for each distinct ray (commensurate with the chosen bandwidth). This property then facilitates parsing of the correlated receive time-series into noise, direct path and reflected ray components using a plug-in channel estimation algorithm. There exist many channel estimation algorithms in the literature, for example, Orthogonal Matching Pursuit (Reference 4) and Sequential Bayesian (Reference 5).

The envisaged mitigation multipath framework therefore comprises * Exploiting some flexibility in the turn-around time in the transponder (T", find) to implement a limited complexity "best-effort" direct-path estimator in software.

* Implementing a higher complexity direct-path estimator in the base-station software using a statistically optimal fusion of the temporal information garnered from matched filtering of chirp-rate diversity on the uplink.

1.6.13 A complete ranging system with downlink and uplink The total time from the transmission of a downlink chirp window from the base-station to the arrival of an uplink chirp #1 aligning with a base-station receive correlation window is given by Equation 14. adi and (71,1 are respectively the HFM constants for the downlink and uplink chirp #1 as specified in Equation 3. abs and a" are the clock error factors, respectively for base-station and transponder. T,"",, is the sum of (1) the HFM time-shift on the downlink, (2) the modified turn-around time caused by transponder clock error, (3) the HFM time-shift on the uplink and (4) the round trip physical signal delay. When all of the terms have been measured and estimated, the range estimate is given by Equation 15.

1/ab5 liatp + Tturnaround abs Ttotal = 1- 1latp babe + -adi atp ath Equation 14 1/ 1 / 1 / abs atp Trurnarouncl /ahs Ttotal

C

1-= 2 adi a1tp Equation 15

A

112009:: Ta:Ae. I -Nanetran NISH 1.7 Referenced documents 1rWa Reference RWRWTNWRMIMT,Wng AWL}.§RifitgiRtiaRti\n}.§K United States Patent 5,017,702, IAA NAM P.-Whyland (Marcell as, NY).

MWAVNT\AMM kIR"M \V; qt,A, t*:**"44411' AVAWA Dec. 31, 199'f US PTO US PTh.

Unite I States%Patent 4,229; K vDe el M. 'in:tiYtiriiddirP1W tlstwr IEEE: Transactions on Communications, vot * 50, no. 3,.,pp,,974,477 March CroSas P. Fehlaa 2009} ovErtag angez-Rubi0 IEEE Journal of Selected Topics In Sig nal ProcessJnq v lie

EEE

no 4 696-706

Claims (31)

1. 2 Claims 1. A method for determining the distance between two points, comprising: transmitting a first radio signal from a first transceiver at a first location to a second transceiver at a second location; transmitting a second radio signal from said second transceiver to said first transceiver; measuring at least one time delay which is indicative of the range between the two said locations; and characterised in that at least one of the said radio signals comprises a portion in which the frequency, when plotted as a function of time, takes the form of a hyperbola, and further characterised in that each of the said transceivers comprises at least one local oscillator relative to which transmitted frequencies are generated and received frequencies selected, and wherein in the local oscillators are not synchronised between the two said transceivers.
2. 2. The method of claim 1 wherein the time delay is one of a) the time taken for the first radio signal to travel from the first location to the second location, or b) the time taken for the second radio signal to travel from the second location to the first location.
3. 3. The method of claim 1 wherein the time delay is the total time taken to complete a process which comprises transmitting the said second signal in response to the said first signal after a predictable processing delay.
4. 4. The method of any previous claim wherein the arrival time of a radio signal is measured by comparing the received signal with a local signal and determining the time at which the received signal correlates most closely with the local signal.
5. 5. The method of claim 4 wherein the noise floor and narrowband peaks are estimated during Fast Fourier Transform correlation processing and are divided out of the spectrum to give narrowband interference suppression and an approximation towards pre-whitened Maximum Likelihood detection.
6. 6. The method of claim 4 or claim 5 wherein a difference in local oscillator frequency between the two said transceivers results in a proportional change in the time at which the received signal correlates most strongly with the local signal.
7. 7. The method of claim 6 further comprising taking the transponder crystal estimate and performing a localised two dimensional grid search in (sample index, transponder crystal error) space in order to find the true maximum correlation of the hyperbolic chirps.
8. 8. The method of any one of the above claims in wherein at least one of the radio signals comprises a series of multiple chirps.
9. 9. The method of claim 8 wherein the series of chirps comprises both chirps where the frequency increases as a function of time and chirps where the frequency reduces as a function of time.
10. 10. The method of claim 9 wherein it is possible to send data from one transceiver to another unsynchronized transceiver using ascending and descending chirps, or groups of chirps, to encode the binary data symbols '0' and '1'.
11. 11. The method of claim 9 where the chirps, or groups of chirps, alternate between increasing frequency and decreasing frequency.
12. 12. The method of any of claim 9 to claim 11 wherein the chirps comprise a plurality of ascending and descending chirp pairs ranging from short duration pairs which can be coherently received in fast channels at close range to longer duration pairs which can be coherently received in slow channels at maximum range.
13. 13. A system for measuring the distance between two points, comprising: a first measurement device comprising a first local oscillator; a second measurement device comprising a second local oscillator; means for transmitting a first radio signal at a frequency relative to said first local oscillator from said first device to said second device; means for transmitting a second radio signal at a frequency relative to said second local oscillator from said second device to said first device; means for measuring at least one time delay relating to the transmission and reception of at least one of said radio signals and which is indicative of the range between the two said locations; and characterised in that at least one of the said radio signals comprises a portion in which the frequency, when plotted as a function of time, takes the form of a hyperbola, and further characterised in that the said local oscillators in the two said measurement devices are not synchronised.
14. 14. The system of claim 13 wherein the time delay is one of a) the time taken for the first radio signal to travel from the first location to the second location, or b) the time taken for the second radio signal to travel from the second location to the first location.
15. 15. The system of claim 13 wherein the time delay is the total time taken to complete a process which comprises transmitting the said second signal in response to the said first signal after a predictable processing delay.
16. 16. The system of any of claims 13 to 15 wherein the same local oscillator which is used for generating the transmitted radio frequency is also used for selecting the radio frequency to be received.
17. 17. The system of claim 16 further comprising a digital signal processor which processes digital representations of those waveforms which are to be transmitted and those which have been received, a digital-to-analogue convertor which converts the digital representation of the waveform to be transmitted into an analogue signal, an analogue-to-digital convertor which converts the analogue received signal into a digital representation, and wherein the sampling rates of said digital-to-analogue and analogue-to-digital convertors are synchronised to the same single local oscillator as used for selecting the transmitted and received radio frequencies.
18. 18. The system of claim 17 wherein the arrival time of a radio signal is measured by comparing the digitised received signal with a local replica signal and determining the time at which the received signal correlates most closely with the local replica signal.
19. 19. The system of claim 18 wherein the replica signal takes the form of a hyperbolic frequency-modulated chirp and wherein this is stored as a series of phase samples and linear interpolation and cos(x) and sin(x) lookup tables are used to generate resampled versions of the signal as a function of hypothesised transponder crystal error.
20. 20. A system for measuring range or distance substantially as described herein and shown in the accompanying figures.Amendments to the claims have been filed as follows: 2 Claims 1. A method for determining range between two points, comprising: a. transmitting a downlink radio signal from a base-station at a first location to a transponder at a second location; b. transmitting an uplink radio signal from said transponder to said base-station in response to receiving said downlink radio signal; c. said base-station computing range by measuring the time delay between transmission of said downlink radio signal and reception of said uplink radio signal; d, and characterised in that at least one of said radio signals comprises Hyperbolic Frequency Modulated (HFM) chirps of specified bandwidth whose phase varies as a logarithmic function of positive or negative time, e. and further characterised in that said base-station and said transponder each comprise a single reference oscillator for generating radio and digital clock frequencies, wherein said reference oscillators are not synchronised.f. and further characterised in that range can be estimated and said downlink and said uplink signals can be transmitted and received effectively in the presence of the non-synchronised said reference oscillators.2. A method according to claim 1 wherein the base-station transmits a downlink radio signal which is partly or wholly a predetermined HFM chirp.3. A method according to claim 1 wherein the base-station simultaneously starts a timer when transmitting the downlink radio signal.4. A method according to claim 1 wherein the transponder correlates the digitized receive signal against the predetermined downlink HFM chirp.5. A method according to claim 4 wherein the correlation generates a discrete time domain waveform with a peak.6. A method according to claim 5 wherein the peak is detected by being greater than a specified threshold and then the time instant of the detected correlation peak is recorded.7. A method according to claim 6 wherein the transponder counts a specified number of reference oscillator cycles starting from the time instant of the detected correlation peak.8. A method according to claim 7 wherein when the timer has counted to the end of its interval, the transponder transmits an uplink radio signal.9. A method according to claim 8 wherein the start timing of the uplink signal is precisely controlled to much greater than single sample accuracy.10. A method according to claim 1 wherein the transmitted uplink signal from the transponder comprises; a. at least one HFM chirp signal whose phase is a logarithmic function of positive time, (the clown-chirp(s)') b. at least one HFM chirp signal whose phase is a logarithmic function of negative time, (the up-chirp(s)') 11. A method according to claim 10 wherein the up-chirps and down-chirps can have a variety of chirp rates and lengths within the specified bandwidth in order to trade-off range with immunity to a time-varying multipath propagation 12. A method according to any preceding claim wherein the relative error between base-station and transponder reference oscillators (the quantity denoted as a) causes a predictable time shift in the correlation peak of the I-1FM chirp signals.13. A method according to claim 10 wherein the base-station separately correlates the digitized receive signal against all predetermined uplink down-chirp(s) and up-chirp(s).14. A method according to claim 13 wherein the correlation peaks are detected by being greater than a specified threshold and the time instants of the detected correlation peaks are recorded.15. A method according to any previous claims wherein the time differences between the detected correlation peak time instants of the up-chirp(s) and down-chirp(s) is converted into a coarse estimate of a.16. A method according to claim 15 wherein timing information from the up-chirp(s) and downchirp(s) correlation and coarse estimate of a is used to correlate the complete uplink signal against a restricted range of time offsets and replica uplink signals in that the energy of the whole uplink signal is integrated.17. A method according to claim 16 wherein the range of replica uplink signals is centred on the coarse estimate of a.CD 18. A method according to claim 16 or 17 wherein the replica uplink signals are transformed from the predetermined up-chirp(s) and down-chirp(s) to represent those resulting from candidate values of a.19. A method according to claim 18 wherein the transformed replica uplink signals are effected by linear operations in phase-domain prior to generation of time-domain waveforms 20. A method according to claim 16 wherein the strongest peak is detected by having a magnitude greater than a specified threshold and the time instant of the detected correlation peak is recorded.
21. 21. A method according to claim 6, 14 or 20, wherein the time instant in sample clock cycles of the detected peak(s) is measured to greater than single sample accuracy by interpolation or super-resolution techniques.
22. 22. A method according to claim 20 wherein the time instant stops the base-station timer
23. 23. A method according to claim 16 wherein the detected peak determines the strongest correlating uplink signal replica and hence the value of the fine estimate of a.
24. 24. A method according to claim 23 wherein the fine estimate of a is converted into an estimate of the transponder downlink correlation time error and the transponder timer counter error which are both contingent on the real value of a.
25. 25. A method according to claim 24 wherein the base-station subtracts the estimates of the transponder downlink correlation time error and the transponder timer counter error from the final base-station timer value in order to estimate range based exclusively on the round trip flight time of the downlink and uplink radio signals.
26. 26. An apparatus adapted to carry out a method according to any preceding claim.
27. 27. An apparatus for determining range between two points, comprising: a. means for transmitting a downlink radio signal from a base-station at a first location to a transponder at a second location; b. means for transmitting an uplink radio signal from said transponder to said base-station in response to receiving said downlink radio signal; c. means for said base-station to compute range by measuring the time delay between transmission of said downlink radio signal and reception of said uplink radio signal; d. means for generating one or more radio frequency HFM chirps of specified bandwidth whose phase varies as a logarithmic function of positive or negative time, e. means for deploying a single reference oscillator for generating radio and digital clock frequencies, wherein said reference oscillators are not synchronised.
28. 28. An apparatus according to claim 27 wherein the base-station and transponder are radios.
29. 29. An apparatus according to claim 28 wherein the radio is a software-defined radio.
30. 30. A method substantially as described herein and/or illustrated with reference to the accompanying drawings.CD
31. 31. An apparatus substantially as described herein and/or illustrated with reference to the accompanying drawings.