Radio receiver synchronization

Abstract

A wireless device is configured to correlate signal data with stored synchronization data to generate synchronization-related data. The signal data represents a received radio frequency signal that encodes a data frame having a synchronization preamble containing multiple instances of a predetermined synchronization sequence. The stored synchronization data represents the predetermined synchronization sequence. The synchronization-related data is generated by correlating signal data representing the synchronization preamble with the stored synchronization data. While generating the synchronization-related data, the wireless device identifies one or more peaks in the synchronization-related data and determines first synchronization information from the first set of one or more peaks. After generating more of the synchronization-related data, the wireless device identifies one or more peaks in the synchronization-related data and determines second synchronization information from the second set of one or more peaks.

Description

Technical Field

[0001] This invention relates to the synchronization of radio receivers. Background Technology

[0002] In order for a radio receiver to reliably decode incoming radio data packets, precise synchronization is required at both the symbol level (i.e., identifying the timing of symbols within a data packet) and the frame / packet level (i.e., identifying the start of a packet). Better synchronization generally results in greater receiver sensitivity.

[0003] Incoherent radio receivers determine timing synchronization information by performing a correlation operation on the input signal. Many radio protocols define a fixed preamble sequence, which achieves effective frame and symbol synchronization by having the radio transmitter send a known modulated waveform at the beginning of each packet. The radio receiver can then receive this waveform and use its arrival to determine frame and symbol timing information. In some protocols, the preamble sequence contains a repeating pattern, which can support the use of more compact or efficient correlators in the radio receiver because the correlator only needs to correlate the received signal with a single unit of the repeating pattern, rather than with the entire preamble sequence.

[0004] However, reliably achieving fast and accurate synchronization can be challenging, especially in noisy channels. Furthermore, when radio signals are mixed with the input frequency, any difference between the transmission frequency used by the transmitter and the reference frequency used by the receiver makes precise synchronization even more difficult. Such frequency offsets can arise due to manufacturing tolerances and varying environmental conditions.

[0005] A radio receiver can determine frequency synchronization information, such as carrier frequency offset estimation, by comparing the frequency or phase information obtained from the input radio signal with the signal from the local oscillator. This information can then be used to correct for the frequency offset when receiving radio signals.

[0006] WO 2017 / 103557 and WO 2018 / 104708 of this application describe a synchronization procedure that can be used when receiving a synchronization preamble containing a sequence of repeating synchronization words. When associated with such a synchronization word, a synchronization event is declared successful once a set of over-threshold correlated peaks, spaced temporally by an amount corresponding to the synchronization word length plus or minus a noise error tolerance, reaches a threshold count. Symbol timing synchronization information (strobe timing) is then determined from said set of peaks for performing symbol timing recovery, and a frequency offset estimate is also determined for applying carrier frequency offset compensation.

[0007] However, it has been found that such methods can lead to undesirable synchronization performance under certain conditions. Therefore, embodiments of the present invention seek to provide an improved method for synchronizing radio receivers. Summary of the Invention

[0008] According to a first aspect, the present invention provides a wireless device configured to:

[0009] The signal data is correlated with the stored synchronization data to generate synchronization correlation data, wherein the signal data represents the received radio frequency signal that encodes a data frame having a synchronization preamble containing multiple instances of a predetermined synchronization sequence, wherein the stored synchronization data represents the predetermined synchronization sequence, and wherein the synchronization correlation data is generated by correlating the signal data representing the synchronization preamble with the stored synchronization data.

[0010] While generating synchronization correlation data, a first set of one or more peaks is identified in the synchronization correlation data, and first synchronization information for the radio device is determined from the first set of one or more peaks; and

[0011] After generating more synchronization-related data, a second set of one or more peaks is identified in the synchronization-related data, and a second synchronization information for the radio equipment is determined from the second set of one or more peaks.

[0012] According to a second aspect, the present invention provides a method for synchronizing wireless devices, the method comprising:

[0013] The signal data is correlated with the stored synchronization data to generate synchronization correlation data, wherein the signal data represents the received radio frequency signal that encodes a data frame having a synchronization preamble containing multiple instances of a predetermined synchronization sequence, wherein the stored synchronization data represents the predetermined synchronization sequence, and wherein the synchronization correlation data is generated by correlating the signal data representing the synchronization preamble with the stored synchronization data.

[0014] While generating synchronization correlation data, a first set of one or more peaks is identified in the synchronization correlation data, and first synchronization information for the radio device is determined from the first set of one or more peaks; and

[0015] After generating more synchronization-related data, a second set of one or more peaks is identified in the synchronization-related data, and a second synchronization information for the radio equipment is determined from the second set of one or more peaks.

[0016] Therefore, it can be seen that, according to embodiments of the invention, synchronization information is determined once from the synchronization correlation data, generated once from the synchronization preamble, and then, as more correlation data becomes available, further (e.g., updated) synchronization information can be generated (when any necessary conditions are met). This advantageously allows the embodiments to quickly obtain initial synchronization information after the reception and processing of the synchronization preamble begins, while also promoting more reliable synchronization by determining additional synchronization information after a significant portion of the synchronization preamble has been received and processed. In this way, the embodiments can synchronize accurately and reliably without having to trade off accuracy for robustness (e.g., robustness for the probability of failing frame detection).

[0017] The first synchronization information may include timing synchronization information (e.g., symbol timing information) and / or frequency synchronization information (e.g., frequency offset estimation, which may be carrier frequency offset estimation). The second synchronization information may include timing synchronization information (e.g., symbol timing information) and / or frequency synchronization information (e.g., frequency offset estimation).

[0018] This contrasts with primitive methods, such as those described in WO 2017 / 103557 and WO 2018 / 104708, which declare synchronization complete as soon as a set of peaks for the required number of valid intervals is detected, and then determine timing and frequency synchronization information once based on each peak in that set. As explained in more detail below, such primitive methods may result in slower, less accurate, or even no synchronization at all if the relevant data packets contain spurious peaks that still conform to the expected timing pattern, leading to packet errors or loss.

[0019] By continuing to potentially identify more peaks than are needed to determine the first synchronization information, embodiments of the invention can produce better receiver sensitivity with a lower risk of inaccurate or failed synchronization, even when the relevant data packets contain spurious peaks.

[0020] It should be understood that not every signal received by the wireless device embodying the present invention is necessarily suitable for determining initial and updated synchronization information; however, the wireless device is configured to determine such information when the device receives an appropriate signal.

[0021] The embodiment can receive radio frequency (RF) signals, which can be radio signals or electrical representations of radio signals. The wireless device can include a radio receiver for receiving RF signals as radio signals, such as for receiving IEEE 802.15.4 radio signals. The wireless device can be configured, for example, to use an analog-to-digital converter to generate signal data from the received RF signals to generate a time series of complex sample values. Synchronization correlation data can be generated while the wireless device is receiving the RF signals, i.e., in real time. The first and / or second synchronization information can be determined before the wireless device has completed receiving the synchronization preamble of the RF signals. Similar to the first synchronization information, the second synchronization information can be determined while the wireless device is still generating synchronization correlation data from the synchronization preamble.

[0022] Each set of identified peaks can contain a single peak or multiple peaks.

[0023] A first set of peaks can be identified from a first portion of the synchronization-related data. A second set of peaks can be identified from a second portion of the synchronization-related data, which may include some or all of the first portion. In some embodiments and / or for some RF signals, the second set of peaks may include one or more of the peaks in the first set; however, this is not always the case.

[0024] A wireless device can be configured to use first synchronization information when receiving at least a portion of an RF signal, and to use second synchronization information when receiving at least a portion of an RF signal. These corresponding portions may be different portions, or they may partially or completely overlap. Specifically, the wireless device can be configured to use the first synchronization information to synchronize the device's reception of at least a portion of a synchronization preamble of the RF signal. It can also be configured to use the second synchronization information to synchronize the device's reception of at least a portion of the synchronization preamble of the RF signal.

[0025] The first set of peak values ​​can be determined immediately, and the second set of peak values ​​can be determined later than the first set.

[0026] In some embodiments, the first synchronization information includes timing synchronization information (e.g., a first strobe time value), while the second synchronization information includes updated timing synchronization information (e.g., a second strobe time value).

[0027] In some embodiments, the first synchronization information includes frequency synchronization information (e.g., a first frequency offset estimate), while the second synchronization information includes updated frequency synchronization information (e.g., a second frequency offset estimate).

[0028] In some embodiments, the first synchronization information includes timing synchronization information, while the second synchronization information includes frequency synchronization information. In some such embodiments, for at least some of the received signals, the first set of peaks may be smaller than the second set of peaks (e.g., three peaks versus five peaks, which may or may not include the three peaks from the first set). This allows for the determination of accurate frequency synchronization information based on a greater number of peaks, without requiring the receiver to be configured in a way that reduces the probability of successful timing synchronization by delaying the generation of timing synchronization information until the same number of peaks have been identified. In some such embodiments, the first information may further include frequency synchronization information, while the second synchronization information includes updated frequency synchronization information.

[0029] Additional synchronization information for the radio equipment can be determined from one or more additional sets of peaks (which may at least partially overlap with the first and / or second sets).

[0030] The wireless device can be configured to use first and / or second synchronization information during frequency offset compensation. It can use the first and / or second synchronization information to rotate signal data, for example, by rotating a sample representing a portion of the signal data received or generated after the corresponding synchronization information has been determined. The device may include a frequency offset compensation unit, which may contain a CORDIC (Coordinate Rotation Digital Computer), and can be configured to pass the first and / or second synchronization information to the frequency offset compensation unit.

[0031] A radio device may include a symbol detector for detecting symbols from signal data. It may be configured to synchronize the symbol detector using first and / or second synchronization information. It may be configured to pass the first and / or second synchronization information to the detector. It may use the first and / or second synchronization information to synchronize the symbol detector for detecting symbols in a portion of signal data received or generated after determining the corresponding synchronization information. This portion may include one or more symbols of a synchronization preamble and / or one or more symbols of message data in a data frame.

[0032] Radio equipment can be configured to accumulate (i.e., combine) frequency synchronization information. It can be configured to accumulate frequency synchronization information determined from corresponding peaks or corresponding groups of peaks (which may be different or overlapping groups of peaks), such as accumulating multiple frequency offset estimates. Accumulation may include calculating a coherent average (e.g., mean) from multiple groups of information. The radio equipment can then use the accumulated information (e.g., accumulated or averaged frequency offset estimates) to synchronize the reception of at least a portion of the RF signal.

[0033] In addition to or as an alternative to accumulated frequency synchronization information, in some embodiments, the radio device may select frequency synchronization information (e.g., a single frequency offset estimate) determined from a single peak or a set of peaks, or from a larger amount of frequency synchronization information (e.g., from multiple frequency offset estimates), where the larger amount of frequency synchronization information is determined from multiple corresponding peaks or corresponding sets of peaks (which may be different or overlapping sets of peaks). Any suitable selection criterion may be used. The radio device can then use the selected information (e.g., the selected frequency offset estimate) to synchronize the reception of at least a portion of the RF signal.

[0034] In some embodiments, a wireless device can be configured to determine whether a later-determined synchronization information should replace an earlier-determined synchronization information. If it determines that the later-determined synchronization information should replace the earlier information, it can use the later-determined synchronization information to receive RF signals. If it determines that it should not replace the earlier-determined synchronization information, it can discard the later-determined synchronization information (e.g., when the information is timing synchronization information), or it can accumulate the later-determined synchronization information with the earlier-determined information (e.g., when the information is frequency synchronization information). It can be configured to accumulate (i.e., combine) the later-determined synchronization information with the earlier-determined synchronization information (e.g., through averaging) to generate accumulated synchronization information, which it can use to receive RF signals.

[0035] The device can generate synchronously relevant data over time, such as time series of relevant values ​​(e.g., relevant samples). Each relevant value can have an associated time value, which can be a sample index or a timestamp.

[0036] Timing synchronization information can be determined based on the time values ​​associated with the peak values ​​of the first and / or second subsets. Frequency synchronization information can be determined based on the phase of the correlation values ​​associated with the peak values ​​of the first and / or second subsets.

[0037] The device can detect peaks within the synchronous correlation data while generating it. For at least one or more peaks, it can determine updated synchronization information in response to the detection of a new peak in the synchronous correlation data. In some embodiments, for at least multiple peaks in the correlation data, it can perform a peak analysis process each time a new peak is detected. Each set of one or more peaks can be identified by performing a peak analysis process on the synchronous correlation data (e.g., on a set of one or more consecutively correlated sample values). In some embodiments, for example, to reduce timing errors, it may be advantageous to perform the process on multiple consecutive samples (e.g., two or three samples) rather than just one sample.

[0038] The peak analysis process may include determining whether a new peak meets qualifying conditions to be included in a set of peaks used to determine synchronization information for a radio device (hereinafter referred to as qualifying peaks). Qualifying conditions may include one or more of the following: amplitude conditions, timing conditions, and symbol detection conditions. Importantly, in a preferred embodiment, the qualifying conditions preferably do not impose a fixed minimum number of already detected qualifying peaks before the new peaks can be used to determine synchronization information.

[0039] Amplitude criteria may require peak values ​​to be associated with correlation values ​​in synchronization-related data, where the correlation values ​​have an absolute value (i.e., amplitude) greater than (which may include greater than or equal to) a threshold. The threshold may be constant or dynamic, changing over the duration of the synchronization preamble of the data frame. In some embodiments, the threshold depends on the correlation values ​​of one or more peaks already identified in the synchronization-related data. At least under certain conditions, the threshold may be determined as the maximum of a predetermined constant threshold and a variable threshold, where the variable threshold may be the maximum of the absolute values ​​of all correlation values ​​of all eligible peaks already identified in the synchronization-related data. Such threshold conditions may need to be met to determine that later-determined synchronization information will replace earlier-determined synchronization information. Lower threshold conditions, such as simply a predetermined constant threshold, may need to be met to accumulate later-determined synchronization information. More generally, the device may need to meet a first threshold condition to accumulate synchronization information and a second (e.g., a more stringent) threshold condition to replace synchronization information. This could be useful because replacing synchronization information, especially when it is timing synchronization information, can have a more significant impact on the reception of radio signals (e.g., a higher probability of failing frame detection if it is incorrect) compared to simply accumulating new information with earlier information, and therefore requires more stringent conditions before using peaks in this way.

[0040] Timing conditions may require separating a peak (or a correlation value corresponding to that peak) from an earlier peak by a time interval corresponding to the duration of a predetermined synchronization sequence, such as an integer multiple of said duration, optionally within a predetermined margin of jitter (e.g., + / - one or two sample periods, or + / - 1%). This may exclude peaks that are impossible due to the preamble sequence. However, in some embodiments, timing conditions can be used to identify one or more peaks that are not separated from earlier, qualified peaks by such a time interval, i.e., the interval exceeds the predetermined margin. This can be used to determine whether to replace earlier, determined timing synchronization information with later-determined timing synchronization information. This is useful for preventing detectors from attempting to use earlier, false peaks to set the symbol timing for decoding data from data frames by allowing later, true peaks to cover false peaks. This can be applied in conjunction with amplitude criteria as described above.

[0041] Symbol detection conditions can be used with a symbol detector to determine whether a peak coincides with a symbol (e.g., a bit or multi-bit word) in a predetermined synchronization sequence. In some embodiments, the synchronization sequence may contain a single symbol (e.g., a four-bit word), which can be extended using a chip sequence. The receiver can use a detector to determine whether the correlation value associated with the peak corresponds to a sample from the single symbol. If the symbol detection conditions are not met, the receiver can discard the data frame. This can improve efficiency. The receiver can use a symbol detector to determine (optionally in conjunction with amplitude and / or timing conditions) whether later-determined synchronization information should replace earlier-determined synchronization information or accumulate together with it.

[0042] The receiver can use a symbol detector to detect the end of the synchronization preamble. It can also use a detector to detect the start-of-frame delimiter symbol or multiple symbols. In response to such detections, it can generate frame synchronization information.

[0043] Synchronization data can be stored in the device's memory. The stored synchronization data can contain a series of sample values ​​representing the baseband waveform. The stored synchronization data can correspond to a single instance of a predetermined synchronization sequence, or to multiple such instances. The synchronization sequence (and optionally other data) in the data frame can be encoded using direct sequence spread spectrum. The data frame can be modulated on the RF signal using phase modulation, frequency modulation, amplitude modulation, or a combination of such modulations. It can be offset quadrature phase shift keying (O-QPSK) modulation. In some embodiments, such as those using "double" correlation operation, the synchronization data can contain a series of values, where each value is equal to the product of a first sample representing the synchronization sequence and the complex conjugate of a second sample representing the synchronization sequence, wherein each second sample is offset from each first sample by a fixed offset (e.g., three sample periods).

[0044] Wireless devices may include a hardware correlator (i.e., circuitry) for correlating signal data with stored synchronization data. The synchronization correlation data may contain a time series of correlation values. The correlation values ​​may contain phase information, such as complex correlation values. The synchronization correlation data may be sampled at regular sample intervals and therefore contain inherent timing information. In some embodiments, the correlator may be configured to correlate the stored synchronization data with a complex conjugate of a first sample of signal data multiplied by a second sample representing the synchronization sequence, wherein each second sample is offset from each first sample by a fixed offset (e.g., three sample periods), referred to herein as a “double” correlation.

[0045] The above synchronization method can be particularly advantageous when the synchronization sequence is repeated several times within the preamble (e.g., four, eight, ten, or more times). Radio protocols such as IEEE 802.15.4 and Bluetooth Low Energy define such repeating synchronization preambles. In some preferred embodiments, the RF signal is an IEEE 802.15.4 or Bluetooth Low Energy signal, and the radio device is configured to decode IEEE 802.15.4 (e.g., Zigbee or Thread) or Bluetooth Low Energy signals.

[0046] Wireless equipment can be integrated, such as a silicon chip. (It should be understood that wireless equipment may still require one or more off-chip components connected to it to operate, such as power supplies, antennas, crystals, discrete capacitors, discrete resistors, etc.) Wireless equipment may contain a radio transmitter.

[0047] Radio equipment may include one or more processors, DSPs, logic gates, amplifiers, filters, digital components, analog components, non-volatile memory (e.g., for storing software instructions), volatile memory, memory bus systems, peripherals, inputs, outputs, or any other suitable electronic components. Radio equipment may include circuitry for performing timing correction, phase correction, or frequency correction operations.

[0048] Some or all of the steps can be implemented in software or hardware or a combination of software and hardware.

[0049] Features of any aspect or embodiment described herein may be applied, where appropriate, to any other aspect or embodiment described herein. When referring to different embodiments or sets of embodiments, it should be understood that these embodiments are not necessarily different, but may overlap. Attached Figure Description

[0050] Some preferred embodiments of the invention will now be described by way of example only with reference to the accompanying drawings, in which:

[0051] Figure 1 It is a schematic diagram of a radio communication system including a receiver embodying the present invention;

[0052] Figure 2 A diagram showing data packets that can be sent and received by a radio communication system;

[0053] Figure 3 This is a schematic diagram of the synchronization and decoding logic of a radio receiver;

[0054] Figure 4 This is a schematic diagram of the relevant amplitude versus time in the first instance scenario;

[0055] Figure 5This is a schematic diagram of the relevant amplitude versus time in the second example scenario;

[0056] Figure 6 It is a graph of the amplitude of three relevant values ​​versus time, used to explain the operating principle of the receiver embodying the present invention;

[0057] Figure 7 This is a flowchart of the operations performed by the receiver that embodies the synchronization process of this invention;

[0058] Figure 8 This is a graph showing the simulated grouping error rate (PER) versus sensitivity for embodiments using different correlation thresholds; and

[0059] Figure 9 This is a simulated grouping error rate (PER) versus selectivity curve for embodiments using different relevant thresholds. Detailed Implementation

[0060] Figure 1 An example embodiment illustrates a radio communication system comprising a wireless thermostat 1 that performs short-range radio communication with a wireless network hub 7. The hub 7 is a radio receiver embodying the invention.

[0061] The wireless thermostat 1 has a connection to a microprocessor 3 (such as an ARM). TM A temperature sensor (Cortex M series) 2. A microprocessor 3 is connected to a radio transmitter 4. The radio transmitter 4 includes an encoder 5 (and other components). The encoder 5 can be implemented via dedicated hardware circuitry, software executed on the processor, or a combination of hardware and software logic. Other conventional components, such as memory and a battery, are also present, but for simplicity, they are omitted from the original text. Figure 1 (The text is omitted.) The microprocessor 3 and the radio transmitter 4 can be integrated onto a single silicon chip. The monitor 1 has a radio antenna 6, which can be integrated onto such a chip or externally.

[0062] In addition to other conventional components (not shown), hub 7 also has an antenna 8 connected to radio receiver 9. Antenna 8 is adapted to receive short-range radio communications from a wireless personal area network device including wireless thermostat 1. Radio receiver 9 includes synchronization and decoding logic 10 and other components. Logic 10 can be implemented by dedicated hardware circuitry, or by software executing on a processor, or by a combination of hardware and software logic. Radio receiver 9 is connected to microprocessor 11 (such as ARM). TM The Cortex M series microprocessor can output data for display on screen 12 via other components, such as another microprocessor (not shown) running the operating system and appropriate software applications.

[0063] In use, the wireless thermostat 1 receives periodic temperature readings from the temperature sensor 2. The microprocessor 3 processes the readings into a suitable format for transmission and sends the message data to the radio transmitter 4. The radio transmitter 4 determines whether the message data is suitable for a single data packet (corresponding to a single data frame) or whether it must be split into two or more data packets. The encoder 5 in the radio transmitter 4 encodes part or all of the message data, for example, using convolution-based forward error correction code, and adds any headers or other metadata to the encoded message data to create a packet payload. It then performs direct sequence spread spectrum (DSSS) encoding on the entire payload using a fixed chip sequence. For example, each four-bit symbol can be represented by its own distinct 32-bit spread sequence. Of course, chip sequences of other lengths can also be used. The transmitter 4 then pre-assigns a synchronization word to the payload, consisting of multiple repetitions of a predetermined sequence. This precedes the data payload containing the message data, followed by a predetermined start-of-frame delimiter (SFD) and / or a payload length header. Radio transmitter 4 uses an appropriate modulation scheme to transmit coded data packets modulated on a radio frequency carrier (e.g., a carrier in the 2.4 GHz band) from antenna 6.

[0064] In some embodiments, the wireless thermostat 1 and hub 7 communicate using a protocol with a physical layer implementing a version of the IEEE 802.15.4 standard. For example, they can use Thread. TM or ZigBee TM Communication is performed. In some such embodiments, each 4-bit symbol is mapped onto a 32-chip extension sequence, and packets are modulated using Offset Quadrature Phase Shift Keying (O-QPSK) operating at a data rate of 250 kb / s. Therefore, each symbol has a duration of 16 μs.

[0065] Figure 2 An exemplary data packet structure used in such an 802.15.4 embodiment is shown. It has a 32-bit (8-symbol) preamble synchronization sequence, followed by an 8-bit Start-of-Frame Delimiter (SFD), an 8-bit Physical Layer (PHY) header, and a variable-length PHY Service Data Unit (PSDU) of 0 to 127 octets. The preamble sequence consists of eight instances of the zero symbol 0000'b. After DSSS encoding, this becomes eight instances of the same 32-chip sequence. The SFD field contains two fixed symbols, 1010 0111'b (0xA7), and introduces the start of the frame's substantive content, which begins with a variable in the PHY header indicating the PSDU length, and then provides the PSDU itself.

[0066] In use, the wireless network hub 7 receives radio data packets at antenna 8. The radio receiver 9 downmixes the received signal to an intermediate frequency (IF) or directly to baseband, and then samples the signal to generate a complex digital sample value stream representing the in-phase and quadrature components of the received signal. The signal may first be filtered in the analog and / or digital domains. Receiver 9 uses synchronization and decoding logic 10 to process the modulated digital signal.

[0067] Synchronization and decoding logic 10 performs incoherent decoding. It first cross-correlates the input sample stream I&Q with stored data representing the baseband waveform of a single instance of the modulation chip sequence corresponding to the synchronization symbol 0000'b. It generates a complex correlation value C by maintaining a buffer of the most recently generated samples and calculating the time series of a complex inner product operation between the stored synchronization template and the currently buffered data. n This is achieved through time series analysis. It analyzes correlation values ​​that change over time in order to perform symbol timing recovery and frequency offset correction. See below. Figures 3 to 7 Let me explain the process in more detail.

[0068] As described in more detail below, the repeating synchronization sequence allows synchronization and decoding logic 10 to detect and synchronize to packets based on the time interval between correlator matches and the correlator output amplitude.

[0069] Synchronization and decoding logic 10 determines the end of the preamble and the beginning of the PSDU by detecting the SFD field, thereby achieving frame (i.e., packet) synchronization. Then, before passing the decoded message data to the microprocessor 11 for processing, the radio receiver 9 can use the acquired frame and symbol timing information to decode the PSDU.

[0070] The microprocessor 11 can process the message data in any suitable manner. In some embodiments, it can display the temperature information graphically on the display screen 12 of the hub 7 for user viewing.

[0071] In some embodiments, the wireless thermostat 1 and the hub 7 can be configured to use Thread TM or ZigBee TM The specification transmits temperature message data from the wireless thermostat 1 to the hub 7. Using the corresponding components described above for performing radio transmission in opposite directions, the wireless thermostat 1 and hub 7 can be equipped for bidirectional radio communication. However, this is not required in all embodiments.

[0072] Figure 3 The diagram schematically illustrates various digital baseband processing units implemented by synchronization and decoding logic 10 for detecting and decoding received data frames. For simplicity, operations such as filtering and residual frequency offset tracking are not shown.

[0073] Complex-valued baseband samples I&Q are received in a data-assisted joint timing and frequency synchronization unit 33 to determine symbol and frame timing synchronization data and frequency offset estimation data. Synchronization unit 33 is coupled to a CORDIC (Coordinate Rotation Digital Computer) unit 34 for performing carrier frequency offset (CFO) compensation on the input samples. The CFO-compensated complex samples are then passed to detector 31, which detects DSSS-encoded data symbols. Detector 31 outputs a decoded symbol stream to microprocessor 11 in 4-bit groups B. These decision symbols are also fed back to timing and frequency synchronization unit 33.

[0074] Figure 3 Use the following symbols:

[0075] n = chip index;

[0076] z(n) = complex basis band sample;

[0077] z'(n) = z(n) compensated for by carrier frequency offset (CFO);

[0078] pdata i (k) = represents the stored data of i different 32-bit DSSS chip sequences.

[0079] The timing and frequency synchronization unit 33 includes a correlator 35, referred to herein as a “dual” correlator 35, for performing data-aided joint timing and frequency estimation and associated synchronization logic 36. This utilizes knowledge of the data in the received symbols to eliminate the influence of modulation on the estimation of the delay and correlation-type carrier frequency offset estimators.

[0080] Because repeated synchronization words are received, additional checks on the time-domain distance between consecutive amplitude responses can be used to filter out false detections. This means that a shorter correlator with a lower detection threshold can be used to achieve a given level of sensitivity while reducing receiver complexity.

[0081] Figure 3 Synchronization unit 33 is associated with repeated synchronization words in order to calculate the following cross-correlation value u for each input baseband sample. n = w I(n) + jQ(n):

[0082]

[0083] Where the coefficient d i Includes pre-computed, stored, synchronized data, where d i =p i * p i+D pi is a sample corresponding to a predetermined synchronization symbol at the baseband.

[0084] Where D is the delay determined at design time (e.g., 8 or 16 samples), and

[0085] Where L corresponds to the length of the synchronization symbol at the sampling rate used in logic 10.

[0086] In some embodiments, the signal may be oversampled and / or upsampled, in which case the stored synchronization data may be proportionally increased accordingly. Cross-correlation operations can be performed using sample-by-sample multiplication.

[0087] Synchronization unit 33 can also generate a carrier frequency offset estimate based on the following equation:

[0088]

[0089] Where T is the sample period.

[0090] Assuming the carrier frequency offset is relatively constant over D samples, this estimate provides a good estimate of the carrier frequency offset, provided it is sampled when the correlation is aligned with the synchronization symbol of the input, i.e., at the moment corresponding to the peak of the absolute correlation value |Cn|, or at a time such as M n The sampled normalized amplitude measurement is given by the following formula:

[0091] in

[0092] As described below, qualified peaks in the relevant data can be determined by comparing them with amplitude thresholds. These peaks are stored in peak pool 60 and processed as described below to determine which peaks to use to generate the carrier frequency offset (CFO) estimate for CORDIC unit 34 and symbol timing information (gating time) for synchronizing detector 31.

[0093] CORDIC unit 34 receives frequency offset estimates from synchronization unit 33 and uses the latest received frequency offset estimate to rotate subsequent input samples by the corresponding phase angle to compensate for any carrier frequency offset. Then, the resulting CFO compensation sequence of complex baseband samples z'(n) is passed to detector 31.

[0094] Logic 10 can be implemented in hardware and can include a finite state machine (FSM) for coordinating the synchronization and decoding processes.

[0095] Figure 4 and Figure 5 This paper illustrates some challenges that may arise when using previously unused synchronization methods, and these challenges are addressed by the embodiments disclosed herein. They show the peak values ​​of the relevant amplitude over time, which are achieved by comparing the input signal with... Figure 2It is generated by correlating a predetermined preamble sequence as shown.

[0096] Unused methods can be used with any appropriate peak-finding algorithm to identify levels above the threshold (by...). Figure 4 and 5 The horizontal dashed line in the figure represents the peak value, and it can be declared that symbol timing synchronization has been achieved once three peak values ​​that meet the interval requirement are identified. The interval requirement is that each consecutive peak value appears after the previous peak value by one preamble symbol period plus / minus a jitter tolerance (e.g., + / -1%).

[0097] When the output is as follows Figure 4 As shown, the first peak 40, the second peak 41, and the third peak 42 appear exactly at the preamble symbol interval, which allows the method to work effectively.

[0098] However, if Figure 5 The output shown will cause a synchronization problem. In this example, the second peak 51 has a sidelobe peak 51a that is above the threshold, but the sidelobe peak appears less than 0.95 symbol periods after the previous peak 50, causing both the first peak 50 and the sidelobe peak 51a to be discarded, even though the first peak 50 is a valid peak. This then delays the declared synchronization by one symbol duration until the second peak 51, the third peak 52, and the fourth peak 53 have been identified. Delayed synchronization is undesirable in itself, but if this occurs several times within a block preamble, synchronization for that block may fail completely. False peaks can be sidelobes of valid peaks or any other erroneous peaks exceeding the threshold, such as peaks due to noise.

[0099] Conversely, if three false peaks that meet the interval condition occur, the receiver may incorrectly declare synchronization based on the timing of these false peaks, which would be incorrect and could lead to packet loss.

[0100] Typically, if synchronization loss can be reduced, the sensitivity of the radio receiver should be increased. Ideally, this should be done without excessively reducing selectivity (i.e., the receiver's ability to reject signals on channels other than the desired tuning channel).

[0101] Therefore, the embodiments disclosed herein employ a different approach. Instead of declaring preamble synchronization complete upon detecting a fixed number of qualified peaks, they simply calculate and output a set of symbol timing information and a carrier frequency offset estimate. Instead, they can apply different conditions to determine when to output symbol synchronization information and when to output the frequency offset estimate (i.e., not necessarily simultaneously). As more synchronization preambles are received, they also continue to generate and process subsequently received synchronization preamble-related data to detect any further qualified peaks and potentially generate updated timing and / or frequency synchronization information, which may be more accurate.

[0102] This could potentially lead to faster and more reliable synchronization of receiver 9. For example, by allowing CFO estimates to be computed based on phase values ​​determined over more than three peaks (e.g., averaged over five or more peaks), while allowing symbol timing to be determined based on a smaller number of peaks (e.g., using only three peaks if noise prevents synchronization over more than three peaks), better frequency offset estimates can be computed. This can improve the accuracy of CFO estimates without reducing the probability of successful frame synchronization.

[0103] Therefore, this synchronization and decoding logic 10 runs unconditionally until an SFD is detected, rather than terminating once synchronization can be declared.

[0104] More details on how to implement the method in some exemplary embodiments will now be provided, along with simulation data to validate the method.

[0105] Receiver Design Using Accumulated Dual Correlation (ADBC) in 802.15.4

[0106] The following description is given for IEEE 802.15.4 receiver 9, which uses the “double” correlator (“DBC”) method described above to repeatedly accumulate frequency offset estimates over the duration of the preamble sequence. For convenience, this method is referred to herein as cumulative double correlator or “ADBC”. However, it should be understood that the same basic principles can be applied to receiving different radio protocols or for different receiver architectures.

[0107] Even in challenging environments, such as strong co-channel interference signals, the dual correlator 35 in the synchronization unit 33 works collaboratively with the symbol detector 31 to unlock the symbol timing configuration.

[0108] Assuming a sampling rate of 8 megasamples per second (or 4 samples per chip), the analog waveform of symbol 0 (i.e., 0000'b) (which is an extended 32-bit chip sequence appearing eight times in the synchronization preamble of each frame) can be represented by a column vector w, consisting of 128 complex samples, written as...

[0109] w = [w0, w1, ..., w 127 (1)

[0110] Using equation (1) and the fact that there should be zero phase difference between the phases at the beginning and end of a symbol, this can be extended to 136 sample sequences v, i.e.,

[0111]

[0112] It can generate 128 sample vectors d, whose i-th element is calculated as

[0113]

[0114] The value of d, as stored synchronization data representing a predetermined synchronization sequence, is stored in a memory accessible to the synchronization and decoding logic 10, providing a reference waveform for symbol timing during the preamble-based synchronization process. These values ​​can be calculated by the receiver 9 as needed, or can be pre-calculated and stored during manufacturing. In other embodiments, different values ​​of the delay D, other than D=8, can be used as needed.

[0115] ADBC receiver 9 calculates the autocorrelation z between the received IQ samples. t andz t-8 ,Right now, When generating signal data from the input radio signal, the receiver will... t The latest 128 values ​​are stored in 128 sample registers, represented by a column vector w. After correlating w with the reference sequence d, the ratio γ is calculated using one of two possible methods.

[0116] In the first method, γ is calculated according to the following formula.

[0117]

[0118] In the second method, γ is calculated according to the following formula.

[0119]

[0120] Equation (5) can be considered an approximation of Equation (1). Although Method 2 uses approximate calculation results, it is expected to achieve similar performance to the first method. The complexity of the two methods is almost the same.

[0121] Figure 6 Three representative continuous cross-correlation samples of the correlation data generated by the dual correlator 35 are illustrated to aid in understanding the reference below. Figure 7 And the synchronization procedure described in the pseudocode below. Figure 6In this context, C represents the complex correlation value, which is determined according to one of the above equations (4) or (5) or further as above. n The calculated real-value ratio. Sample index D1 represents the peak value in γ, while D2 is the index of the sample immediately preceding the peak value, and unindexed values ​​are the samples immediately following the peak value. Considering three samples, rather than just the peak sample, can improve synchronization accuracy by allowing for possible timing errors.

[0122] Figure 7 The main steps of the synchronization process are illustrated, which can be implemented in synchronization unit 33 by a set of hardware finite state machines (FSMs), implementing the program shown in the following pseudocode. In variant embodiments, some or all of these steps or programs may alternatively be implemented by software executing on the processor, or as a combination of hardware and software. For a complete understanding, the following pseudocode should be considered in conjunction with... Figure 7 Come and read.

[0123] Figure 7 The pseudocode uses the following variables with the following meanings:

[0124] S: State variable -0 = IDLE; 1 = Accept new peaks; 2 = Ignore new peaks in γ

[0125] R = γ local The previous maximum peak intensity (initial value R=0)

[0126] H D2 H D1 H: Relevant total of CFO estimates

[0127] Δf = F: The latest CFO estimate

[0128] N: The gating offset of the trigger detector (initial value N=0)

[0129] C: The number of significant bits from the detector (initial value C = 0)

[0130] n: gating counter, n = 0, ..., 127, packed once every 128 samples (i.e., every 4 bits of symbol).

[0131] m: symbolic boundary variable

[0132] B: The latest four bits of xxxx'b output by detector 31

[0133] I DBC : Synchronization indicator, which indicates that the correlator (DBC) 35 has generated a flag indicating that the symbol timing has been reached, meaning that the estimated symbol boundary offset has been assigned to m.

[0134] I strobe: A gating trigger that indicates the gating signal is activated. When n==m, I strobe Set to 1 if it is set to 1, otherwise set to 0.

[0135] I invalid Invalid output indicator: Indicates that detector 31 has given invalid outputs that should be ignored.

[0136] I sync : Frame synchronization indicator, indicating that a valid frame synchronization word has been captured.

[0137] I drop1peak : Invalid peak indicator, due to incorrect spacing, indicating that the correlator (DBC) 35 should ignore subsequent peaks, possibly due to the detection of a symbol

[1110] . This allows for consideration of detection delays, such as those that may occur when detector 31 has a pipelined design.

[0138] It uses two threshold parameters, which can be configurable in some embodiments, for example, under the control of firmware executed in processor 11:

[0139] A: Threshold used to identify valid peak values

[0140] D: Threshold used to determine whether to accumulate frequency offset estimates

[0141] The process begins in an idle state (S=0) with a waiting time of 2. These events may be:

[0142] i) New peaks detected in the relevant data,

[0143] ii) Triggering from strobe counter n, or

[0144] iii) The 4-bit symbol output by detector 31.

[0145] In use, synchronization unit 33 calculates the ratio γ of the IQ samples for each input. For example... Figure 6 As shown, it performs a simple peak detection process to detect when three consecutive values ​​of γ rise and then fall. This signals the peaks, although not necessarily qualified peaks in terms of intensity or interval, to determine updated timing and / or frequency synchronization information.

[0146] Initially, the receiver searches for effective correlation peaks on γ to determine the start point of an effective 802.15.4 frame.

[0147] When a new peak is detected in γ, rewrite branch 71 is invoked. This checks whether unit 33 is accepting a new peak and whether the peak has an amplitude higher than threshold A and also higher than any previously identified peaks. It also checks whether the peak is not close to the interval of the last valid peak identified by rewrite branch 71 by an integer number of symbol widths (i.e., not in the expected position) (e.g., within a configurable limit of one or two samples). Assuming all these checks pass, this will detect the first peak of the new frame, but thereafter only peaks in unexpected positions will be detected (if they are very strong peaks). When a valid peak is detected, branch 71 starts detector 31. It also calculates a new frequency offset estimate Δf (also referred to as F in the following pseudocode) and outputs this estimate Δf to CORDIC 34. Instead of accumulating frequency offsets with earlier frequency offsets, it builds a new CFO estimate Δf for CORDIC 34, effectively “rewriting” any earlier estimates. It also outputs initial or updated symbol timing information to detector 31 by setting N = n. If this is not the first peak of the frame, the symbol timing information will overwrite any earlier symbol timing information—either immediately or when the final frame synchronization is declared. Lines 25 through 40 of the ADBC ​​program “Program 3” below specifically deal with rewriting branch 71.

[0148] The trigger from the gating counter initiates the cumulative branch 72. This checks whether unit 33 accepts a new peak and whether the current peak exceeds the threshold D used for cumulative frequency offset estimation. It also checks whether the peak is an integer number of symbols from the previous qualified peak interval, i.e., k x 128 samples. If all these checks pass, it continues to update the maximum peak intensity variable R and performs peak perimeter calculations using the corresponding initial or cumulative values ​​from previous peak detections (see [link to previous peak detection]). Figure 6 The three relevant sample values ​​C) D2 C D1 The coherent accumulation of C. It is based on the complex correlation value of the accumulation with the maximum amplitude (to account for any sampling timing errors) to calculate the updated frequency offset estimate Δf for use by CORDIC 34. Lines 10 to 24 of the ADBC ​​program “Program 3” below specifically deal with the accumulation branch 72.

[0149] By using these branches 71 and 72, synchronization unit 33 determines symbol timing information (denoted by N) and calculates the initial and updated frequency offset estimate Δf (hereinafter also referred to as F in pseudocode) and symbol synchronization solely based on peak amplitude and interval, without detecting a fixed number of peaks. Assuming that further qualified new peaks are detected while processing the preamble, the frequency and symbol estimates can be updated over time. Using an adaptive threshold to detect qualified peaks in rewrite branch 71 effectively reduces the risk of losing true peaks due to peak-locked receiver synchronization with spurious frames, while also effectively reducing the risk of true peaks being overwritten by spurious peaks.

[0150] Compared to the synchronization accuracy that correlator 35 can achieve alone, logic 10 uses detector 31 to improve synchronization accuracy, especially in the presence of noise or interference.

[0151] A new symbol from detector 31 triggers a "Reset or Stop" branch 73. This uses the output of symbol detector 31 to check whether the preamble contains only the synchronization symbol 0000'b, or whether the SFD has been reached at 0xA7 = 11100101'b (the bits are represented here in reverse bit order, purely for implementation reasons). If the first SFD symbol is detected, detection of new peaks stops 74, and the arrival of the second SFD symbol, which is the next detected symbol, causes synchronization unit 33 to signal to detector 31 and / or microprocessor 11 that frame synchronization has been achieved 76. If another symbol is detected during the preamble, or if neither the first nor the second SFD symbol is detected in the sequence, an error is detected and the synchronization unit is reset 75. This causes the peak search process to restart with default initial values. The synchronization word procedure "Program 2" below deals more specifically with the reset or stop branch 73.

[0152] Synchronization unit 33 implements three concurrently operating programs: a gating counter program, a synchronization word capture program, and an accumulation correlation program. Studying the following pseudocode will provide a better understanding of the actions of each program.

[0153] The following "Gantler Counter" program manages the gantler counter, which is used to determine symbol timing information and the interval used to check for peak values.

[0154] Program 1: Gantt Counting FSM

[0155]

[0156] The following "synchronization word" procedure specifically involves Figure 7 The "Reset or Stop" branch 73. Specifically, lines 15 through 19 involve the detection of symbols

[1110] and

[0101] of the Start Frame Delimiter (SFD). If symbol

[0101] is output by detector 31, a signal is issued in line 18; and due to an unexpected symbol, synchronization unit 33 is reset 75 in line 19.

[0157] Program 2: Synchronization word capture

[0158]

[0159] In the ADBC ​​program below, lines 25 through 40 specifically involve... Figure 7 The rewrite branch 71, while lines 10 through 24 involve the cumulative branch 72.

[0160] Program 3: Accumulating Dual Correlator FSM

[0161]

[0162] Simulation results

[0163] The relative performance of embodiments using different correlator threshold ranges was evaluated in Matlab simulations. Figure 8 and Figure 9 The different thresholds in the model are the values ​​of threshold A, but in the simulation, threshold D also varies by setting D = A - 0.03.

[0164] Figure 8 Sensitivity performance is shown. It simulates group error rate (PER) performance with sensitivities ranging from -105 dBm to -85 dBm. According to the simulation, a sensitivity of -103 dBm at a group error rate level of 0.01 should be achievable by lowering the DBC threshold to approximately 0.37, and no error flattening was observed in the high SNR region.

[0165] Figure 9 The selectivity performance is shown. Performance is simulated at selectivity levels from 0 to -20 dB. According to the simulation, receiver 9 should achieve approximately -2 dB of selectivity at 0.01 PER when the DBC threshold is 0.37.

[0166] Therefore, the method described in this paper has been shown to provide good performance by utilizing long repeating preambles to accurately and reliably obtain symbol timing and frequency offset estimates.

[0167] Those skilled in the art will understand that the invention has been described by way of one or more specific embodiments, but is not limited to these embodiments; many variations and modifications are possible within the scope of the appended claims.

Claims

1. A wireless device, comprising: Radio receiver; Hardware correlator; as well as Synchronization and decoding logic, The radio receiver is configured as follows: Receive radio frequency signals as radio signals, wherein the radio frequency signals encode data frames having a synchronization preamble containing multiple instances of a predetermined synchronization sequence, and When the radio receiver receives the radio signal, it generates signal data representing the received radio frequency signal from the received radio frequency signal. The hardware correlator is configured to correlate the signal data with stored synchronization data to generate synchronization correlation data, wherein the stored synchronization data represents the predetermined synchronization sequence, and wherein the synchronization correlation data is generated by correlating signal data representing the synchronization preamble with the stored synchronization data; and The synchronization and decoding logic is configured as follows: While generating the synchronization-related data, a first group of one or more peaks is identified in the synchronization-related data, and first synchronization information for the wireless device is determined from the first group of one or more peaks; The first synchronization information is used to enable the wireless device to synchronously receive at least a first portion of the radio frequency signal; After generating more of the synchronization correlation data, a second set of one or more peaks is identified in the synchronization correlation data, and second synchronization information for the radio device is determined from the second set of one or more peaks; and The second synchronization information is used to enable the wireless device to synchronously receive at least a second portion of the radio frequency signal.

2. The wireless device according to claim 1, wherein the first synchronization information includes symbol timing information.

3. The wireless device according to claim 1 or 2, wherein the first synchronization information includes a frequency offset estimate.

4. The wireless device according to claim 1 or 2, wherein the second synchronization information includes symbol timing information.

5. The radio device according to claim 1 or 2, wherein the second synchronization information includes a frequency offset estimate.

6. The wireless device according to claim 1 or 2, wherein the wireless device is configured to generate the signal data from the received radio signal when the radio receiver is receiving the radio signal.

7. The wireless device according to claim 1 or 2, wherein the wireless device is configured to determine the first synchronization information and the second synchronization information when the wireless device is generating the synchronization-related data from the signal data representing the synchronization preamble.

8. The wireless device according to claim 1 or 2, wherein the wireless device is configured to use the first synchronization information to synchronize the reception of at least a first portion of the synchronization preamble of the radio frequency signal, and to use the second synchronization information to synchronize the reception of at least a second portion of the synchronization preamble of the radio frequency signal.

9. The wireless device of claim 1 or 2, further comprising a symbol detector for detecting symbols from the signal data, wherein the wireless device is configured to synchronize the symbol detector using at least the first synchronization information or the second synchronization information.

10. The wireless device of claim 1 or 2, wherein the wireless device is configured to accumulate frequency synchronization information determined from one or more peaks of a corresponding group, and to use the accumulated information to synchronize the reception of at least a portion of the radio frequency signal by the wireless device.

11. The wireless device of claim 10, wherein the wireless device is configured to determine an average frequency offset estimate as a coherent average of a plurality of frequency offset estimates determined from corresponding peaks in the synchronization correlation data, and to use the average frequency offset estimate to synchronize the reception of at least a portion of the radio frequency signal by the wireless device.

12. The wireless device of claim 1 or 2, wherein the wireless device is configured to select frequency synchronization information determined by one peak or a set of peaks from a larger amount of frequency synchronization information determined by a plurality of corresponding peaks or corresponding groups of peaks, and to use the selected frequency offset estimation to synchronize the reception of at least a portion of the radio frequency signal by the wireless device.

13. The wireless device according to claim 1 or 2, wherein the wireless device is configured to determine whether a later-determined synchronization information should replace an earlier-determined synchronization information, and if the wireless device determines that the later-determined synchronization information should replace the earlier-determined synchronization information, then uses the later-determined synchronization information to synchronize the reception of at least a portion of the radio frequency signal by the wireless device, and if the wireless device determines that the later-determined synchronization information should not replace the earlier-determined synchronization information, then discards the later-determined synchronization information or accumulates the later-determined synchronization information with the earlier-determined information.

14. The wireless device of claim 1 or 2, wherein the wireless device is configured to detect peaks within the synchronization correlation data when generating the synchronization correlation data, and to determine corresponding updated synchronization information in response to the detection of a new peak in the synchronization correlation data for at least one or more peaks.

15. The wireless device of claim 1 or 2, configured to identify each set of one or more peaks by performing a peak analysis process on the synchronization-related data, wherein the peak analysis process includes determining whether a new peak satisfies a defined condition to be included in a set of one or more peaks used to determine synchronization information of the wireless device.

16. The wireless device of claim 15, wherein the limiting condition includes an amplitude condition requiring that the peak value be associated with a correlation value in the synchronization correlation data having an amplitude greater than a threshold.

17. The wireless device of claim 15, wherein the limiting condition includes a timing condition requiring that the peak in the synchronization-related data be separated from an earlier peak by a time interval corresponding to the duration of the predetermined synchronization sequence.

18. The radio device of claim 15, wherein the radio device includes a symbol detector, wherein the limiting condition includes a symbol detection condition, and the peak analysis process includes using the symbol detector to determine whether a peak in the synchronization correlation data is consistent with the symbol of the predetermined synchronization sequence.

19. A method for synchronizing radio devices, the method comprising: The signal data is correlated with the stored synchronization data to generate synchronization correlation data, wherein the signal data represents the received radio frequency signal, the received radio frequency signal encodes a data frame having a synchronization preamble having multiple instances of a predetermined synchronization sequence, wherein the stored synchronization data represents the predetermined synchronization sequence, and wherein the synchronization correlation data is generated by correlating the signal data representing the synchronization preamble with the stored synchronization data. While generating the synchronization-related data, a first group of one or more peaks is identified in the synchronization-related data, and first synchronization information for the wireless device is determined from the first group of one or more peaks; The first synchronization information is used to enable the wireless device to synchronously receive at least a first portion of the radio frequency signal; After generating more of the synchronization-related data, a second set of one or more peaks is identified in the synchronization-related data, and second synchronization information for the radio device is determined from the second set of one or more peaks; as well as The second synchronization information is used to enable the wireless device to synchronously receive at least a second portion of the radio frequency signal.

20. The method of claim 19, wherein: The first synchronization information includes timed synchronization information; The second synchronization information includes frequency synchronization information; and The first set of peaks contains fewer peaks than the second set of peaks.

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