63 results about "Spreading factor" patented technology

The invention relates to the technical field of wireless communication signal big data analysis, and discloses a LoRa unmanned aerial vehicle communication signal-oriented identification and analysis method, which comprises the steps of obtaining radio signal discrete data in a monitoring area, executing short-time Fourier transform to generate a time-frequency two-dimensional spectrogram, and identifying and intercepting a LoRa signal noisy IQ time sequence by using a convolutional neural network; mapping the sequence into a high-dimensional feature tensor, inputting the high-dimensional feature tensor into a slope statistical attention generative adversarial network, calculating a first-order differential tensor by using a generator, carrying out kernel convolution on the first-order differential tensor and preset linearity statistics to generate an attention mask, and reconstructing a de-noised IQ time sequence by using a bidirectional long-short-term memory network after Hadamard product gating; according to the method, the tensor gating operator based on the physical statistical law is embedded in the neural network, so that the common problem that physical semantic drift is easily generated by a generative model at an extremely low signal-to-noise ratio is solved.

The invention relates to the technical field of wireless communication, in particular to an emergency LoRa communication method based on multi-band cooperation and dynamic resource modulation. The method comprises the following steps: S1, dynamically acquiring communication environment information, channel quality information and network load information; s2, dynamically analyzing and selecting an initial target spreading factor based on the information; s3, setting a preset factor optimization target by taking the minimum bit error rate as a target, and dynamically adjusting and obtaining a current optimal spreading factor; and S4, based on the current optimal spread spectrum factor, performing dynamic allocation of spectrum resources by adopting a dynamic channel allocation mechanism and a reinforcement learning algorithm of adaptive network load balance, and learning a network state in real time through the reinforcement learning algorithm so as to dynamically select an optimal channel allocation strategy to perform emergency communication. According to the method, communication parameters can be adaptively adjusted, the network efficiency and reliability are remarkably improved, the system capacity, the real-time performance and the robustness in a mobile scene are enhanced, and reliable communication guarantee is provided for rescue in an extreme environment.

The invention discloses a LoRa signal demodulation and decoding method and system based on blind identification, and the method comprises the steps: carrying out the down-conversion processing of a LoRa signal, and generating a baseband signal corresponding to the LoRa signal; identifying linear sweep frequency characteristics of the baseband signal based on short-time Fourier transform, and judging whether the baseband signal is a CSS modulation signal according to the linear sweep frequency characteristics; if the signal is a CSS modulation signal, detecting the signal bandwidth based on spectrum estimation, and identifying a spreading factor by adopting a peak detection and zero-cross detection method; and configuring parameters of a preset LoRa demodulation and decoding module in real time according to the signal bandwidth and the spreading factor, and demodulating and decoding the LoRa signal according to the configured LoRa demodulation and decoding module to obtain LoRa communication signal content. Through development of a deep learning-based adaptive detection algorithm, blind identification and parameter estimation of LoRa signals in a complex electromagnetic environment are realized, and then robust demodulation and decoding are completed.

A method and system for improving channel estimation for multi-user, multiple-input, multiple-output (MU-MIMO) systems through dynamic DM-RS port allocation in a 5G New Radio network is provided. The method comprises of allocating, by a Scheduler aware UE port allocation unit, one or more MU-MIMO ports to a plurality of code division multiplexing (CDM) groups for a plurality of UE users, performing, by a code selection unit, a code selection based on a number of allocated MU-MIMO ports, determining, by a spreading factor unit, a spreading factor allocated for each of the MU-MIMO ports in each of the plurality of CDM groups, determining, by a signalling unit, a Downlink Control Information (DCI) signalling of a Partial Port Occupancy (P-Poi) transmission for each UE and obtaining, by a channel estimation unit, channel estimates at the receiver through VSFOCC de-spreading based on the P-POI assigned for each of the MU-MIMO ports.

A method (400, 500) of transmitting data, by a utility metering device (200) and to a further device, using long range, LoRa, communications. The method (400, 500) comprises assigning, to each item of data (302a-j) of a plurality of data (300) to be transmitted by the utility metering device (200), a priority level from a plurality of priority levels; determining a desired transmission interval based a desired energy consumption from a power source powering the utility metering device (200), during transmission, by the utility metering device, of a predetermined size of data at a first data rate associated with a first spreading factor, wherein the first data rate is one of a plurality of predefined data rates, each data rate of the plurality of data rates being associated with a corresponding spreading factor, and wherein the first data rate is the lowest data rate of the plurality of predefined data rates and the first spreading factor is the highest spreading factor of the corresponding spreading factors; determining a transmission data rate; determining which one or more items of data, of the plurality of data, to transmit at the desired transmission interval, based on the determined transmission data rate and the priority level assigned to each item of data; and transmitting the determined one or more items of data to the further device at the desired transmission interval using the determined transmission data rate.

The invention belongs to the technical field of wireless system application, and particularly relates to a radio frequency-based wireless signal test platform system and a building method thereof, and the system comprises an Android master control terminal, a radio frequency communication module and an environment sensing unit; the android master control terminal carries an industrial-grade android equipment operating system, an integrated presentation layer, a business logic layer and a data access layer; the radio frequency communication module is connected with the Android master control terminal through a serial interface and is used for dynamically configuring frequency bands, spreading factors and bandwidth parameters; an environment database is established by setting an Android master control terminal, a radio frequency communication module and an environment sensing unit, adaptive communication capability testing of various radio frequency modules is realized, wireless signal data can be visually tested anytime and anywhere by using an established testing platform and environment data, and dependence on a traditional darkroom and a frequency spectrograph is avoided; and self-adaptive setting of frequency bands, spreading factors and bandwidths of the module in different environments is realized through an existing environment database.

A communications system may include first and second electronic devices. The first device may transmit an ultra-wideband (UWB) signal to the second device. The UWB signal may include pulses that represent a ranging frame. The pulses may include a series of pulses representing a physical layer (PHY) payload of the ranging frame. The second device may estimate a range to the first device and / or a location of the first device based on a correlation of the series of pulses representing the PHY payload of the ranging frame. The first device may apply a coding scheme to the PHY payload that reduces, or minimizes, a bit error rate of the correlation at the second device, may apply a cyclic redundancy check, may transmit the PHY payload using a spreading factor greater than one, and / or may apply encryption to the PHY payload for integrity check purposes.

A modulation control system for a power electronic converter, comprising: a power electronic converter comprising a controllable electronic switch; and a control device configured to: determine a carrier frequency range based on the primary carrier frequency and a spreading factor, where the spreading factor is a value not equal to 1; generating a control signal including a variable switching frequency, where the variable switching frequency has a first switching frequency value within a carrier frequency range, and after a predetermined number of cycles elapsed at the first switching frequency value, the variable switching frequency has a second switching frequency value within the carrier frequency range; and providing a control signal to the power electronic converter such that the controllable electronic switch changes state at a variable switching frequency.

Disclosed are a signal power adjustment method, system, device and medium for a reference station, the method being suitable for a reference station connected with a plurality of mobile stations, the method comprising: sending a LoRa signal to a plurality of mobile stations at the same time according to a preset transmission power, so that each mobile station calculates a sensitivity gain value according to the LoRa signal, the spreading factors of the mobile stations are different from one another; and determining a corresponding target adjustment power according to the sensitivity gain value fed back by each mobile station, and adjusting the communication power of each mobile station to the target adjustment power. According to the method, the signal transmitting power of the mobile stations with different spreading factors can be determined and regulated, the contradiction that the power consumption of a high-spreading-factor user is too high and the reliability of a low-spreading-factor user is insufficient is effectively balanced on the premise of ensuring that all users reach the target communication reliability, remarkable optimization of the total power consumption of the system is realized, and the system reliability is improved. And meanwhile, the self-adaptive capability and the overall energy efficiency of the network in a complex channel environment are improved.

The present disclosure provides a method for satellite communication comprising: transmitting, by an endpoint, a set of protocol data units (PDUs) at different spreading factors with a session request bit; receiving, by a satellite, a subset of the PDUs based on link conditions; constructing, by the satellite, a hash based on an endpoint ID and a minimum spreading factor of received PDUs; packing the hash with other data in a feedback channel; monitoring, by the endpoint, the feedback channel for a matching hash; if a matching hash is found, continuing transmission at the signaled spreading factor and monitoring a command packed in the feedback channel; and if no matching hash is found, attempting transmission at different spreading factors. The method further comprises reacting to received commands by stopping transmission, increasing spreading factor, decreasing spreading factor, or continuing transmission based on the command value.

The invention discloses a LoRa physical layer data tamper-proofing method based on signal orthogonality. The method comprises the steps of obtaining a to-be-embedded position based on a payload in LoRa physical layer data; embedding the original mark information in the to-be-embedded position to obtain a composite signal; transmitting the composite signal; decoding the composite signal to obtain the position change condition of the original mark information in transmission; and based on the position change condition, obtaining a judgment result of whether the LoRa physical layer data is tampered or not. According to the LoRa physical layer data tamper-proofing method based on the signal orthogonality, the inherent characteristics of the LoRa physical layer signals are fully utilized, the mark information is embedded into the spectrum leakage area of the LoRa physical layer data in a low-power and low-spreading-factor orthogonal signal form, and the tamper-proofing efficiency of the LoRa physical layer data is improved on the premise that the hardware complexity is not remarkably increased. And high-security data transmission is realized.

The invention relates to a bidirectional wireless communication frequency hopping method, system and device and a medium. The method comprises the following steps: introducing a frequency hopping mechanism based on a double-base-frequency channel and a plurality of wireless communication channels into bidirectional wireless communication connection between a master end and a slave end, and when communication of the master end and the slave end is disconnected, automatically switching to an idle channel without interference for communication reconnection through channel frequency hopping and one-by-one channel self-inspection. And when the master end and the slave end enter a normal communication connection state, initializing the master end and the slave end to be a synchronous frequency hopping sequence, calculating an optimal spreading factor of a wireless communication channel synchronously skipped by the master end and the slave end by adopting a self-adaptive spreading factor algorithm, and keeping synchronous frequency hopping data transmission between the master end and the slave end based on the optimal spreading factor. By adopting the method, the speed and success rate of reconnection after communication disconnection of the master end and the slave end can be improved, and the reliability and stability of wireless communication data transmission are enhanced.

To prevent a self-interference signal from being generated while using a fractional spreading factor for an LoRa modulation scheme.SOLUTION: A communication system (1) includes a transmission terminal (2) that performs FSF-LoRa modulation using a spreading factor (s) and a fractional coefficient (ρ) on transmission data to generate a transmission signal, and a gateway (3) that demodulates a reception signal obtained by receiving the transmission signal using the spreading factor and the fractional coefficient and outputs an estimated demodulation signal obtained by estimating the transmission data. The transmission terminal converts transmission data into a combination of symbols, and spreads each of the symbols included in the combination with a first reference chirp signal generated based on a spreading factor and the fractional coefficient. The gateway performs a sampling process on the received signal at a sampling frequency that satisfies a Nyquist criterion to generate an equivalent low-pass signal, and despreads the equivalent low-pass signal with a second reference chirp signal generated based on a spreading factor and the fractional coefficient.SELECTED DRAWING: Figure 8

This invention discloses a LoRa chip adaptive spreading factor selection terminal device and method. The terminal device includes a main control microprocessor, an RF transceiver, and a mechanical state sensor connected to the main control microprocessor. The main control microprocessor extracts the first-order differential values ​​of RF parameters and simultaneously acquires vibration acceleration magnitude values, mapping them to a two-dimensional discrete state set. An environment mask is generated based on the comparison between the instantaneous rate of change of the vibration acceleration magnitude and a set threshold. In response to the environment mask being in a first logic state, the spreading factor is updated and issued according to an action value lookup table. In response to the environment mask being in a second logic state, the update operation is blocked, and a spreading factor locking command is issued. This application can achieve cross-domain feedforward intervention by fusing physical states, blocking the invalid spreading factor rise caused by instantaneous broadband noise, and reducing node ineffective power consumption.

This invention belongs to the field of non-cooperative signal processing technology, specifically relating to a method for estimating LoRa communication signal parameters based on fractional Fourier transform. The invention constructs a fractional Fourier transform model of the LoRa signal and determines the search range and accuracy of the fractional order. It then performs a fractional Fourier transform on the LoRa signal and obtains the matching order of the LoRa signal's fractional Fourier transform by searching for the peak values. Subsequently, under the matching order, the fractional-domain frequencies of the two peak values ​​of the LoRa fractional Fourier transform are searched. Finally, the bandwidth and spreading factor parameters of the LoRa signal are calculated based on the relationship between bandwidth, spreading factor, matching order, and peak frequencies. The performance of this method under different signal-to-noise ratio conditions is evaluated using Monte Carlo simulation. This method can achieve relatively good parameter estimation of LoRa signal bandwidth and spreading factor.

The invention relates to an uplink LoRa adaptive transmission method based on RIS differential index modulation, and the method comprises the steps: introducing RIS and IM into the uplink transmission of LoRa, and carrying out the differential modulation of a joint IM entity in a space-time domain. The RIS is deployed near the LoRa node as part of a transmitter, and additional information is communicated by building RIS space-time blocks, thereby enhancing the uplink transmission link of the single antenna LoRa node with the gateway. Meanwhile, in order to further improve the performance of the system, an adaptive spreading factor (SF) selection strategy is introduced. According to the invention, under the design based on the RIS differential IM, the CSI demand is effectively eliminated, and the LoRa transmission rate is significantly improved.

The invention provides an observation data transmission method and system based on LoRa modulation, and the method comprises the steps: obtaining observation data, and carrying out the multi-stage polarization code coding under a preset spreading factor sequence, and obtaining a plurality of bit sequences; the spreading factors corresponding to the bit sequences are different; respectively executing a LoRa modulation step based on the plurality of bit sequences to obtain a plurality of LoRa symbols with different frequencies, and transmitting the plurality of LoRa symbols; the LoRa modulation step comprises the following steps: generating a chirp signal based on a spreading factor of a bit sequence; dividing a bit sequence according to the spreading factor, and obtaining a plurality of pre-modulation data; and performing frequency offset based on the chirp signal and the plurality of pre-modulation data to generate a LoRa symbol. According to the invention, a plurality of LoRa symbols with different frequencies are obtained based on different spreading factors, so that when the LoRa symbols in a frequency range are interfered in a transmission process, other LoRa symbols can still be continuously transmitted without being influenced by interference, and the reliability of data transmission is improved.

A system and a method thereof for performing modulation and demodulation based on a chirp spread band technique are disclosed. A system for performing modulation and demodulation based on a chirp spread band technique according to one embodiment of the present disclosure includes: a transmitter that transmits a chirp signal; and a receiver that receives and demodulates the chirp signal. The transmitter determines the number of data bits (M) modulated in a unit symbol based on a first residual carrier frequency offset and a spreading factor (SF), and transmits a first chirp signal obtained by modulating the first data bits in at least one symbol according to the determined number of data bits modulated in the unit symbol to the receiver. The receiver may transmit information indicating a second residual carrier frequency offset detected based on the received first chirp signal to the transmitter.

A resource configuration method and device. The method comprises: a terminal device receives configuration information from a network device, wherein the configuration information is used for configuring a transmission bandwidth of a waveform for the terminal device, so that the terminal device can transmit data with the network device on the basis of the transmission bandwidth. The transmission bandwidth is determined on the basis of a sequence spreading factor, the sequence spreading factor is a preset value, and the waveform generation comprises performing, on the basis of the sequence spreading factor, sequence spreading and frequency-domain spectral shaping (FDSS) on a symbol sequence carried by the waveform. A transmission bandwidth is allocated to a terminal device by means of a sequence spreading factor, so as to ensure the communication capacity or increase the communication capacity on the basis of a given sequence spreading factor (i.e., on the basis of ensuring the OBO gain and PAPR gain).

The present invention discloses a multi-user spatial IoT transmission method based on LFM, configuring corresponding slopes for LFM-modulated time-frequency waveforms for different users in order to determine the modulated signal of any user, wherein the slope configured for said user satisfies a fractional multiplicative slope without changing the frequency spreading factor; determining, on the basis of the phase-frequency relationship, a time-domain signal for the LFM-modulated signal of any user, in order to perform a transmission on the basis of the determined time-domain signal; determining a time-domain signal of the unmodulated and down-chirped LFM signal corresponding to any user;the processing of the time-domain signal from any of said users based on the time-domain signal of said unmodulated and down-chirped LFM signal; the signal obtained after signal processing is subjected to a discrete Fourier transform, which is used to demodulate the signal received from any of the users. To reduce the transmission power demand, obtain low energy consumption, propose a simultaneous multi-user scheme and achieve simultaneous multi-user access and transmission with the same time-frequency resources. [Fig.1];

The application relates to the technical field of wireless networking, in particular to a dynamic ad hoc networking method and system for intercoms, which comprises the following steps: for a pre-established intercom network, in the process of adjusting the transmission rate of each node by an RRAA algorithm, the length of the next window of each window of each node is obtained; the time interval of two adjacent adjustment of the spreading factor of each node is recorded as a spreading factor stable interval, whether to adjust the spreading factor of each network is evaluated by comparing the frame error rate of each node in each window and the value of MTL and ORI in the spreading factor stable interval of each window; the spreading factor of each node is adjusted; in the route discovery process of the AODV protocol, the RREQ received by each node is updated; whether to discard the non-first RREQ received by each node is evaluated; and the routing selection of the intercom is carried out according to the AODV protocol. The application aims to improve the throughput and communication performance of the intercom network.

The present application relates to the technical field of communications, and in particular to an encoding method, a decoding method, and an apparatus. The present application can be applied to the IEEE 802.11ax standard, the 802.11be standard, and the 802.11bn standard, as well as other standards of the IEEE 802.11 series, such as the 802.15 standard, the 802.11bf standard, the IMMW standard, or the SparkLink standard. The method comprises: a first station acquires information bits, performs LDPC encoding on the information bits on the basis of a check matrix, obtains encoded bits, and outputs a sequence. After obtaining information to be decoded, a second station performs LDPC decoding in combination with the check matrix to obtain information bits. A code length corresponding to the check matrix is 7776, a code rate corresponding to the check matrix is 2 / 3, and a spreading factor of the check matrix is 162. The check matrix can better match a longer code length, thereby improving encoding and decoding performance.

The invention discloses a multi-user anti-interference decision-making method based on sparse strategy propagation. The method comprises the following steps: step 1, determining the number of divided sub-time slots of users according to an interference detection history; 2, determining the information transmission rate of the sub-time slot according to the spreading factor; 3, determining system throughput and an optimization target according to the signal-to-noise ratio of a receiving end; 4, determining a state space, an action space, a state transition probability matrix and rewards in the decision process; step 5, obtaining lower-layer main network parameters according to the empirical samples and the loss function; step 6, obtaining an upper layer main network parameter according to the experience sample and the loss function; and 7, obtaining an optimal anti-interference strategy according to iterative training. According to the method, the decision complexity is reduced, and dimension disasters are avoided.

The application relates to a bidirectional wireless communication frequency hopping method, system, device and medium. The method comprises the following steps: introducing a frequency hopping mechanism based on a double-base frequency channel and a plurality of wireless communication channels in a bidirectional wireless communication connection between a master and a slave, when the master and the slave are disconnected, the channel is hopped and self-checked one by one, the master and the slave can be automatically switched to an idle and interference-free channel to reconnect, when the master and the slave are in a normal communication connection state, the master and the slave are initialized as a synchronous frequency hopping sequence, an adaptive spreading factor algorithm is used to calculate the optimal spreading factor of the wireless communication channel of the synchronous jump of the master and the slave, and the synchronous frequency hopping data transmission between the master and the slave is kept based on the optimal spreading factor. The method can improve the speed and success rate of the master and the slave after the communication is disconnected, and the reliability and stability of wireless communication data transmission are enhanced.

The invention relates to a transmission frame construction method and device, computer equipment, a readable storage medium and a program product. The method comprises the following steps: acquiring a total frame length of a preset transmission frame, a number of subframes of the preset transmission frame and a subframe length, and acquiring a first ratio between a first length of a shielding part of the preset transmission frame and the total frame length; for at least one information missing sub-frame in the preset transmission frame, sorting the information missing sub-frames along the intra-frame field analysis direction of the preset transmission frame, and for the frame header of the last sub-frame in the sorting result, acquiring a second length of the shielded part of the frame header shielded by the obstacle; determining a data extraction proportion of the preset transmission frame based on the first ratio, the number of subframes, the second length and the subframe length; further selecting an interleaving parameter and a coding rate based on the data extraction proportion and the transmission efficiency; and obtaining a spreading factor based on the anti-interference tolerance, and finally determining a target transmission frame. According to the method provided by the invention, reliable transmission of signals can be ensured to the greatest extent.

The invention provides an adaptive modulation communication method, terminal equipment and gateway equipment. The communication method comprises the following steps: periodically receiving broadcast signals sent by a gateway in a common channel; determining a signal-to-noise ratio based on the signal power of the broadcast signal; determining a spreading factor based on the signal-to-noise ratio; and after establishing communication with the gateway, performing communication on the private channel by using the spreading factor. In this way, when the distances between the terminal devices and the gateway are different or the environment is changed, different terminal devices can communicate with the gateway by adopting different spreading factors, the false wake-up rate and power consumption of the terminal devices are remarkably reduced, and signal transmission interference between the terminal devices is reduced.

This invention discloses a low-power, high-throughput 5G LDPC decoder implementation method, specifically comprising: Step 1, calculating the parameters required for decoding from the input parameters; Step 2, based on the spreading factor Z... c The values ​​are stored in different blocks according to different storage methods; Step 3: Based on the expansion factor Z c The value of determines whether to perform layer splitting transformation on the base matrix and update the required posterior probability information of the variable nodes; Step 4: Update the information of the check nodes and the posterior probability information of the variable nodes within the layer; Step 5: Implement layered iterative decoding; Step 6: After updating the information of all check nodes in each layer and reaching the set number of iterations, the decoding iteration is completed, and the output processing of the decoding result begins. This method significantly reduces the required resources; and by utilizing the orthogonality of adjacent layers of the split matrix, the intra-layer pipelining operation improves the decoder throughput after reducing the decoding parallelism. A low-consumption, high-throughput 5G LDPC decoder implementation device is also disclosed.

The invention discloses a code rate adjusting method and system based on RTK differential data transmission, and belongs to the field of low-power-consumption wide area networks, and the method comprises the steps: setting a spreading factor of a LoRa-RTK communication radio station; acquiring receiving sensitivity and a code rate, and acquiring a first threshold value and a second threshold value of the receiving sensitivity based on the spreading factor; based on a first threshold value and a second threshold value, judging the receiving sensitivity and the code rate: if the receiving sensitivity is smaller than the first threshold value and the code rate is not equal to a preset default code rate value, increasing the code rate, and repeating the acquisition and judgment process until the receiving sensitivity is larger than the first threshold value and the code rate is not equal to the preset default code rate value; and if the receiving sensitivity is greater than a second threshold value and the code rate is not equal to a preset default code rate value, reducing the code rate, and repeating the acquisition and judgment process until the receiving sensitivity is less than the second threshold value and the code rate is not equal to the preset default code rate value. According to the method disclosed by the invention, the communication efficiency and reliability of the LoRa-RTK communication radio station can be effectively balanced.

The application discloses a LoRa physical layer data tamper-proofing method based on signal orthogonality, which comprises the following steps: obtaining a to-be-embedded position based on a payload in LoRa physical layer data; embedding original mark information in the to-be-embedded position to obtain a composite signal; transmitting the composite signal; decoding the composite signal to obtain a position change condition of the original mark information in transmission; and obtaining a judgment result of whether the LoRa physical layer data is tampered with based on the position change condition. The LoRa physical layer data tamper-proofing method based on signal orthogonality fully utilizes inherent characteristics of LoRa physical layer signals, embeds mark information in the form of low-power and low-spread factor orthogonal signals into a frequency spectrum leakage area of LoRa physical layer data, and realizes high-security data transmission without significantly increasing hardware complexity.

This invention relates to the field of data link anti-interference transmission technology, specifically to a method and system for anti-interference transmission of data links for high-speed aircraft. The method involves transforming the digital baseband received signal of the high-speed aircraft to obtain a two-dimensional time-frequency energy distribution map, identifying the interfering signal, and extracting its received power value. It then performs spatial spectrum estimation on the interfering signal to obtain its direction of arrival (AOA), and calculates the estimated distance of the interfering source by combining this with terrain elevation data. The method also calculates the AOA and transmission distance of the useful signal. Based on the estimated distance of the interfering source, the transmission distance of the useful signal, and the received power value, it calculates the current interference-to-signal ratio (ISR) estimate. Finally, it processes the digital baseband received signal to obtain the current transmission frame bit error rate (BER). Based on the BER and the current IRR estimate, it adjusts the spreading factor and coding rate of the next transmission frame. This method improves the anti-interference capability of data link transmission for high-speed aircraft in low-altitude flight scenarios such as mountainous valleys.