Proximity determination using radio devices

Abstract

A radio system is provided which comprises a radio receiver and a processing system, wherein the radio receiver is configured to detect radio signals transmitted from a radio transmitter on a plurality of frequency channels, and to measure respective signal strengths of the radio signals for each of the plurality of frequency channels. The processing system is configured to evaluate a measure of statistical dispersion of the respective signal strengths over the plurality of frequency channels, and to use the measure of statistical dispersion to determine information relating to a proximity of the radio transmitter to the radio receiver.

Claims

1. A radio system comprising a radio receiver and a processing system, wherein: the radio receiver is configured to detect radio signals transmitted from a radio transmitter on a plurality of frequency channels, and to measure respective signal strengths of the radio signals for each of the plurality of frequency channels; and the processing system is configured: to evaluate a measure of statistical dispersion of the respective signal strengths over the plurality of frequency channels, and to use an average of the respective signal strengths of radio signals in the plurality of frequency channels, in combination with the measure of statistical dispersion to determine information relating to a proximity of the radio transmitter to the radio receiver, said information comprising a separation metric that increases with increasing geometrical distance between the radio transmitter and the radio receiver and decreases monotonically with decreasing statistical dispersion for at least some average signal strengths.

2. The radio system of claim 1, wherein the processing system is configured to apply a weight to the average of the respective signal strengths, when determining the information relating to the proximity of the radio transmitter to the radio receiver, wherein the weight depends on the measure of statistical dispersion.

3. The radio system of claim 1, wherein the processing system is configured to determine a separation metric that decreases monotonically with decreasing statistical dispersion for some or all values of average signal strength, and that decreases monotonically with increasing average signal strength for some or all values of statistical dispersion.

4. The radio system of claim 1, wherein the processing system is configured to evaluate a measure of change in the measure of statistical dispersion, over time, when determining the information relating to the proximity of the radio transmitter to the radio receiver.

5. The radio system of claim 1, wherein the radio receiver is configured to transmit data to or receive data from the radio transmitter in response to the information relating to the proximity of the radio transmitter to the radio receiver satisfying a proximity criterion.

6. The radio system of claim 5, wherein said data relates to a payment.

7. The radio system of claim 5, wherein the radio receiver comprises an antenna that the radio receiver is configured to use both for receiving the aforesaid radio signals on the plurality of frequency channels and for transmitting or receiving said data.

8. The radio system of claim 1, wherein the measure of statistical dispersion is equal to, or representative of, variance or standard deviation or spread.

9. The radio system of claim 1, further comprising at least one sensor which is configured to provide additional sensor data, wherein the radio system is configured to utilise said additional sensor data when generating said information relating to proximity.

10. The radio system of claim 9, wherein the at least one sensor comprises an accelerometer, and the additional sensor data comprises gesture information.

11. The radio system of claim 1, wherein the radio system comprises the radio transmitter.

12. The radio system of claim 1, wherein the processing system comprises a processor and a memory storing software instructions for execution on said processor, wherein the processor is at least partially provided as part of the radio receiver or the radio transmitter or a smart card or a remote server, or is included with the radio receiver in a receiver device, or is included with the radio transmitter in a transmitter device.

13. The radio system of claim 1, wherein: the radio receiver is configured to detect radio signals on a plurality of frequency channels from a plurality of radio transmitters; the radio receiver is configured to measure a respective signal strength of each of the radio signals; and the processing system is configured to evaluate, for each radio transmitter, a measure of statistical dispersion of the respective signal strengths over the respective plurality of frequency channels, and to use the measures of statistical dispersion to identify a closest radio transmitter of the plurality of radio transmitters to the radio receiver.

14. The radio system of claim 1, further comprising a plurality of radio receivers, wherein: each of the radio receivers is configured to detect the radio signals from the radio transmitter; each of the radio receivers is configured to measure respective signal strengths of the radio signals for each of the plurality of frequency channels; and the processing system is configured to evaluate, for each radio receiver, a measure of statistical dispersion of the respective signal strengths over the plurality of frequency channels, and to use the measures of statistical dispersion to identify a closest radio receiver of the plurality of radio receiver to the radio transmitter.

15. A method of controlling a radio system, the method comprising: a radio receiver detecting radio signals transmitted from a radio transmitter on a plurality of frequency channels; measuring respective signal strengths of the radio signals for each of the plurality of frequency channels; and evaluating a measure of statistical dispersion of the respective signal strengths over the plurality of frequency channels, and using the measure of statistical dispersion to generate information relating to a proximity of the radio transmitter to the radio receiver, said information comprising a separation metric that increases with increasing geometrical distance between the radio transmitter and the radio receiver, such that the separation metric decreases monotonically with decreasing statistical dispersion for at least some average signal strengths.

16. The method of claim 15, further comprising: the radio receiver detecting radio signals from a plurality of radio transmitters; measuring a respective signal strength of each of the radio signals; and evaluating, for each radio transmitter, a respective measure of statistical dispersion of the signal strengths over the respective plurality of frequency channels, and using the measures of statistical dispersion to identify a closest radio transmitter of the plurality of radio transmitters to the radio receiver.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Certain preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

(2) FIG. 1 is a schematic drawing of a transmitter and receiver, embodying the invention, in close proximity to each other;

(3) FIG. 2 is a graph of intensities measured by the receiver when positioned as in FIG. 1;

(4) FIG. 3 is a schematic drawing of the transmitter and receiver when they are further apart from each other;

(5) FIG. 4 is a graph of intensities measured by the receiver when positioned as in FIG. 3;

(6) FIG. 5 is a schematic drawing of the transmitter and receiver in close proximity with intervening attenuating material;

(7) FIG. 6 is a graph of intensities measured by the receiver when positioned as in FIG. 5;

(8) FIG. 7 is a schematic drawing of the transmitter and receiver when they are further apart, with intervening attenuating material;

(9) FIG. 8 is a graph of intensities measured by the receiver when positioned as in FIG. 7;

(10) FIG. 9 is a schematic drawing of a second transmitter and receiver, embodying the invention, as part of a proximity-threshold-based payment system;

(11) FIG. 10 is a schematic drawing of the second transmitter and receiver closer together;

(12) FIG. 11 is a schematic drawing of a third transmitter and receiver, embodying the invention, as part of another payment system;

(13) FIG. 12 is a schematic drawing of a fourth embodiment of a transmitter and receiver;

(14) FIG. 13 is a schematic drawing of a fifth embodiment of a transmitter and receiver;

(15) FIG. 14 is a schematic drawing of a sixth embodiment of a transmitter and receiver;

(16) FIGS. 15A-15D are time-aligned plots of—respectively—separation, average RSSI, variance and masked RSSI, in a first hypothetical use case, over time; and

(17) FIGS. 16A-16D are time-aligned plots of—respectively—separation, average RSSI, inverse variance and weighted RSSI, in a first hypothetical use case, over time.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(18) FIG. 1 shows a radio transmitter 2, a radio receiver 10, and a reflective surface 14, such as a wall.

(19) The radio transmitter 2 broadcasts first, second and third radio signals 4, 6, 8 in turn, with equal power, according to the Bluetooth™ Low Energy (BLE)™ protocol. The radio transmitter 2 may be a cell phone or other mobile device. The first, second and third radio signals 4, 6, 8 have carrier frequencies of 2402 MHz, 2426 MHz and 2480 MHz respectively, corresponding to the three advertisement channels according to the BLE™ protocol. The radio transmitter 2 may make these broadcasts at a rate of around thirty transmissions per second (30 Hz) on each frequency.

(20) The radio receiver 10 is positioned at a transmitter-receiver distance 12 from the transmitter 2 and is configured to receive the first, second and third radio signals 4, 6, 8. The reflective surface 14, such as a floor, ceiling, wall, or face of an object such a table, is situated at a distance 16 from the transmitter 2 and receiver 10, the reflector distance 16 being much greater than the transmitter-receiver distance 12. There may, of course, be further reflective surfaces in the environment, which are omitted for the sake of simplicity.

(21) The radio signals 4, 6, 8 are broadcast in all directions from an antenna of the transmitter 2. Certain paths are represented as lines in FIG. 1, but the position and spacing of these lines is for schematic convenience only. The receiver 10 receives not only directly transmitted radio signals 4, 6, 8, but also reflected signals 4′, 6′, 8′ that have been reflected from the reflective surface 14. The paths travelled by the reflected signals 4′, 6′, 8′ and the directly transmitted signals 4, 6, 8 are of different lengths, and as such the two sets of signals interfere.

(22) The receiver 10 therefore, receives signals on three frequency channels, which each comprises a superposition of a directly transmitted signal 4, 6, 8 and at least one reflected signal 4′,6′,8′. In practice, the receiver 10 is likely to receive many reflections off many surfaces in the environment on each channel. The received signals each have an intensity, or strength, which the receiver 10 is configured to measure, to obtain a received signal-strength indication (RSSI) for each frequency channel. These values may be updated continually, at intervals (e.g., thirty times a second for each advertising frequency), as successive signals are received by the receiver 10. Because the signals 4, 6, 8 have different wavelengths, they interfere constructively and/or destructively to differing degrees, based on the lengths of the identical direct and reflected paths travelled by the signals 4, 6, 8.

(23) FIG. 2 is a graph showing illustrative intensities 24, 26, 28 of the first, second and third signals 4, 6, 8, respectively, that might be measured by the receiver 10. The measured intensities 24, 26, 28 have a mean value 20, and a spread 30. Because the reflector distance 16 is much greater than the transmitter-receiver distance 12, the intensities of the reflected signals 4′, 6′, 8′ at the receiver 10 are much smaller than those of the directly transmitted radio signals 4, 6, 8; therefore the resultant interference does not cause large levels of dispersion in the measured intensities 24, 26, 28. The average intensity 20 is relatively high, as the transmitter-receiver distance 12 is relatively small, and the spread 30, indicative of the statistical dispersion across the frequency channels, is relatively small, because of the minor impact of interference from the reflected signals 4′, 6′, 8′.

(24) FIG. 3 depicts the same radio transmitter 2 and radio receiver 10, but spaced apart by a greater transmitter-receiver distance 12, such that the transmitter-receiver distance 12 is comparable to the reflector distance 16.

(25) As before, radio signals 4, 6, 8 are broadcast, in rotation, in all directions from the transmitter 2. The receiver 10 receives both directly transmitted radio signals 4, 6, 8 and reflected signals 4′, 6′, 8′ that have been reflected from the reflective surface 14.

(26) However, in contrast to the situation illustrated in FIG. 1, because the transmitter-receiver distance 12 is comparable to the reflector distance 16, the intensities of the reflected signals 4′, 6′, 8′ are similar to those of the directly transmitted signals 4, 6, 8. The impact of interference intensities as measured by the receiver 10 is therefore much greater than in the scenario illustrated in FIGS. 1 and 2.

(27) FIG. 4 is a graph showing example intensities 24, 26, 28 of the first, second and third signals 4, 6, 8 respectively, as might expect to be measured by the receiver for the scenario shown in FIG. 3. The measured intensities 24, 26, 28 have a mean value 20 that is lower than that in FIG. 2, because the transmitter-receiver distance 12 in FIG. 3 is greater than it was in FIG. 1. As explained above, the impact of interference is greater when the transmitter-receiver distance 12 is comparable to the reflector distance 16, and as such the spread 30 of the measured intensities is greater than that seen in FIG. 2.

(28) A fractional dispersion in the measured intensities 24, 26, 28 may be calculated by dividing the spread 30 by the mean intensity 20. Fractional dispersion may be a more robust indicator of proximity of the receiver 10 to the transmitter 2 than the absolute value of the spread 30, especially, as will be explained below, if attenuating materials are present. Instead of calculating an absolute or scaled spread 30, as a measure of statistical dispersion, the receiver 10 may calculate the variance or standard deviation, or any other appropriate measure of dispersion, from the RSSI values.

(29) The receiver 10 can use the dispersion over the frequency channels 4, 6, 8 to determine how close it is to the transmitter 2, or to determine when it satisfies a proximity condition such as being within a threshold separation distance from the transmitter 2. It will be appreciated that the dispersion measure may be only loosely correlated with the separation distance 12, so an accurate, quantified distance (e.g., in metres) may not always be obtainable. Nevertheless, this approach can provide a useful indication of proximity at much lower cost than a time-of-flight measuring device. The receiver 10 may also make use of the mean signal strength 20, independently of the dispersion, as an input to a proximity-determination algorithm. However, the utility of this value, on its own, may be limited, as explained below.

(30) A calibration operation may optionally be performed using the same apparatus as seen in FIGS. 1 and 3, by varying the transmitter-receiver distance 12 and observing the resulting dispersion across the measured intensities 24, 26, 28 at different distances. A look-up table of dispersions against distances can be generated from these data. The receiver 10 may therefore use a look-up table to enable quantified proximity determination based on the intensities of received signals (although there may be a significant error margin in the measurements).

(31) An advantage of the approach disclosed herein is the reliability of the proximity information determination even when there are attenuating materials present.

(32) FIG. 5 depicts a scenario in which a region of material 22 that significantly attenuates radio energy at frequencies around 2.4 GHz is disposed around the receiver 10. The material 22 could, for example, be the user's hand, gripping around the antenna of a cell phone embodying the receiver 10. This reduces the power of both the directly transmitted signals 4, 6, 8 and the reflected signals 4′, 6′, 8′.

(33) FIG. 6 is a graph showing example measured intensities 24, 26, 28 as might be measured by the receiver 10 for the scenario in FIG. 5. The directly transmitted signals 4, 6, 8 are attenuated by the attenuating material 22 such that their intensity at the receiver 10 is significantly reduced compared to the scenario illustrated in FIG. 1. The reflected signals 4′, 6′, 8′ are similarly attenuated such that the effect of interference is still minor and the statistical dispersion is small. In this particular example, the mean value 20 of the measured intensities 24, 26, 28 is equal to the mean measured intensity 20 for the scenario depicted in FIGS. 3 and 4. This shows why the mean intensity level 20 can be a poor indicator of the transmitter-receiver distance 12 as it cannot distinguish between the scenarios in FIGS. 3 and 5, despite the large difference in transmitter-receiver distance 12. In general, therefore, in an environment with surfaces that are significantly reflective to radio waves, signal intensity alone, on one frequency channel or averaged over multiple channels, correlates poorly with transmitter-receiver separation.

(34) However, by measuring the level of dispersion in the measured intensities 24, 26, 28 (indicated here by the spread 30), it is possible to determine the transmitter-receiver distance 12 much more reliably (i.e., with less error), even when attenuating materials 22 are present.

(35) FIG. 7 shows a scenario in which a region of attenuating material 22 is disposed around the receiver 10, impacting both the directly transmitted signals 4, 6, 8 and the reflected signals 4′, 6′, 8′ for a relatively large transmitter-receiver distance 12, in which the transmitter-receiver distance 12 and the reflector distance 16 are comparable. FIG. 8 is a graph showing example intensities 24, 26, 28 of the first, second and third signals 4, 6, 8 respectively, as might be measured by the receiver 10 for the scenario shown in FIG. 7.

(36) When the transmitter-receiver distance 12 is increased, as in FIG. 7, the spread (shown in FIG. 8) in the measured intensities 24, 25, 26 increases. Because the reflected signals 4′, 6′,8′ and the directly transmitted signals 4, 6, 8 are all similarly attenuated (causing the same fractional decrease in intensity), the fractional dispersion observed is roughly equivalent to that seen in the scenario shown in FIG. 2 (i.e. it is largely unaffected by the presence of the attenuating material 22), and as such provides a robust indicator of the transmitter-receiver distance 12.

(37) One particularly beneficial application of the ideas outlined herein is within the field of payment systems. FIG. 9 illustrates the operation of a proximity-threshold-based payment system using a payment terminal 102 and a mobile payment source device 104. The payment terminal 102 may be static (e.g., mounted on a shop counter), or may be mobile (e.g., carried by a waiter in a restaurant). The payment terminal 102 comprises a receiver and processing system similar to that described above, while the mobile payment source device 104 comprises a transmitter similar to that described above. Of course, the devices 102, 104 preferably also support two-way radio communication.

(38) A user (not shown), wishing to perform a payment, presents the payment source device 104, which is a device-distance 108 away from the payment terminal 102. The user initiates a payment transaction on the device 104 through an appropriate user interface (although this may instead be automatic and require no user input). The payment source device 104 transmits a plurality of radio signals on a plurality of frequency channels, which are detected by the payment terminal 102. The payment terminal 102 analyses the detected radio signals to determine whether the payment source device 104 meets a proximity condition, which in this case corresponds to a maximum separation threshold 106. The analysis performed by the payment terminal 102 comprises measuring signal strengths of the radio signals in each of the plurality of frequency channels, and evaluating a measure of statistical dispersion of the respective signal strengths. As explained earlier, the dispersion of the respective signal strengths can be a relatively-robust measure of the proximity, assuming there are appropriate reflective surfaces in the vicinity of the device 102, 104, which will typically be the case (e.g., the floor or ground will usually significantly reflect radio frequencies). The dispersion is used by the payment terminal 102 to determine whether or not the maximum separation distance 108 is met.

(39) Should the payment terminal 102 determine that proximity condition is met, it performs a data exchange with the payment source device 104 in order to process the payment transaction. The data transferred may comprise, for example, an authentication token. The payment terminal 102 may communicate with a remote system, such a bank server, or may process the transaction locally. In FIG. 9, the device distance 108 exceeds the maximum separation distance 106 and accordingly no such data transfer is performed and the payment is not processed. In FIG. 10, however, the payment source device 104 is within the maximum separation distance 106, for example due to the user having moved the payment source device 104 closer to the payment terminal 102. The payment terminal 102 periodically analyses the detected radio signals, and detects that the payment source device 104 now meets the proximity condition, based on the statistical dispersion across the frequencies dropping below a threshold level, and initiates the processing of the payment.

(40) In some payment scenarios, there may be multiple payment source devices near to a payment terminal device. FIG. 11 illustrates a scenario in which first, second and third payment source devices 204, 206, 208 are located at a plurality of distances from a payment terminal 202. It is desired that only the first payment source device 204, which is closest to the payment terminal 202, processes the payment. This may be, for example, because each of the payment source devices 204, 206, 208 belongs to a different respective shopper, standing in a single line while queuing to pay for their respective purchases in a shop. Only the user at the front of the queue, who is carrying the first payment source device 204 and is nearest the payment terminal 202 (which may be a component of a till) is attempting to pay for their purchases.

(41) The payment terminal 202 receives radio signals in a plurality of frequency channels from each of the payment source devices 204, 206, 208. For reasons explained earlier, because the second and third payment source devices 206, 208 are farther away from the payment terminal than the first payment source device 204, the dispersion seen in the signal strengths of the radio signals received from the second and third payment source devices 206, 208 is expected to be greater than that seen for the first payment source device 204. The payment terminal 202 therefore evaluates a measure of statistical dispersion of the respective signal strengths for each of the payment source devices 204, 206, 208, over the frequency channels. It determines that the first payment source device 204 has the lowest dispersion and infers that it is the closest source device 204 to the payment terminal 202. The payment terminal 202 consequently performs a radio data exchange with the first payment source device 204 in order to facilitate processing of a payment.

(42) FIG. 12 shows a schematic diagram of a transmitter device 302 and a receiver device 304 according to one set of embodiments. The transmitter device 302 comprises a radio transmitter module 306 and a sensor module 307. The receiver device 304 comprises a radio receiver module 308, and a processing module 310. The radio transmitter module 306 and the radio receiver module 308 may comprise suitable radio transmitters and receivers as known in the art, and although not shown, may comprise conventional components such as antennae, amplifiers, and filters. The radio transmitter module 306 and the radio receiver module 308 may be Bluetooth™ or BLE™ radio modules. The processing module 310 may comprise conventional components—for example a CPU, a memory, and one or more inputs and/or outputs. The devices 302, 304 may also include power supplies, such as batteries (not shown), user interfaces, inputs, outputs, etc.

(43) In use, the transmitter device 302 transmits radio signals on a plurality of frequency channels via the radio transmitter module 306. The receiver device 304 detects the radio signals via the radio receiver module 308. The processing module 310 evaluates a measure of statistical dispersion of the respective signal strengths over the plurality of frequency channels and determines information relating to a proximity of the radio transmitter device 302 to the radio receiver device 304. The processing module 310 may use this to determine whether to execute a particular function, such as making a data transfer, or sounding an alarm. The sensor module 307 outputs sensor data, for example the sensor module 307 may comprise an accelerometer that outputs data indicating movement of the transmitter device 302. This sensor data is transmitted to the processing module 310 and may be used when determining whether to execute the particular function. For example, data transfer may only take place if accelerometer data indicates that the transmitter device 302 is stationary/not accelerating.

(44) FIG. 13 shows an alternative set of embodiments of a transmitter device 402, having a radio transmitter module 406 and a sensor module 407, and a receiver device 404, having a radio receiver module 408. In these embodiments, the processing module 410 is a separate device, e.g. a remote server, which is in communication with the receiver device 404. The receiver device 404 may, of course, comprise its own processing logic (not shown).

(45) FIG. 14 shows a further set of embodiments of a transmitter device 502, having a radio transmitter module 506 and a sensor module. 507, and a receiver device 504, having a radio receiver module 508. In these embodiments, the processing module 510 is part of the transmitter device 502 (e.g., in a common housing, or integrated on a common semiconductor substrate).

(46) Any of the architectures shown in FIGS. 12, 13 and 14 may be used in any of the embodiments described herein.

(47) FIGS. 15A-15D show representative graphs (not to scale, and not based on actual data) that illustrate the operation, in a hypothetical scenario, of a radio system embodying the invention, comprising a radio transmitter and a radio receiver (such as those illustrated in FIGS. 9 and 10). The system is arranged to determine if and/or when a separation between transmitter and receiver meets and/or exceeds a predetermined proximity criterion. The system may, for example, comprise a proximity-based payment system made up of a payment device (e.g. comprising the transmitter) and a payment terminal (e.g. comprising the receiver), where a payment is only performed by the payment device and the payment terminal when the separation between the payment device and the payment terminal is determined to have dropped below a threshold value.

(48) The transmitter and receiver are separated by a separation distance, as shown in FIG. 15A. The transmitter and receiver are moved towards each other (e.g. so as to initiate a payment) such that the separation distance decreases over time. At a time t.sub.prox, it drops below a threshold separation S.sub.th.

(49) The transmitter broadcasts a plurality of radio signals on a corresponding plurality of different frequency channels (e.g. on three Bluetooth Low Energy (BLE)™ advertising channels). The receiver receives these signals and monitors (e.g. by sampling repeatedly) the strength of each signal to generate a time series of received signal-strength indications (RSSIs) for each frequency channel. The receiver calculates a time series of average RSSIs (over all three frequencies) which is shown in FIG. 15B. It can be seen that the average RSSI fluctuates (e.g. due to multipath effects and/or a changing orientation of the mobile device), but generally increases over time (as the separation distance decreases).

(50) The receiver also calculates, at intervals, a measure of statistical dispersion of the RSSIs across the frequencies (in this case the variance, although other measures may be used).

(51) FIG. 15c shows how this measure changes over time as the receiver-transmitter separation decreases. The variance fluctuates (e.g. due to differential frequency-dependent multipath effects), but generally decreases over time.

(52) As mentioned above, the average RSSI generally increases as the separation distance decreases. However, the fluctuations in the average RSSI (e.g. due to multipath effects) make it difficult to use this as a reliable indicator of proximity. E.g., in the hypothetical scenario illustrated in FIGS. 15A-D, the average RSSI would pass a threshold value RSSI.sub.th (e.g. predetermined to correspond with a threshold proximity based on typical RSSI behaviour) well before the threshold separation S.sub.th was actually met.

(53) Therefore, in order to more reliably determine when the separation drops below the threshold value, the system applies a mask (i.e. zero weighting) to the average RSSI using the measure of statistical dispersion. Time periods in which the variance exceeds a predetermined threshold value V.sub.th are identified (shown with hatching in FIG. 15D), and a masked RSSI (shown in FIG. 15D) is generated which does sets the RSSI measurements to zero in these identified time periods.

(54) The system determines if the proximity criterion is met by comparing the masked RSSI, at intervals, to the threshold value RSSI.sub.th. FIG. 15D shows that this RSSI.sub.th is reached at t.sub.trigger, which is close to the time, t.sub.prox, at which the separation threshold is actually met. Thus, by masking average RSSI values at times when the variance is above V.sub.th, earlier misleading peaks in the average RSSI are not considered and the system more accurately determines when the proximity criterion is met.

(55) FIGS. 16A-D show another radio system embodying the invention, arranged to determine if and/or when a separation between transmitter and receiver meets and/or exceeds a predetermined proximity criterion (such as a proximity-based payment system).

(56) The transmitter and receiver are separated by a separation distance as shown in FIG. 16A. The transmitter and receiver are moved towards each other (e.g. so as to initiate a payment) such that the separation distance decreases over time. At a time t.sub.prox, it drops below a threshold separation S.sub.th.

(57) As with the system described with reference to FIGS. 15A-D, the transmitter broadcasts a plurality of radio signals in a corresponding plurality of different frequency channels and the receiver receives these signals. The receiver monitors (e.g. by sampling repeatedly) the strength of each signal to generate a time series of received signal-strength indications (RSSIs) for each frequency channel. The receiver calculates a time series of average RSSIs (over all frequencies) which is shown in FIG. 16B. The average RSSI fluctuates, but generally increases over time (as the separation distance decreases).

(58) The receiver also calculates a measure of statistical dispersion of the RSSIs (the variance) at intervals. FIG. 16D shows an inverse of this measure which fluctuates (e.g. due to varying frequency-dependent multipath effects), but generally increases over time as the separation reduces.

(59) The receiver calculates a weighted RSSI, shown with the solid line in FIG. 16D. The “non-weighted” average RSSI is also shown for reference in FIG. 16D with a dot-dash line. The weighted RSSI is the product of the inverse variance (FIG. 16C) and the average RSSI (FIG. 16B). The average RSSI is thus suppressed in time periods of high variance (i.e. when the average RSSI is a poor indicator of separation) and amplified in time periods of low variance (i.e. where the average is a good indicator of separation).

(60) The system determines if the proximity threshold is met by comparing the weighted RSSI to a threshold value RSSI.sub.th (e.g. based on previous weighted RSSI behaviour), shown with a dashed line in FIG. 16D. This is met at time t.sub.prox. It can be seen that combining the average signal strength and the signal strength dispersion to produce the weighted RSSI may enable the system to more accurately determine when the separation threshold is met than using either of these measures independently; it may also, at least in some situations, be a more useful approach than the masking method explained above with reference to FIGS. 15A-D.

(61) It will be appreciated by those skilled in the art that the invention has been illustrated by describing one or more specific embodiments thereof, but is not limited to these embodiments; many variations and modifications are possible, within the scope of the accompanying claims.