BACKGROUND OF THE INVENTION

This invention relates to a coding scheme for transmitting and/or receiving signals. Some examples of possible uses include pulsed radar applications such as ultra- wideband radar. Other uses include ultrasound imaging and also transmission of data between a transmitter and a receiver (which may be via electromagnetic waves or ultrasound).

Transmitted pulses can be restricted in power for various reasons. For example, transmitters implemented in CMOS can have limited output power levels due to limited operating voltages (around 1 volt), or in some applications such as ultra wide band transmissions, there are enforced limits on instantaneous output power. One way to improve the transmitted power (and therefore facilitate reception of the signal) is to transmit a stream or burst of pulses one after the other. A disadvantage of this in monostatic systems where the receiver and transmitter share a transmission/reception interface (such as an antenna or transducer) is that the receiver generally cannot receive until the transmitter has finished transmitting. Therefore a longer burst of pulses interferes with short range operation.

SUMMARY OF THE INVENTION

From a first aspect, the invention provides a method of transmitting a signal, the method comprising: transmitting a series of pulse bursts, wherein the series of pulse bursts comprises a plurality of pulse bursts, wherein each of the plurality of pulse bursts comprises at least a first pulse and a second pulse; wherein the series of first pulses comprises a first sequence, the first sequence having low off-peak periodic autocorrelation values in a region surrounding the peak value; and wherein the series of second pulses comprises a second sequence, the second sequence being a circular shift of the first sequence. According to a second aspect, this invention provides a transmitter configured to: transmit a series of pulse bursts, wherein the series of pulse bursts comprises a plurality of pulse bursts, wherein each of the plurality of pulse bursts comprises at least a first pulse and a second pulse; wherein the series of first pulses comprise a first sequence, the first sequence having low off-peak periodic autocorrelation values in a region surrounding the peak value; and wherein the series of second pulses comprise a second sequence, the second sequence being a circular shift of the first sequence.

Transmitting bursts of pulses provides increased average power transmission when compared to transmitting individual pulses. In other words, by transmitting two or more pulses per burst, the total transmitted energy is increased. As the transmitted series of first pulses and the transmitted series of second pulses both comprise a sequence having periodic autocorrelation values that are low in a region surrounding the peak value, and the second sequence is a circular shift of the first sequence, cross-correlation of the transmitted series of pulse bursts at an appropriately configured receiver may be performed more effectively than in existing approaches. This is because when the cross-correlation is performed in the receiver, the desired result for detection purposes is the peak correlation value that is obtained when the transmitted signal and receiver template align perfectly. When the signal and template do not align, the output should ideally be zero. However, many sequences have other non-zero values in their autocorrelation which generate unwanted noise in the receiver output when the transmitted signal and the receiver template overlap partially. These non-zero values can be difficult to distinguish from a genuine transmitted signal from greater range or a weaker source and hence they create ambiguity in the receiver. For example, in the case of radar, a strong receive pulse followed by a weaker receive pulse could either be the result of the autocorrelation (which would ideally be ignored or discarded) or it could be the result of two separate reflectors (which should ideally be detected and output). Therefore minimising the off-peak autocorrelation values reduces range ambiguity. The first and second aspects of the invention use a sequence which has low off-peak values in its periodic autocorrelation. Whereas the standard autocorrelation process correlates the signal with itself under various delays, the periodic autocorrelation process correlates the signal with itself under various rotations (circular shifts). The use of a sequence which has low off-peak periodic autocorrelation values, together with a second sequence that is a rotation (circular shift) of the first sequence has the advantage that the first sequence will not correlate strongly with the second sequence in the receiver. This allows transmission of multiple pulses in each burst, thereby increasing the transmitted energy, while avoiding unwanted correlation artefacts from the interaction of those multiple pulses.

Ideally the off-peak values will be low across the whole of the periodic autocorrelation, i.e. for every non-zero circular shift. However, in many applications it may be sufficient to have low off-peak values just in a region around the peak value, i.e. some larger off-peak values may be tolerated if they only appear at circular shifts far from the peak value. The size of the region around the peak value that has low periodic autocorrelation values should be wide enough for the required unambiguous region. The unambiguous region depends on the circular shift between the first sequence and the second sequence (or in the case where further sequences, e.g. third, fourth, etc. sequences are used, the maximum shift among all of them), so the low off-peak values in the periodic autocorrelation are only required within the length of that maximum circular shift. Thus in some embodiments the region surrounding the peak value extends at least as far from the peak as the amount of circular shift between the first sequence and the second sequence. In some embodiments the region surrounding the peak covers at least a quarter, at least a third or at least a half of the length of the periodic autocorrelation values.

In some embodiments, the first sequence has near-perfect periodic autocorrelation. A perfect periodic autocorrelation refers to a sequence where the off-peak autocorrelation values are all zero, i.e. only the zero-shift autocorrelation value is non-zero. Near-perfect periodic autocorrelation refers to sequences which do not quite achieve the perfect condition, but which have low-enough off-peak periodic autocorrelation values that those values do not introduce receiver ambiguity. In such embodiments, the off-peak values of a periodic autocorrelation of the first sequence (corresponding to non-zero circular shifts) are significantly lower than the peak value (corresponding to zero circular shift). For example, the off-peak periodic autocorrelation values of the first sequence may be less than a fifth, a tenth, a twentieth, a fiftieth or a hundredth of the peak value. In some such examples, the first sequence may be a binary maximum length sequence, also known as an m- sequence. In examples where the first sequence is an m-sequence, the periodic autocorrelation of the first sequence is two-valued. The peak value (corresponding to zero shift) equals the length of the sequence (for a bipolar m-sequence of values 1 and -1), and the off-peak values (corresponding to non-zero shifts) are equal to -1 Alternatively, the sequence peak value may be represented as having a peak value of 1 , and off-peak values of -1/N. Accordingly, in some embodiments the off-peak autocorrelation values of the first sequence may be no more than the peak value divided by the sequence length.

The tolerable magnitude of the low values in the periodic autocorrelation will depend on the particular system design and what may be considered to be an ambiguous signal. In the case of perfect periodic autocorrelation, the off-peak values are zero which is ideal. However, this may not be necessary in some implementations. Therefore in some examples the low off-peak values (i.e. those in the region surrounding the peak value) have a periodic autocorrelation value with magnitude no greater than the minimum non-zero value (which in the case of a binary sequence may be one, but in the case of higher order sequences may be more than one). In some embodiments, the value may be up to twice the minimum non-zero value.

In some embodiments the first sequence has perfect periodic autocorrelation. In such embodiments, the off peak values of the periodic autocorrelation (i.e. the output of a correlation of the first sequence with any non-zero circular shift of the first sequence) are equal to zero, while the peak value (correlation of the first sequence with itself) results in a non-zero output value. In some embodiments, the first sequence may be an Ipatov sequence. In some such embodiments, the first sequence may be an Ipatov sequence of length 7, 13, 21 , 31, 57, 63, 73, 91, 127, 133, 183, 273, 307, 381 , 511 , 553, 651 , 757, 871 , 993, 1057, 1407, or 1723. Ipatov sequences have perfect periodic autocorrelation. In some embodiments, the first sequence may be a sequence of binary values, e.g. the first sequence may be made up of T or ‘0’ values (unipolar) or ‘-T and T values (bipolar). In such embodiments, the amplitude of each of the series of first pulses may be set based on one of the binary values in the sequence. For example, where the sequence has a positive or T value, the corresponding first pulse may be a signal with positive amplitude, while where the sequence has a negative or ‘-T value, the corresponding first pulse may be a signal with negative amplitude (e.g. with inverted polarity).

In some embodiments, the first sequence may be a sequence of ternary values, e.g. the first sequence may be made up of positive (+1), negative (-1) or zero amplitude (0) values. In such embodiments, the amplitude of each of the series of first pulses may be set based on one of the ternary values in the sequence. For example, where the sequence has a positive or T value, the corresponding first pulse may be a signal with positive amplitude. Where the sequence has a zero value, the corresponding first pulse may be a signal with zero amplitude. Where the sequence has a negative value, the corresponding first pulse may be a signal with negative amplitude (e.g. inverted polarity). In some embodiments higher order code types (e.g. quaternary, etc.) may also be used.

In some embodiments, the first and second pulse of each pulse burst are sent at different times, such that there is a delay between the first and second pulses. For example, the second pulse of each pulse burst may be transmitted after the corresponding first pulse of that pulse burst. Each of the plurality of pulse bursts may also comprise one or more further pulses, each sent at a different time to the first and second pulses. There may therefore be a delay between each of the pulses of a pulse burst. The delay between each pulse of a burst may be the same between each successive pulse. In other embodiments the first and second pulse of each pulse burst may be transmitted by different transmitters. In such cases, the first and second pulse of each pulse burst may be transmitted simultaneously, thus achieving the higher energy transmission while not extending the total burst transmission time. The receiver may then apply two (or more) separate correlation templates to the receive signal, i.e. one for the signal of each transmitter. The pulse bursts of the series of pulse bursts may be separated in time by a delay. In some embodiments therefore transmitting the series of pulse bursts comprises transmitting the plurality of pulse bursts at predetermined intervals. The delay between each of the pulse bursts may be the same between each successive pulse burst. The interval between pulse bursts may be referred to as a burst repetition interval. The delay between pulse bursts may be predetermined. The delay between pulse bursts may be selected such that the pulse bursts are transmitted at predetermined intervals.

The delay between pulse bursts may be significantly longer (e.g. ten, twenty, thirty, fifty or one hundred times longer) than the delay between each pulse of a burst. In some embodiments the delay between each successive pulse of a burst may be of the order of a nanosecond, e.g. two, three or five nanoseconds, and the delay between each successive burst may be of the order of tens of nanoseconds, e.g. at least ten, twenty, fifty, sixty or one hundred nanoseconds. Thus in some embodiments, the duration of the predetermined intervals at which the plurality of pulse bursts is transmitted is greater than the predetermined delay time between individual pulses of a burst.

In some embodiments, the series of bursts may comprise one or more padding bursts before the bursts that form the first and second sequences. In some embodiments, the series of bursts may comprise one or more padding bursts after the bursts that form the first and second sequences. In some embodiments, padding signals may be transmitted both before and after the bursts that form the first and second sequences. Although the pulses of the padding bursts are not themselves part of the first and second sequences, they are preferably repetitions of the first and second sequences such that a sequence of bursts spanning part of the first sequence and part of the padding and encompassing a number of bursts equal to the length of the first sequence will form a circular shifted form of the first sequence and a circular shifted form of the second sequence. The purpose of the padding bursts is so that when a receiver has a correlation template matching the first sequence and second sequence (and any further sequences if present), the receive signal at the receiver (including the padding bursts) will not produce a correlation output while the first and second sequences are in partial overlap with the template and within the valid receive window. This is because any pulses matched against the template during such conditions will form a circularly shifted form of the first and second sequences in the template and will therefore produce only a low value (or no value) in the correlation output.

In some embodiments, the circular shift of the second sequence relative to the first sequence may be selected so as to define a non-ambiguous range of the transmitted signal. A greater shift will result in a greater non-ambiguous range. In cases where each burst comprises more than two pulses, (i.e. where third, fourth, etc. pulses are added, forming corresponding third, fourth, etc. sequences), each sequence is circularly shifted from the first sequence by a different amount. Each sequence is thus a circularly shifted form of each other sequence and may have a certain circular shift from each other sequence. In such cases, the minimum circular shift between any two sequences defines the non-ambiguous range. In such embodiments the number of padding bursts before the sequences is preferably equal to one less than that minimum circular shift so as to ensure that the non-ambiguous range experiences the best correlation properties arising from the low off-peak periodic autocorrelation values. In other words, the padding before the sequences determines how far away distant signals can be cancelled effectively in earlier burst repetition intervals. Ideally this covers the whole of the unambiguous range as defined by the circular shifts. Padding after the sequences determines how far away you can look for targets without getting ambiguities from closer targets. The amount of padding before may equal the amount of padding after, but this need not necessarily be the case.

The non-ambiguous range may be considered as a range (or correspondingly a time period after transmission) in which the transmitted signal may be uniquely identifiable, i.e. received signal within the non-ambiguous range can be assumed to have come from the source rather than from interference or correlation artefacts.

As noted above, the invention is not limited to bursts that contain only a first pulse and a second pulse. In some embodiments, each of the plurality of pulse bursts may further comprises a third pulse, wherein the series of third pulses comprises a third sequence, the third sequence being a circular shift of the first sequence and the second sequence. In this way, the plurality of pulse bursts can be used to transmit three sequences, each of which is a circular shift of a common sequence (i.e. the first sequence). As the first sequence has low off-peak periodic autocorrelation values in a region surrounding the peak value, the first, second and third sequences will have low correlation with each other providing that the circular shift between them is within the region surrounding the peak value. In the case of sequences with perfect periodic autocorrelation, the various sequences may be entirely mutually orthogonal. It will be appreciated that these principles may equally be applied to further pulses beyond a third pulse. In some embodiments, the plurality of pulse bursts further comprises one or more further pulses, wherein each series of further pulses comprises a respective further sequence, and wherein each respective further sequence is a circular shift of each other sequence of pulses of the plurality of pulse bursts. The plurality of pulse bursts can be used to transmit any number of sequences, each of which is a circular shift of a common sequence (i.e. the first sequence).

The transmitter may operate in any suitable medium. For example it may be an electromagnetic transmitter (e.g. an RF transmitter such as an ultra-wideband (UWB) transmitter) or it may be a sound transmitter such as an ultrasound transmitter. Thus the first and second pulse may be in some embodiments be electromagnetic pulses or in other embodiments may be acoustic pulses. In some embodiments, the first pulse and second pulse are radio-frequency (RF) pulses. In some embodiments, the first pulse and second pulse may be ultra-wideband (UWB) pulses. In some embodiments, the first pulse and second pulse may be LIDAR (light detection and ranging) pulses. In some alternative embodiments, the first pulse and second pulse may be ultrasound pulses.

According to a third aspect, the invention provides a method of receiving a signal, the method comprising: receiving a receive signal, forming a template, and cross-correlating the receive signal with the template; wherein the template comprises a series of element groups, wherein the series of element groups comprises a plurality of element groups, wherein each of the plurality of element groups comprises at least a first element and a second element; wherein the series of first elements comprises a first sequence; wherein the series of second elements comprises a second sequence; wherein the first sequence has low off-peak periodic autocorrelation values in a region surrounding a peak value, and the second sequence is a circular shift of the first sequence.

According to a fourth aspect, this invention provides a receiver configured to: receive a receive signal, form a template, and cross-correlate the receive signal with the template; wherein the template comprises a series of element groups, wherein the series of element groups comprises a plurality of element groups, wherein each of the plurality of element groups comprises at least a first element and a second element; wherein the series of first elements comprises a first sequence; wherein the series of second elements comprises a second sequence; and wherein the first sequences has low off-peak periodic autocorrelation values in a region surrounding a peak value, and the second sequence is a circular shift of the first sequence.

It will be appreciated that the receiver and method of the third and fourth aspects are related to the transmitter and method of the first and second aspects and are preferably designed to operate together. Thus the advantages and preferred or optional features described above in relation to the transmitter and method apply equally to the receiver and method.

Accordingly, in some embodiments, the first sequence has near-perfect periodic autocorrelation. The off-peak autocorrelation values of the first sequence may be less than a fifth, a tenth, a twentieth, a fiftieth or a hundredth of the peak value. The first sequence may be a binary maximum length sequence, also known as an m- sequence. In some examples the low off-peak values (i.e. those in the region surrounding the peak value) have a periodic autocorrelation value with magnitude no greater than the minimum non-zero value. In some embodiments the first sequence has perfect periodic autocorrelation. The first sequence may be an Ipatov sequence. The Ipatov sequence may have a length of 7, 13, 21, 31 , 57, 63, 73, 91 , 127, 133, 183, 273, 307, 381, 511, 553, 651, 757, 871 , 993, 1057, 1407, or 1723.

The first sequence may be a sequence of binary values. The first sequence may be a sequence of ternary values.

In some embodiments, the method may comprise identifying one or more objects in an environment based on the cross-correlated receive signal. As the first sequence has low off-peak periodic autocorrelation values in a region surrounding the peak value and the second sequence is a circular shift of the first sequence, the crosscorrelated receive signal may be used to unambiguously determine the distance of identified objects from the receiver. When the receive signal is cross-correlated against the stored template in the receiver, the correlator output will be high when the receive signal aligns with the template, i.e. when all pulses of all sequences align with the template. Either side (in time) of this peak output, there will be times when the second sequence in the receive signal aligns with the first sequence in the template and when the first sequence in the receive signal aligns with the second sequence in the template. However, due to the low off-peak autocorrelation values, these correlations will be relatively small compared to the peak correlator output. In the case of perfect periodic autocorrelation sequences, there will be zero correlator output. A threshold may be used to distinguish between the high correlator output from the low correlator output. Thus, in some embodiments, identifying one or more objects comprises identifying elements in the crosscorrelated receive signal for which the magnitude of the cross-correlated receive signal is greater than a threshold value.

In some embodiments, one or more elements of the cross-correlated receive signal may be modulated based on the time at which the signal was received. This may serve to account for times at which the signal could not be fully received, e.g., in embodiments in which the method is implemented using a half-duplex device. While such a device is transmitting, it may be unable to receive some or all of the receive signal. If only part of a receive signal is received, the cross-correlated receive signal may be modulated (e.g. a gain may be applied) to compensate for the lost part of the signal.

In some embodiments, the series of groups may further comprise one or more padding element groups. In some embodiments, one or more padding element groups may be positioned in the template before the element groups that comprise the first and second sequences. In some embodiments, one or more padding element groups may be positioned in the template after the element groups that comprise the first and second sequences. In some embodiments, one or more padding element groups may be positioned both before and after the element groups that comprise the first and second sequences.

In some embodiments, the circular shift of the second sequence relative to the first sequence may be selected so as to define a non-ambiguous range of the receive signal.

In some embodiments, each of the plurality of element groups may further comprise a third element, wherein the series of third elements comprises a third sequence, the third sequence being a circular shift of the first sequence and the second sequence. In some embodiments, the plurality of element groups further comprises one or more further elements, wherein each series of elements comprises a respective further sequence, and wherein each respective further sequence is a circular shift of each other sequence of elements of the plurality of element groups. In some embodiments, the transmitter and receiver of the present invention may be combined, e.g. to form a transceiver. In some embodiments, the transmitter and the receiver may use a common (e.g. shared) transmission interface (e.g. antenna or transducer) to transmit and receive signals.

Features of any aspect or embodiment described herein may, wherever appropriate, be applied to any other aspect or embodiment described herein. Where reference is made to different embodiments or sets of embodiments, it should be understood that these are not necessarily distinct but may overlap.

BRIEF DESCRIPTION OF THE DRAWINGS Certain preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

Fig. 1 is a schematic representation of a radar system 100 in accordance with embodiments of the present invention;

Figs. 2a and 2b schematically illustrate radar transmission schemes according to the prior art; and

Fig. 3 schematically illustrates a coded transmission scheme;

Fig. 4 shows a radio transmission scheme in accordance with embodiments of the present invention;

Fig. 5 shows a series of pulse burst radar signals transmitted in accordance with the embodiments of the present invention;

Fig 6a illustrates the output of a cross-correlation of reflections of a signal transmitted in accordance with the embodiments of the present invention; Fig. 6b shows the cross-correlation of Fig. 6a in a wider time context; and Fig. 7 shows an example of the form of transmitted signals employed in a system according to embodiments of the present invention.

DETAILED DESCRIPTION

Figure 1 shows a radar system 100 comprising transceiver circuitry 101 for transmitting and receiving RF signals (such as ultra-wideband radar signals) using an antenna 102, and a battery 103 for supplying power to the pulsed radar system 100. The pulsed radar system 100 also includes a controller 104 for sampling and processing received RF signals, and a memory 105 (which may include volatile and/or non-volatile memory) for storing data and/or for storing software instructions to be executed by the controller 104. The radar system 100 may have further standard electronic components such as further RF transceivers (or separate transmitters and/or receivers) or antennae, amplifiers, filters, analogue to digital convertors, input/output peripherals etc.

The radar system 100 is arranged to identify objects in an environment, such as objects 110 and 120 shown in Figure 1, using a transmitted signal in the form of a pulse 106 (e.g. an RF or UWB pulse). The transmitted pulse 106 is reflected by the objects 110, 120, causing reflected signals 111 , 121 to be received at the antenna 102. By analysing the reflected signals 111 , 121 , the presence of objects 110 and 120 in the environment can be identified, and their respective distances, Duo, D120 from the radar system 100 can be determined, e.g. based on the time at which the reflected signals 111 , 121 are received at the antenna 102.

It will be appreciated that Figure 1 is equally illustrative of an ultrasound system where 102 represents an ultrasound transducer transmitting ultrasonic pulses 106 and receiving echoes 111 , 121. The environment for such transmissions may be internal to the body, or it may be external to the body (e.g. for in-air distance measurements).

An example of the operation of a typical radar system 100 is illustrated in Figure 2a, which shows a timing diagram for transmission and reception of pulses according to the prior art. Figure 2a shows a series of transmitted pulses 201a and two series of reflected pulses 202a, 203a, associated with first and second objects at first and second distances respectively from the source of the transmitted pulses 201a, where the second distance is greater than the first distance. Each horizontal line in Figure 2a represents a timeline with time increasing from left to right. Different lines represent different stretches of time, with lower lines being later in time than the lines above. Thus a full timeline may be created by appending the top line, middle line and bottom line in that order.

In the example shown in Figure 2a, the transmitted pulses 201 are separated by a repetition interval (Rl) such that each pulse 201a has an associated repetition interval 211a-213a, such that there is a delay between the transmission of successive pulses. As monostatic or pseudo-monostatic radar systems typically operate in a half-duplex mode and hence are unable to transmit and receive simultaneously, the use of repetition intervals allows time for transmitted pulses to be reflected from objects within a predetermined range of interest before the following pulse is transmitted. In the example shown in Figure 2a, following the transmission of a given pulse, further pulse transmissions are delayed by a time AtRi in order to listen for reflected signals, i.e. the signals 202a, 203a from objects in the range of interest. The duration of the repetition interval therefore sets the range that can be probed by the transmitted pulses 201a. In Figures 2a, 2b, 3 and 4, transmitted pulses are indicated by squares with a solid outline and received pulses are indicated by squares with a dashed outline. As shown in Figure 2a, after a pulse is transmitted, an echo of the pulse is received after reflection from the first, closer, object after a first time AtEi, and after reflection from the second, more distant object after a second time AtE2. Based on the time at which the reflected pulses from the first and second objects are received relative to the time at which they are transmitted, the distance to each of the first and second objects can be identified.

As the echo signals can be very faint and difficult to detect, the accuracy of the system obtained using the transmission scheme shown in Figure 2a can be increased by transmitting and receiving a greater number of pulses and processing the accumulated data, or by increasing the amount of power transmitted in each pulse. Received power can be accumulated over time by repeating the process with one pulse per repetition interval. If this is done fast enough (in relation to the moving speeds of the objects) a significant power can be obtained. However, this does involve a significantly increased measurement time.

Increasing the amount of power transmitted in each pulse may also pose difficulties in implementation, particularly in the case of system on-chip radar systems or those implemented in complementary metal oxide semiconductor (CMOS) systems, in which low operating voltages (e.g. around 1 Volt) limit the power output. Simply increasing the amplitude of each pulse in such systems is unlikely to be feasible. However, an increase in average transmitted power may be achieved by transmitting multiple pulses in a single “burst” comprising e.g. three individual pulses in quick succession before listening for reflected signals. A plurality of bursts may be sent in successive “burst repetition intervals” (BRI), analogous to the repetition intervals of the single pulses of the scheme shown in Figure 2a. For the purposes of the present disclosure, a burst repetition interval may be defined as a period of time between the starts of two successive bursts.

In the “burst” mode of operation shown in Figure 2b, multiple RF pulses are sent in quick succession, i.e. in a time period much shorter than the burst repetition interval such that these pulses form a group. After all of the RF pulses of a burst have been sent, the radar system listens for reflections of the RF bursts (i.e. of the sequence of pulses), and analyses the reflected pulses to detect more accurately the first and second objects.

Transmitting a plurality of pulses in a burst before performing detection improves the accuracy of measurements of distant objects by increasing the transmitted power in each burst repetition interval. Very close objects (e.g. those for which one or more reflected pulses arrive at the receiver before the entire burst has completed transmitting) may be at least partially masked and may therefore not benefit from the increased power transmission to the same extent. However, as such objects are close, their reflections will generally be measurable with a high signal to noise ratio even in the case that only a single pulse (e.g. the final pulse of a burst) is received after switching from transmit to receive mode.

The time taken to send the plurality of pulses within a burst does however result in longer periods of time in which the radar system is ‘blind’. Each time a burst is transmitted (i.e. every burst repetition interval), the half-duplex system is temporarily unable to receive for a longer period than in non-burst systems. This results in ‘blind zones’ for which the signal to noise ratio of received signals is reduced.

An example of a radar transmission scheme employing bursts of multiple RF pulses is illustrated in Figure 2b, which shows a second timing diagram for such a transmission scheme according to the prior art. Specifically, Figure 2b shows a series of transmitted bursts 201 b and two sets of reflections of the transmitted bursts 202b, 203b, associated with first and second objects at first and second distances from the radar system respectively, where the second distance is greater than the first distance.

Each burst can be seen to comprise a plurality of RF pulses (shown as three pulses in Figure 2b), separated by short time interval AtpR, set by the peak pulse repetition frequency, i.e. the frequency at which pulses within a burst are transmitted. In Figure 2b, the burst repetition interval is shown as AtBRi, and actions taking place in the same burst repetition interval are shown on the same line. The number of pulses forming each burst may be selected based on the distance to be measured and/or the required power transmission. In the example shown in Figure 2b, the transmitted RF bursts of pulses are sent in a series of burst repetition intervals (BRI) 211b-213b that allow sufficient time for a transmitted burst to be reflected from objects within a predetermined range of interest before the following RF burst is transmitted. As in the example shown in Figure 2a, this ensures that, after a burst comprising multiple pulses is transmitted, the following burst is delayed by a time At _B Ri in order to listen for reflections of the pulses comprised in the bursts from objects in the range of interest. The burst repetition interval therefore sets the range probed by the transmitted RF bursts 201b.

After each burst is transmitted, the plurality of pulses forming the burst are reflected from the first, closer, object after a first time AtEi, and from the second, further object after a second time AtE2. Based on the time at which the bursts from the first and second objects are received relative to the time at which they are transmitted, the distance to each of the first and second objects can be identified. Unlike in the example shown in Figure 2a, each burst repetition interval allows transmission of several pulses, i.e. associated with a greater transmitted power. This allows for more reliable detection and measurement using the scheme of Figure 2b in comparison to that of Figure 2a.

In the examples shown in Figures 2a and 2b, there may be ambiguity if a reflection from a distant object arrives at the receiver after a time interval greater than the burst repetition interval. In such cases, the receiver cannot tell whether the reflection is from the distant object from the previous transmitted pulse or from a close object from the current transmitted pulse. Range ambiguity can be alleviated to some extent by encoding schemes which transmit a code instead of a single pulse. A code may comprise several pulses and thus can increase the average transmitted power as described in relation to Figure 2b. Different codes may be used for successive bursts so that they are distinguishable. If the codes are orthogonal then when a code is present in the receive signal, it will generate a high correlation when aligned with its own template and a zero correlation when aligned with the template of a different code. Therefore as different templates correspond to different burst repetition intervals, the codes will only correlate with the template of the burst repetition interval in which they were transmitted. However, there will still be side lobes in the cross-correlation when the received code is not fully aligned with the template. These sidelobes still provide unwanted artefacts in the crosscorrelation output.

An example encoding scheme allowing such a reduction in range ambiguity is illustrated in Figure 3, which shows a timing diagram for a radar transmission scheme. Specifically, Figure 3 shows a series of bursts 301 , transmitted by the radar system 100 of Figure 1 , and two series of reflected bursts 302, 303, associated with first and second objects at first and second distances respectively from the source of the transmitted signal, where the second distance is greater than the first distance.

Each of the series of transmitted bursts 301 comprises three pulses, and is associated with a respective burst repetition interval 311 , 312, 313. The pulses within each burst are separated by a short time interval, AtpR, set by the peak pulse repetition frequency.

As described in relation to Figure 2b, the time between successive burst repetitions is shown as AtBRi, and actions taking place in the same burst repetition interval are shown on the same line. The time between bursts At _B Ri is much greater than the time between the pulses, AtpR. For example, the time between bursts may be of the order of tens of nanoseconds in a pulsed radar system (in one particular example, the BRI was 66 nanoseconds), while the time between pulses of a burst may be of the order of a single nanosecond (in one particular example, the time between pulses in a burst was two nanoseconds). It will be appreciated that these orders of magnitude or simply examples and that the intervals may vary greatly between applications. For example, the intervals will depend on factors such as the desired bandwidth (and hence the width of transmitted pulses), the frequency band(s) of the transmission, the speed of the waves (sound or electromagnetic) and the ranges of interest for the transmissions.

The three pulses within each burst form a code with each pulse being an element of that code, the elements being represented in Figure 3 by ‘a1’-‘a3’ ‘b1’-‘b3’ and ‘cT- ‘c3’. Each code element can take one of a plurality of values. For example in a binary code, each element may be either T or ‘O’, or may be either T or ‘-T. In a ternary code, each code element may be a T, ‘0’ or ‘-T which may represent a positive (+1), negative (-1) or zero amplitude (0) pulse in a transmitted signal. Higher order code types (e.g. quaternary, etc.) may also be used. As described in relation to Figure 2b, after transmission of a burst, reflected signals 302 and 303 are received after time intervals determined by the distance between the radar system 100 and the first and second objects 110, 120 respectively. Unlike the example shown in Figure 2b however, pulses from a first burst repetition interval (e.g. burst repetition interval 311) may be received during a subsequent burst repetition interval (burst repetition interval 312), while still being identifiable as having been transmitted in the first burst repetition interval, as a result of the difference in encoding of successive bursts. Thus range ambiguity is reduced.

In the first burst repetition interval 311 , a first burst is sent comprising three pulses (shown as ‘aT ‘a2’ and ‘a3’ in Figure 3), each separated in time by AtpR. After a time AtEi, set by the distance between the first object 110 and the radar system 100, a reflection of the burst is received from the first object 110. No reflection from the second object is received in the burst repetition interval 311 , as the second object 120 is located at a distance greater than the signal can travel in the duration of the first burst repetition interval 311.

Once the first burst repetition interval 311 has elapsed (i.e. At _B Ri after the first pulse is transmitted), the second burst repetition interval, 312 begins, and a second burst, also comprising three pulses (shown as the sequence ‘bT ‘b2’ ‘b3’ in Figure 3), each separated in time AtpR, is sent. As described in relation to the first burst repetition interval 311 , a reflection of the second burst is then received from the first object 110 after a time interval AtEi. In contrast to the first burst repetition interval 311 however, a second set of pulses is also received during the second burst repetition interval 312: the reflection of the first burst (i.e. the sequence ‘aT ‘a2’ ‘a3’) from the second object 120, that has taken a total time of At _B Ri + AtE2 to be received. Thus the received signal in the second burst repetition interval 312 includes a code ‘b ‘b2’ ‘b3’ that correlates with the transmission template of the second burst repetition interval 312 and a code ‘aT ‘a2’ ‘a3’ that correlates with the transmission template of the first burst repetition interval 311. A cross-correlation of the received signal from the second burst repetition interval 312 with the template ‘bT ‘b2 ’b3’ will give a strong correlation with the reflection from the close object 110. If the codes ‘bT ‘b2’ ‘b3’ and ‘aT ‘a2’ ‘a3’ are orthogonal then the received code ‘aT ‘a2’ ‘a3’ will have a weak correlation with the template ‘b ‘b2’ ‘b3’, but will still produce some unwanted sidelobes in the correlation output. If a crosscorrelation of this signal from the second burst repetition interval 312 is also performed against the template ‘aT ‘a2’ ‘a3’ from the transmission in the first burst repetition interval 311 then the reflection ‘aT ‘a2’ ‘a3’ from the distant object 120 will have a strong correlation while the reflection ‘bT ‘b2’ ‘b3’ from the near object 110 will have a weak correlation (with sidelobes). Thus the use of such coding schemes can reduce range ambiguity, although it still produces artefacts in the crosscorrelation output that can be falsely identified as reflections, leading to inaccuracy in the receiver output.

According to embodiments of the invention, a different approach to coding is taken which can improve the accuracy of processing the receive signal and which also has good transmit power.

The invention makes use of sequences that have low off-peak periodic autocorrelation values in a region surrounding the peak value. More specifically, certain embodiments described here make use of perfect periodic autocorrelation sequences to encode a set of pulses for transmission and/or to generate templates for cross-correlation with a received signal. By applying the coding scheme of the present disclosure, imperfect cross-correlation of received pulses, e.g. sidelobes in the correlator output can be significantly reduced or even overcome.

Perfect period cross-correlation can be defined as follows. For two sequences of length n, e.g. a first sequence a = [a ₀ , a _lt ••• , a _n -i] and a second sequence b = [b ₀ , bi, ••• , b _n _ i] , with a shift T relative to the first sequence, the periodic crosscorrelation can be given by

Where i + T is computed modulo n. If the two sequences are identical, and differ only in that they are rotated relative to one another by the value T, the periodic cross-correlation is instead a periodic autocorrelation. The periodic autocorrelation of a sequence of length n, e.g. s = [s ₀ , •••,£„_!] may be given by 0 _S (T) = 6 _SIS (T). The periodic autocorrelation is therefore calculated by performing a multiplication of each element of the sequence s by an element of the sequence that is offset by performing a circular shift by T values within the sequence, then summing the results of those multiplications.

Certain sequences are found to have a ‘perfect’ periodic autocorrelation, such that the periodic autocorrelation 0 _S (T) = 6 _SIS (T) has a value of zero for all non-zero shifts

T.

A family of ternary sequences having this property are known as Ipatov sequences, although these are not the only sequences with this property. A number of such sequences have been identified in this family, of various lengths. Ipatov sequences have been demonstrated at least for lengths 7, 13, 21, 31 , 57, 63, 73, 91 , 127, 133, 183, 273, 307, 381, 511, 553, 651, 757, 871, 993, 1057, 1407, and 1723, however further sequences of other lengths, e.g. length 6 or length 14 have also been demonstrated. Some sequences with perfect periodic cross-correlation are binary sequences. Some sequences are ternary sequences (e.g. made up of positive (+1), negative (-1) or zero amplitude (0) pulses).

According to embodiments of the invention, sequences having perfect periodic autocorrelation may be used to generate sets of transmit pulses for improved correlation accuracy and increased signal to noise ratio. For example, in pulseecho systems such as radar and ultrasound, this can allow better identification of reflected signals, as will be explained below in relation to Figure 4.

Figure 4 shows a timing diagram of signals that may be transmitted and received by the radar system 100 of Figure 1 and the rest of this example will be described in relation to a radar implementation, although it will be appreciated that the transmission and reception may be applied more generally. The encoding scheme of the present disclosure uses a sequence of ternary code elements, the sequence having perfect periodic autocorrelation. Figure 4 shows a ternary sequence of length 6 which has perfect periodic autocorrelation. As described above, the use of a sequence having perfect periodic autocorrelation allows improved identification of received signals, and hence improves the measurement accuracy of the radar system 100.

Figure 4 shows a series of transmitted bursts 401, and two series of reflected bursts 402, 403, associated with first and second objects 110, 120 at first and second distances from the radar system 100 respectively, where the second distance 120 is greater than the first distance 110.

Each burst in the series of transmitted bursts 401 comprises three pulses in this example, although other examples may have any number of pulses greater than one. Each burst of pulses is associated with a respective burst repetition interval 420-430. Each of the pulses within a burst is separated by short time interval AtpR, set by the peak pulse repetition frequency. As described above in relation to Figures 2b and 3, the time between successive burst repetitions is shown as AtBRi, and events taking place in the same burst repetition interval are shown on the same line. The time between bursts At _B Ri is much greater than the time between the pulses, AtpR. For example, the time between bursts may be of the order of tens of nanoseconds, while the time between pulses of a burst may be of the order of one nanosecond. In other examples, these time intervals may be vastly different. The actual time intervals are not a key part of the invention.

The three pulses within each burst are labelled with an identifier in Figure 4, the identifiers being the numbers 1-6. Each identifier represents a certain pulse encoding, (e.g. in the case of a ternary sequence, each pulse may be selected from a positive (+1), a negative (-1) or a zero amplitude (0) pulse, and all pulses with the same identifier have the same selected pulse form). The pulse encodings of the full stream 401 of transmitted pulses (i.e. from the first row ‘ 5 3 T to the last row ’2 6 4’) are selected to ensure transmission of one or more sequences having perfect periodic autocorrelation, as will be explained in further detail below. While the sequences are primarily selected to have perfect periodic autocorrelation, this is not the only property that is considered when selecting sequences to be used. There may also be limitations on acceptable encoded pulse values based on regulatory compliance. For example, the American Federal Communications Commission (FCC) places a limit on the amount of power that may be transmitted using UWB signals within 50 MHz resolution bandwidth centred on the frequency that has the greatest radiated emission for certain applications. As a result, certain combinations of pulses within a burst (e.g. all positive pulses (‘+1 , +1 , +1’) or all negative pulses (-1 , -1 , -1)) may not be usable in practice if that would breach the power limit. However, with ternary sequences for example, an appropriate choice of sequence can ensure that a suitable number of ‘0’s appear within each burst so as to keep the transmitted power below the required limit. The pulse density (proportion of ‘0’s in the sequence length) of the sequence may therefore be a key factor in the choice of sequence.

Figure 4 shows transmitted pulses 401 and received pulses 402 and 403. As with the previous figures, the pulses 402 are reflections from a first object 110 and the pulses 403 are reflections from a second object 120 which is further away than the first object 110. As can be seen from this figure, the full set of transmit pulses 401 is spread across several burst repetition intervals 420-429 and these transmit pulses 401 are interspersed with received pulses 402 and 403. Thus, although the full sequence 401 includes a relatively large number of pulses (30 in this example), when this encoding is used in a monostatic transceiver, the short range capabilities of the transceiver are not limited by the full length of the transmission. Instead, the short range capabilities are determined by the length of the burst (3 pulses in this example) after which signal can be received until the next burst transmission.

In the first burst repetition interval 420, a first burst is sent comprising three pulses (shown as ‘5’ ‘3’ T in Figure 4), each separated in time by AtpR. After a time AtEi, set by the distance between the first object 110 and the radar system 100, a reflection of the burst is received from the first object 110. No reflection from the second object 120 is received in the burst repetition interval 420, as the second object is located at a distance too greater for the reflected signal to travel back to the receiver in the duration of the first burst repetition interval 420.

Once the first burst repetition interval 420 has elapsed (i.e. At _B Ri after the first pulse is transmitted), the second burst repetition interval 421 begins, and a second burst, also comprising three pulses (shown in Figure 4 as ‘6’ ‘4’ ‘2’), each separated in time by AtpR, is sent. As described in relation to the first burst repetition interval 420, a reflection of the second burst is then received from the first object 110 after a time interval AtEi. A reflection of the first burst (shown as ‘5’ ‘3’ ‘1’ on BRI 421 in Figure 4) is also received from the second object 120, that has taken a total time of At _B Ri + AtE2 to be received.

This process repeats in successive burst repetition intervals 421-429, in which a series of reflected pulses 402 from the first object 110 are received in the burst repetition interval in which they are transmitted, and in which a series of reflected pulses 403 from the second object 120 are received in the burst repetition interval after that in which they are transmitted. In burst repetition interval 430, no burst is transmitted, however a reflected burst (‘2’ ‘6’ ‘4’) from the second object 120 is received from the burst transmitted in the previous burst repetition interval 429.

The transmitted bursts 401 are used to encode one or more sequences having perfect periodic autocorrelation, i.e. sequences having a periodic autocorrelation of zero for all non-zero circular shifts of the sequence. These sequences are shown in Figure 4 as a set of 18 elements in a transmission template 405. Although Figure 4 shows sequences for a single transmitter, it is also possible to use multiple transmission channels, each employing their own respective sequences and transmission templates. When receiving reflected signals in such a system, a correlator output sequence would be received for each individual transmitter channel (i.e. the results of a cross-correlation of the received signal with separate templates associated with each transmitted sequence).

As can be seen in Figure 4, three sequences are built up by the transmission of successive bursts: a first sequence is formed from the sequence of first pulses in each burst sequence (shown vertically in the first column as “123456” within box 405 in Figure 4), a second sequence is formed from the sequence of second pulses in each burst (shown vertically in the second column as “561234” within box 405 in Figure 4), and a third sequence is formed from the sequence of third pulses in each burst (shown vertically in the third column as “345612” within box 405 in Figure 4). Each sequence is therefore identical except that it is shifted circularly relative to the two other sequences. Each sequence may be shifted by any amount relative to each of the other sequences, provided some non-zero circular shift is present between all pairs of sequences. Although any shift may be applied, the number of places by which the sequences is shifted may impact the range in which reflected bursts can be validly detected, as outlined below.

The full set of transmitted bursts 401 also includes elements outside of the transmission template 405, i.e. sent before and after the transmission template. These act as padding values, which serve to ensure that the periodic autocorrelation properties of the transmitted sequences come into play such that the cross-correlation in the receiver avoids ambiguous detections. As will be described later, these transmitted padding values are not necessary in some embodiments.

The receive signal can be processed by using cross-correlation against the template 405. As the second and third sequences are rotated forms of the first sequence, the perfect periodic autocorrelation property of the sequences means that they will never correlate with each other. In other words, during the crosscorrelation process, the first column of the receive block 409a (i.e. the column “123456” will have zero correlation with the second and third columns of the template block 405. Therefore correlation of the 18 pulse receive block 409a will generate the highest correlation output when all 18 pulses are aligned with those of template 405. This results in a very high spike in the correlation output with no side lobes and is therefore more accurate and easier to detect. As the perfect periodic autocorrelation sequence has no side lobes, there are no spurious correlator outputs in the valid region that do not correspond to genuine reflections.

In addition, receive box 409b represents a signal received more than one burst repetition interval later than the signal of box 409a. However, even though the pulse of receive signals 409a and 409b are interspersed with each other, they do not create any range ambiguity as the first 15 pulses of box 409b together with the pulses ‘6’ ‘4’ ‘2’ of BRI 422 (which arrive in the same burst repetition intervals as the 18 pulses of box 409a) do not correlate with the template 405. In fact, here the pulses ‘6’ ‘4’ ‘2’ which were transmitted as part of the padding in the second transmit burst 401 complete the full sequence with perfect periodic autocorrelation, so there will be zero correlation and therefore zero range ambiguity. When the cross-correlation is extended further in time, the receive box 409b will correlate with the template 405 indicating the correct time lag and thus allowing proper detection and range distinction to be made for the two receive signals 409a, 409b. In the case of a radar system, this means that reflections from longer range can be successfully detected without having to increase the burst repetition interval.

The padding values ensure that the result of the cross-correlation of the template and received signal is zero except in the case that the time lag is correct (corresponds to the object distance). In order to achieve this, enough rows of padding should be transmitted that no correlation happens in burst repetition intervals prior to the correct one. As the circular shift offset between transmitted sequences puts a limit on the unambiguous range, it also puts a limit on the amount of padding that is beneficial. The maximum amount of padding that is beneficial is equal to one less than the minimum circular shift offset between transmitted sequences. Less padding may be transmitted, but this will further limit the unambiguous range.

For example, if the smallest shift of a first sequence of the transmitted bursts relative to another sequence of the transmitted bursts is, e.g., two burst repetition intervals (as is the case in Fig. 4), the padding must be, at minimum, one burst in length to allow unambiguous identification of the reflected signal. As can be seen in Fig. 4, if the reflected bursts 403 were received one BRI later, the box 409b would begin on BRI 424 and there would be a correlation with the template 405, even with the two rows of padding shown. On the other hand, if the padding is shorter than the minimum circular shift offset by more than one burst (i.e. is included over fewer burst repetition intervals), then partial correlations of a sub-range of the transmitted signal with a sub-range of the template will occur, giving a non-zero correlator output. Thus, a valid ‘range’ for the transmission may be determined based on the number of burst intervals in which padding has been sent and/or the minimum circular shift offset between sequences of the transmitted bursts. Outside of this valid range, reflections cannot be unambiguously identified.

In some examples, the padding may not be transmitted, but instead can form part of an extended template stored in the memory 205 of the radar system 100. In such examples, cross-correlation of the received signals is performed against the extended template. This provides the same result as the case in which the padding is transmitted, but removes the need for padding pulses to be transmitted by the radar system 100, thus potentially saving power in the transmitter.

The dashed receive boxes 407a and 407b in Figure 4 show two examples of pulse sequences in the receive signal that result in zero correlation with the template 405. Receive box 407a has no signal in the first two columns (only noise) but has the full first sequence “123456” in its third column. When this is correlated with the template 405, it overlaps the third sequence “345612” of the template 405 and therefore has a zero correlation output due to the perfect periodic autocorrelation property. Similarly, receive box 407b has the second sequence in its first column and the third sequence in its second column and no signal (just noise) in its third column. When this overlaps the template 405, second and third sequences align with the first sequence and the second sequence respectively from the first and second columns of template 405. Once again, these both have zero correlation output due to the perfect periodic autocorrelation property of the sequences and therefore do not result in unwanted receiver outputs.

A further useful property of this encoding scheme is that a receive signal that is partially obscured such that early pulses in each burst are missing, can still be detected. This situation occurs in monostatic pulse-echo systems such as radar and ultrasound when the reflection is from a very close reflector. The receiver cannot detect any signal while it is transmitting and so may fail to receive the earlier pulses in a burst while still receiving later pulses in the burst. For example, referring to the receive signal box 409a of Figure 4, if the first two columns “123456” and “561234” are zero (not received), the third column “345612” can still overlap the third column of the template 405 producing a perfect correlation with a strong correlator output (albeit not as strong as a full three-column match). Thus, close range detection is still possible with a partial receive signal.

The use of the use of a sequence having perfect periodic autocorrelation, transmitted multiple times with a circular rotation offset between each version ensures that signal reflected from the first and second objects 110, 120, may be unambiguously identified. As a non-zero autocorrelation value is achieved only in the case of zero shift of the received sequences relative to the transmission template 405 (and hence the transmitted bursts 401), burst transmission (and hence increased power output) can also be implemented without introducing ambiguity.

Although the example described above uses sequences having perfect periodic autocorrelation, such that the correlation output is zero in the case of any non-zero circular shifts of the sequences shown in the columns of the transmission template, this is not a required feature of the invention. Instead, ‘nearly-perfect’ sequences, having periodic correlations that yield low off-peak values in a region surrounding the peak value may be used. These include binary maximum length sequences (m- sequences), for which the periodic autocorrelation is two-valued. Specifically, the normalized autocorrelation of an m-sequence of length N, takes two values: N and - 1. For example, for a sequence of length 31 , the autocorrelation takes the form {31 , -1, -1, -1, ...}. Such sequences may therefore produce a significantly lower (but nonzero) output for any non-zero circular shifts of the sequences. These sequences may therefore be used in place of the Ipatov sequences, and produce a weak correlator output for all non-zero circular shifts.

In some examples, sequences with non-perfect periodic autocorrelation can be used providing they have good (i.e. low, ideally zero or near-zero) correlation values in a region surrounding the peak value. As an example, taking a Barker code of length 13: barker_13 = [1111 1 -1 -11 1 -11 -11] a sequence can be formed as follows:

[barker_13, 0, -barker_13, 0]

= [1111 1 -1 -11 1 -11 -110-1 -1 -1 -1 -11 1 -1 -11 -11 -10]

This length 28 sequence has a periodic autocorrelation of:

[260000000000000 -26000000000000 0]

The second non-zero value of -26 means that this is not a perfect periodic autocorrelation, but the large number of zeros in the region surrounding the peak value 26 still give this sequence good properties for use in the invention. The large off-peak value (the -26) puts a limit on the unambiguous range, but in many implementations this will be a less onerous restriction than the range restrictions imposed by the lowest circular offset between sequences. However, because of the extra -26 correlation value, only half as much shift per column can be used. For example, four pulses per burst and a shift of three per column would work, and in that case the unambiguous range would be defined by the shift of three, i.e. the unambiguous range would be three times the burst repetition interval. For a longer unambiguous range, a shift of four is possible, but only with three columns, so the transmissions would have less total energy. A shift of up to seven is possible with only two columns for yet another tradeoff between unambiguous range and transmitted energy.

Figure 5 shows an example of a series of pulse burst radar signals transmitted, in accordance with the present disclosure. Figure 5 shows a series of transmitted bursts 501, and three series of reflected bursts 502, 503, 504, associated with three targets at first, second and third distances from the radar system respectively, where the third distance is greater than the second distance, and the second distance is greater than the first distance.

Each burst in the series of transmitted bursts 501 comprises six pulses in this example and is associated with a respective burst repetition interval, denoted by the vertical position of the burst. Each of the pulses within a burst is separated by short time interval, illustrated by the horizontal distance between pulses. As described above in relation to Figure 4, the time between successive bursts is much greater than the time between the pulses of the transmitted signal. Therefore, the transmitted pulses 501 appear as six columns in Figure 5, the leftmost column corresponding to the series of first pulses (i.e. the series comprising the first pulse from the first pulse, then the first pulse from the second pules, then the first pulse from the third burst, etc.), the second column corresponding to the series of second pulses, etc.

The six pulses within each burst can take one of three forms so that they can form ternary sequences. Thus, in this example, each pulse has either a positive (+1), a negative (-1) or a zero amplitude (0). In Figure 5, positive pulses are shown in black, negative pulses are shown in grey, and zero amplitude pulses are shown in white. The pulse encodings of the full stream 501 of transmitted pulses are selected to ensure transmission of six sequences having perfect periodic autocorrelation, i.e. sequences having an autocorrelation of zero for all non-zero circular shifts of the sequence. These sequences are shown in Figure 5 as the six vertical columns of elements forming a transmission template 505 from rows 23 to 79, i.e. having a sequence length of 57. In this example, the sequence is an Ipatov sequence. Each sequence of bursts is identical except that it is shifted circularly by a shift T relative to the preceding sequence. As described in relation to Figure 4, the full set of transmitted bursts 501 also includes padding elements outside of the transmission template 505, i.e. sent before and after the transmission template (i.e. the bursts indicated on the vertical axis from rows 11 to 22 and from 80 to 91).

It can be seen in Figure 5 that the receive signal includes contributions from three targets, in the form of three sets of reflected bursts 502, 503, 504.

The first set of reflected bursts, 502, is the result of transmitted signals reflecting from a target that is very close to the transmitter, also known as a “masked target”. The masked target is sufficiently close to the transmitter that for a given single transmitted burst of the set 501, one or more reflected pulses arrive at the receiver before the entire burst has completed transmitting. In the example shown in Figure 5, only three of the six pulses of each burst (the last three to be transmitted) can be seen to have been detected. As the reflected bursts 502 are received so soon after the burst is transmitted, the final three pulses of each transmitted burst 501 can be seen to be received in the same burst repetition interval as that in which they were transmitted. As described above, the received bursts 502 from the masked target can be processed by using cross-correlation against the template 505. The received burst 502 will have perfect correlation with the fourth, fifth and sixth columns of the template 505, resulting in a spike in the correlation output. However, as no correlation is made with columns 1-3 of the template, the correlation output will not reach its highest possible value, i.e. that which occurs when all elements of the template are aligned with a corresponding element of the template.

The second set of reflected bursts, 503, is the result of transmitted signals reflecting from a target that is somewhat close to the transmitter, yet located far enough from the transmitter that all of the pulses are sent prior to the reflected signals from the target being received (i.e. these reflections are not masked by the transmission). As with the masked target, the reflected pulses 503 are received in the same burst repetition interval to that in which they were transmitted. However, unlike the signals 502 reflected from the masked target, all six pulses of each transmitted burst 501 can be seen to be received. As this includes all six pulses of each burst of the template 505, cross-correlation against the template 505 will result in the highest correlation output, comprising a high spike in the correlation output with no side lobes. There are no sidelobes because of the perfect periodic autocorrelation property of the sequences which means that column 1 of the receive signal 503 will only correlate with column 1 of the template and will have zero correlation with each of columns 2-6 of the template.

The final set of reflected bursts, 504, is the result of transmitted signals reflecting from a target that is located far from the transmitter, such that the reflected bursts 504 are received in a later burst repetition interval to that in which they were transmitted. This can be seen in Figure 5 from the fact that the box 509b identifying the signal that matches the template 505 is shifted vertically down relative to the template 505. All six columns of the template 505 are seen to be present in the signal reflected from the far away target (as shown in box 509b). As a result, when cross-correlation is performed, a non-zero result will be obtained only when the receive box 509b correlates with the template 505, i.e. with an associated time lag corresponding to the distance to the target. As with the bursts 503, this will result in the highest correlation output, comprising a high spike in the correlation output with no side lobes. As the time for which this correlation occurs can be unambiguously determined, range distinction is possible between the two receive signals 509a, 509b. Even though the pulse of set 504 are received interspersed with the pulses of set 503, no spurious correlations will occur when the correlation is performed across the whole template 505 so as to bring in the perfect periodic autocorrelation properties.

An example of the cross correlator output for each of the signals described in relation to Figure 5 is illustrated in Figure 6a. Specifically, Figure 6a shows the results of cross-correlation of the transmission template 505 with the transmitted bursts 501 (for reference) and the received bursts 502-504, detected in the valid range of the transmitted signal. The results of the cross-correlation of the transmission template 505 with the transmitted bursts 501 is shown in Figure 6a as 601. This represents cross-correlation before any losses, and hence the output value is 1. The results of the cross-correlation of the transmission template 505 with the received bursts 502 from the masked target, nearby target, and far-away target are shown as 602, 603 and 604 respectively. It can be seen in Figure 6a that the more time passes before a signal is received (and hence the further a target is located from the transmitter), the lower the cross-correlator output. This is the result of attenuation over distance and results in a lower signal to noise ratio.

The cross-correlator outputs shown in Figure 6a have compensated by applying a masking gain to the receive signal as shown in the lower graph. This is why the masked target 602 shows a higher correlator output than the close-by target 603, even though its actual correlation result was lower (due to only matching three columns out of six). The masking gain shown in the lower graph of Figure 6a is essentially the ratio of the current possible received signal to the maximum possible receive signal and is therefore low when the signal is heavily masked and 1 when the signal is unmasked. Thus the received signal needs to be divided by the masking gain to compensate it.

The black dots 608 in the masking gain graph show the effective receive capability of the receiver with value of 0 when the transmitter has been transmitting for a full burst such that it has been blind for a burst length. Either side of that fully-blind period, the effective receive capability increases as a single column of receive signal can be matched, then two columns of receive signal can be matched, then three columns, etc. until full receive capability is achieved when the whole burst length can be received. The solid line 610 in the graph shows the masking gain as the divisor of the receive signal and follows the pattern of the black dots except that it is set to 1 at the points of zero receive capability to avoid a divide-by-zero error. Thus, the masking gain is set to 1 at sample numbers 0, 66, 132, 198... etc.

For context, Figure 6b shows the valid region of the receive signal in the context of a longer time period of cross-correlator output. The dots in this graph show nonzero correlator outputs, many of which are very close to zero and some of which are significantly larger. The valid region shown with grey shading (and corresponding to the zoomed version in Figure 6a) has no non-zero values other than the desired ones, i.e. the masked target, the close-by target and the far-away target. Outside of the valid region it can clearly be seen that there is more clutter in the correlator output which may be harder to distinguish from genuine receive signal. Thus the perfect periodic autocorrelation sequences together with the transmission scheme described here have resulted in a much cleaner crosscorrelator output.

Figure 7 shows an example of the form of a correlation template 700 that may be used in a system according to the invention, as well as a received signal 702 that may be received by a receiver according to the present invention. The correlation template 700 can be seen to comprise a series of bursts 704a-704e each comprising a number (six in this example) of individual pulses. For example, the first burst of the template 704a can be seen to comprise four negative pulses and two positive pulses.

The received signal 702 can be seen to include transmitted bursts 714a-714e which match the corresponding elements of the correlation template 704a-704e shown in Figure 7, as well as a padding pulse 716 transmitted before the bursts 714a-714e and which is not present in the template 700. Reflections of each of the bursts 714a-714e from a nearby target can also be seen in the received signal 702, and are shown as reflected bursts 724a-724e. A reflection of the padding pulse 716 from a nearby target and from a distant target can also be seen, and are shown as reflected bursts 726 and 736 respectively. Reflections from a masked target are also shown in Figure 7 and appear as lower amplitude copies of the last three pulses of the transmitted bursts, immediately following the transmitted bursts. An example can be seen at 715a following burst 714a. The masked target reflections for the other bursts are also visible, but not labelled for simplicity.

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.