CN115733547A - OSIC detection method under transmitting-receiving misalignment of underwater optical Massive MIMO communication system - Google Patents
OSIC detection method under transmitting-receiving misalignment of underwater optical Massive MIMO communication system Download PDFInfo
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Abstract
The invention discloses an OSIC detection method under receiving and transmitting misalignment of an underwater optical Massive MIMO communication system, which can judge the offset direction of a receiving and transmitting end according to the magnitude of each direct current gain in a channel gain matrix after estimating the gain of each sub-channel by using an LS channel estimation algorithm, further determine the sequence of a detection column and the sequence in the column according to the offset direction pair, and eliminate interference to complete the detection of each signal. The invention carries out sequencing according to the offset direction, preferentially detects the signal without interference and then detects the signal with interference, greatly reduces error propagation brought by sequencing, ensures that the detected signal is more accurately subtracted by the later stage, ensures that the residual signal used in the subsequent stage has less interference, thereby improving the bit error rate performance and solving the problem of increased UWOC system bit error rate caused by inaccurate transceiving end and offset and diffusion of imaging light spots in an underwater imaging light Massive MIMO communication system.
Description
Technical Field
The invention relates to the technical field of an underwater optical Massive MIMO communication system, in particular to an OSIC (Ordered Successive Interference Cancellation) detection method under the condition of receiving and transmitting misalignment of the underwater optical Massive MIMO communication system.
Background
China has a wide ocean area, and activities such as underwater disaster early warning, resource exploration, environment, pollution monitoring and the like need to transmit data to the water surface in real time or quasi-real time by using an underwater communication technology and then transmit the data to a shore base or a satellite. However, at present, underwater acoustic communication and underwater radio frequency communication suitable for long-distance underwater communication have defects, wherein the underwater acoustic communication has the problems of narrow bandwidth and large time delay, and the underwater radio frequency communication has the problem of rapid propagation attenuation. Considering that the underwater environment has relatively small attenuation to the blue-green light with the wavelength of 450nm to 550nm, the underwater wireless optical communication technology based on the blue-green light wave band can be used as powerful supplement of underwater communication. With the increasing development of underwater data transmission, the MIMO system constructed based on the light source array can fully utilize space division multiplexing gain, and the system capacity and the anti-interference capability are improved. However, due to the rapid increase of underwater transmission demand, the conventional small-scale optical MIMO communication system is not enough to meet the marine information transmission demand.
In order to expand channel capacity, improve error rate performance of a communication system, and increase transmission distance of the communication system, it is considered to introduce a massive MIMO communication technology into an underwater optical communication system, as shown in fig. 1. However, the link misalignment of the underwater wireless optical communication can be caused by the environmental changes of the underwater communication link (such as the motion of the transmitting end and/or the receiving end of the underwater vehicle caused by the autonomous system, the ocean current and other turbulence sources, and the change of the refractive index of the underwater substance caused by the water depth, the temperature, the salinity and the like), so that the transceiving misalignment of the underwater optical Massive MIMO communication system can be caused. However, under the condition that the receiving and transmitting of the underwater optical Massive MIMO communication system are misaligned, a separation light spot formed on a detection surface by the imaging lens group cannot accurately fall on the detector array, and a relative horizontal and/or horizontal deviation occurs (as shown in fig. 2), so that the interference between optical paths is increased, the correlation between sub-channels is increased, the signal detection is difficult and complicated, and further the error rate of the underwater wireless optical communication system is increased.
Compared with a common MIMO communication system, the underwater optical Massive MIMO communication system has a very serious problem of misalignment of transmission and reception, so that signal detection of the underwater optical Massive MIMO communication system cannot be successfully completed if a signal detection algorithm of the common MIMO communication system is adopted. For example, a conventional OSIC detection algorithm used in a general MIMO communication system performs detection sequencing based on the power of received signals, and then completes signal demodulation based on the detection sequencing. Although for a common MIMO communication system with a small transceiving misalignment and a small MIMO scale, a conventional OSIC detection algorithm can complete signal detection, for an underwater optical Massive MIMO communication system with a serious transceiving misalignment and a large MIMO scale, a receiving-end detector may receive multiple light spots at the same time, which results in that a detector with the maximum receiving optical power of the receiving-end detector is also the maximum interference between light beams. Therefore, the traditional OSIC detection algorithm cannot be applied to an underwater optical Massive MIMO communication system.
Disclosure of Invention
The invention aims to solve the problem that an underwater optical Massive MIMO communication system has difficulty and complexity in signal detection caused by mis-transceiving, and provides an OSIC detection method under the mis-transceiving of the underwater optical Massive MIMO communication system.
In order to solve the problems, the invention is realized by the following technical scheme:
an OSIC detection method under the condition of transmitting-receiving misalignment of an underwater optical Massive MIMO communication system comprises the following steps:
step 1, estimating the direct current gain of each path of sub-channel of the received electric signal sent by a detector array by using an LS channel estimation method to obtain a channel gain matrix;
step 2, sequentially taking out each column of the current channel gain matrix, and correspondingly comparing the channel gain of each row of sub-channels of the current column with the channel gain of each row of sub-channels of other columns of the current channel gain matrix respectively: if the channel gain of each row of sub-channels of the current column is smaller than the channel gain of each row of sub-channels of all other columns of the current channel gain matrix, deleting the current column from the current channel gain matrix, selecting the current column as a detection column, and turning to the step 3; otherwise, repeating the step 2;
step 3, sorting the channel gains of the sub-channels in each row of the detection column from small to large, thereby obtaining the in-column detection sorting of the sub-channels in each row of the detection column;
step 4, for the detection column selected at the jth time:
if j =1, sequentially sending the original signals of each row of sub-channels to a subsequent signal demodulation process for signal demodulation according to the in-column detection sequencing of each row of sub-channels of the j-th selected detection column;
if j is not equal to 1, subtracting the product of the original signal of each row of sub-channels of the detection column selected at the jth time and the channel gain from the original signal of each row of sub-channels of the detection column selected at the jth-1 th time to obtain the residual signal of each row of sub-channels of the detection column selected at the jth time; and sequentially sending the residual signals of the sub-channels in each row to a subsequent signal demodulation process for signal demodulation according to the in-column detection sequence of the sub-channels in each row of the j-th selected detection column.
In the step 1, the LS channel estimation method inserts a pilot signal into each sub-channel signal at intervals of 4 data, and obtains the dc gains of all sub-channels by linear interpolation after performing gain estimation on the pilot positions of the signals.
Compared with the prior art, the invention provides the improved OSIC detection algorithm (I-OSIC) based on the minimum interference sequencing on the basis of the traditional OSIC detection algorithm in consideration of the problem that the receiving and transmitting misalignment is serious due to the characteristics that an underwater optical Massive MIMO communication system is changed due to the environment of an underwater communication link and the MIMO scale is extremely large. Aiming at the difficulty in obtaining the minimum interference sequence of an underwater optical Massive MIMO communication system and the fact that the interference condition is not considered in the traditional OSIC detection algorithm based on received signal power sorting, a receiving end detector can simultaneously receive a plurality of light spots, and the maximum received light power is also the signal with the maximum interference among light beams. The invention provides a method for estimating channels and offset directions to obtain the minimum interference sequence, namely after the gain of each sub-channel is estimated by an LS channel estimation algorithm, the offset direction of a transmitting and receiving end can be judged according to the magnitude of each direct current gain in a channel gain matrix, and then the sequence of a detection column and the sequence in the column are determined according to the offset direction pair, interference elimination is carried out, and the detection of each signal path is completed. The method carries out sequencing according to the offset direction, preferentially detects the signal without interference and then detects the signal with interference, greatly reduces error propagation brought by sequencing, ensures that the detected signal is more accurately subtracted by a later stage, ensures that the residual signal used in the subsequent stage has less interference, thereby improving the error rate performance, and solves the problem of increased error rate of the UWOC system caused by misalignment of a receiving and transmitting end and offset and diffusion of an imaging light spot in an underwater imaging optical Massive MIMO communication system.
Drawings
FIG. 1 is a schematic diagram of an optical portion of an underwater optical Massive MIMO communication system;
FIG. 2 is a schematic diagram showing the distribution of imaging spots in a detector array under misalignment of transmission and reception;
FIG. 3 is a schematic diagram of an underwater optical Massive MIMO communication system;
FIG. 4 is a graph comparing error rate performance under a condition of small misalignment with the existing signal detection algorithm;
fig. 5 is a graph comparing the error rate performance under the condition of large misalignment with the conventional signal detection algorithm.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to specific examples.
In an underwater large-scale optical Massive MIMO communication system, a sending end firstly modulates a binary bit data stream to be sent, and then converts a modulated electric signal into a plurality of paths of sending optical signals by using a light source array consisting of light sources to send the signals to a receiving end; the multi-channel transmitting optical signals pass through the imaging lens at a receiving end and then form separated light spots on a detection surface, the separated light spots are converted into multi-channel receiving electric signals by a detector array formed by detectors, and the multi-channel receiving electric signals are restored into binary bit data after being subjected to signal detection and signal demodulation.
OSIC detection is based on signal detection and interference cancellation by a set of linear receivers, each detecting one of the parallel data streams, and in each stage being able to successfully subtract the detected signal components from the received signal, so that the remaining signal for the subsequent stage has less interference. Since the erroneous decision of the previous stage may cause error propagation, the detection order may significantly affect the overall performance of the detection of the OSIC. In consideration of the characteristics of serious receiving and transmitting misalignment and large MIMO scale of an underwater optical Massive MIMO communication system, the invention provides an improved OSIC detection algorithm based on minimum interference ordering, namely, after gain estimation is carried out on each path of sub-channel by using an LS channel estimation algorithm, the offset direction of a receiving and transmitting end can be judged according to the magnitude of each direct current gain in a channel gain matrix, and then the detection column sequence and the sequence in the column are determined according to the offset direction pair, interference elimination is carried out, and signal detection of each path is completed.
Specifically, the invention provides an OSIC detection method under the condition of receiving and transmitting misalignment of an underwater optical Massive MIMO communication system, which specifically comprises the following steps:
step 1, estimating the direct current gain of each path of sub-channel of the received electrical signal y sent by the detector array by using an LS channel estimation method to obtain a channel gain matrix.
And the receiving end carries out LS channel estimation according to the pilot frequency interval in the OFDM modulation process of the transmitting end. In the preferred embodiment of the present invention, the pilot interval for OFDM modulation at the transmitting end is 4, so that the sub-channel signal received by the receiving end is a signal obtained by inserting one pilot into 4 data. In addition, in the LS channel estimation process, a linear interpolation algorithm is used for interpolating all OFDM symbol frequency point data to obtain OFDM symbol frequency response, and then statistical averaging is carried out on the OFDM symbol frequency response to obtain channel gain. According to the method, a pilot frequency signal is inserted into each sub-channel signal at intervals of 4 data by an LS channel estimation method according to the absorption scattering attenuation condition of an underwater Massive MIMO channel and the requirement for reducing pilot frequency overhead, and after gain estimation is carried out on the pilot frequency position of the signal, the pilot frequency position of the signal is adoptedLinear interpolation obtains the dc gain of all sub-channels. The channel gain matrix of the LS channel estimation is
Wherein Y is a received signal, X is a pilot signal, and X is H Is a matrix of X conjugate transposes, X -1 Is an inverse matrix of X.
Is directly estimated by the pilot frequency, so that only the channel gain of the pilot frequency inserting position can be obtained, and the channel gain of other positions of the subcarrier without the pilot frequency can be estimated by linear interpolation, namely
After linear interpolation, obtaining
Step 2, sequentially taking out each column of the current channel gain matrix, and respectively and correspondingly comparing the channel gain of each row of sub-channels of the current column with the channel gain of each row of sub-channels of other columns of the current channel gain matrix;
if the channel gain of each row of sub-channels of the current column is smaller than the channel gain of each row of sub-channels of all other columns of the current channel gain matrix, the current column is considered to be the most severely offset column in the current channel gain matrix, at this moment, the current column is deleted from the current channel gain matrix, and the current column is selected as a detection column, and the step 3 is carried out;
otherwise, the current column is not considered to be the most seriously offset column in the current channel gain matrix, the step 2 is repeated, and the most seriously offset column in the current channel gain matrix is reselected.
And 3, sequencing the channel gains of the sub-channels in each row of the detection column from small to large, thereby obtaining the in-column detection sequencing of the sub-channels in each row of the detection column.
Step 4, for the detection column selected at the jth time:
if j =1 (namely the detection column selected for the first time), the original signals of each row of sub-channels are sequentially sent to the subsequent signal demodulation process for signal demodulation according to the in-column detection sequence of each row of sub-channels of the detection column selected for the j time. Since the first selected detection column is the most severely shifted column (such as the leftmost column in fig. 2) in the whole received electrical signal, it will not generate interference, so that the original signal is directly used for signal demodulation;
if j is not equal to 1 (namely the detection column is not selected for the first time), subtracting the product of the original signal of each row of sub-channels of the detection column selected for the j-1 th time and the channel gain from the original signal of each row of sub-channels corresponding to the detection column selected for the j-1 th time to obtain the residual signal of each row of sub-channels of the detection column selected for the j-th time; and sequentially sending the residual signals of the sub-channels in each row to a subsequent signal demodulation process for signal demodulation according to the in-column detection sequence of the sub-channels in each row of the j-th selected detection column. Since the detected column selected subsequently is not the most severely shifted column (e.g. the third column from the left in fig. 2) in the whole received electrical signal, the original signal is interfered by the signals of the adjacent columns (e.g. the second column from the left in fig. 2), and therefore, the interference of the corresponding rows of the adjacent columns needs to be subtracted from the original signal before signal demodulation.
The interference caused by the detected adjacent signals is subtracted from the original signals of each sub-channel in the later period of detection, so that the subsequent receiver contains less interference in the detection stage.
The performance of the invention is illustrated below by means of a specific example.
Fig. 3 is a schematic diagram of an underwater optical Massive MIMO communication system, which includes an optical part and an electrical part.
(1) An optical portion:
the transmitting end adopts a 64X 64 light source array, and the receiving end adopts a 64X 64 detector array. The imaging lens at the receiving end is formed by combining a convex lens and a concave lens, the main optical axes of the convex lens and the concave lens are coincident, and the convex lens is positioned at the front end of the concave lens. The convex lens converges the multiple paths of optical signals sent by the sending end onto the concave lens, and the concave lens performs light spot separation on the converged optical signals to obtain multiple paths of optical signals. The front end face and the rear end face of the convex lens and the concave lens of the imaging lens are paraboloids, and the paraboloids of the convex lens and the concave lens are designed, so that the interference caused by imaging aberration can be effectively reduced, and the imaging lens is better suitable for underwater environment. In order to achieve accurate adjustment of the lens surface while simplifying the lens design, the curvature radius and the cone coefficient of the lens paraboloid are set to zero while the first-order and second-order coefficients of the lens paraboloid are considered, and the surface rise expression of the simplified lens paraboloid is obtained as follows:
z＝αr 2 +βr 4
wherein z is the sag of the lens paraboloid, r is the radial coordinate of the axially rotationally symmetric lens surface,
alpha is the first order coefficient of the lens paraboloid, and beta is the second order coefficient of the lens paraboloid. By optimizing the imaging lens according to the formula, the correlation of a system channel gain matrix is reduced while higher optical gain is obtained by increasing the focal length F and the diameter D of the lens. In the present embodiment, the first-order coefficient and the second-order coefficient of the convex lens front end surface parabola are α =0.02 and β =5 × 10, respectively -6 First-order coefficient and second-order coefficient of the convex lens rear end surface parabola are respectively alpha =0.01, beta =1 × 10 -6 The aperture (mm) of the convex lens is 30mm, and the thickness is 15mm; the first order coefficient and the second order coefficient of the parabola on the front end surface of the concave lens are respectively alpha = -0.03 and beta = -1 multiplied by 10 -6 The first order coefficient and the second order coefficient of the parabola on the rear end face of the concave lens are respectively alpha =0.03, beta =1 × 10 -6 The aperture (mm) of the concave lens is 20mm, and the thickness is 2mm. The biconvex lens has the same surface coefficient sign at the front and back ends because the surface bulges are in the same direction, and the biconcave lens has the same surface coefficient sign at the front and back ends because the surface bulges are in the same directionInside the lens, the front and rear end surfaces are convex in opposite directions so that the coefficients of the front and rear end surfaces of the concave lens are opposite in sign.
(2) An electrical part:
the signal modulation process at the transmitting end comprises serial-parallel conversion, 4QAM mapping, hermite symmetry, IFFT, CP adding, parallel-serial conversion and wave elimination. The signal demodulation process of the receiving end comprises serial-to-parallel conversion, CP removal, FFT, data subcarrier extraction, 4QAM demodulation and parallel-to-serial conversion. In addition, the sending end needs to perform analog-to-digital conversion on the signal after signal modulation and then send the signal into the light source array, and the receiving end needs to perform digital-to-analog conversion on the signal received by the detector array and then perform signal detection.
At a sending end, binary bit stream is modulated into an ACO-OFDM signal after being subjected to serial/parallel conversion, 4QAM mapping, hermite symmetry, IFFT, cyclic prefix adding, parallel/serial conversion and clipping processing in sequence, and then the ACO-OFDM signal is sent to a light source array after being subjected to analog/digital conversion to convert an electric signal into an optical signal to enter a channel for transmission. At a receiving end, a detector array receives a signal and then carries out photoelectric conversion and analog/digital conversion on the signal, the signal is sent to the signal detection method of the invention for detecting the received signal, and the detected signal is demodulated and restored into an original binary bit stream after serial/parallel, cyclic prefix removal, FFT, data subcarrier extraction, 4QAM demodulation and parallel/serial operation.
The invention discloses an underwater optical Massive MIMO communication method using an improved OSIC detection algorithm (I-OSIC), which comprises the following steps:
when the binary bit stream is input into the system, the signal modulation part of the transmitting end firstly carries out serial/parallel conversion to convert the serial bit stream into parallel bit streams, and 4QAM modulation is adopted for each path of parallel signals. After Hermite symmetry and IFFT operation, 4QAM star maps corresponding to each path of data are mapped into a real number form, and OFDM signals are obtained after digital-to-analog conversion. After adding cyclic prefix, each path of signal is parallel/serial converted, and in order to make the following optical signal suitable for underwater channel transmission, the signal processing portion also makes clipping treatment. After the clipping processing, the signal is sent to a 64 x 64 light source array through analog/digital conversion, so that the signal is converted into an optical signal to enter a channel for transmission. After receiving the optical signal at the receiving end of the 64 × 64 detector array, the received analog signal is first digitized by analog-to-digital conversion, and the digital signal is transmitted to LS channel estimation. The LS channel estimation part carries out LS channel estimation according to the pilot frequency inserted in the sending signal by the sending end, and obtains a channel gain matrix to be transmitted to the OSIC signal detection part at the later stage. The OSIC signal detection part can calculate the direct current gain of each column in the channel gain matrix, then the misalignment is related to the direct current gain, when one column has all columns of channel gains smaller than other columns and the element values in the columns have no great difference, the column can be judged as a first detection column, namely, a first column in the opposite direction of the light spot deviation direction is taken as a first detection column. In the first column, the signals are sequentially selected from top to bottom, the first path of signals is used as the signals to be detected firstly, in the column, interference is eliminated and detected sequentially according to the sequence, and then the second column to the last column are determined sequentially towards the light source offset direction, so that the detection sequence of the OSIC signal detection is obtained. The OSIC signal detection portion employs a set of linear receivers, each of which detects one of the parallel data streams and subtracts the detected data from the received data after detection, so that the subsequent detection stage has less interference. In this way, the reception signal detected by the OSIC can be obtained after passing through the portion. After the detection of the OSIC signal, the reverse operations of the transmitting end, namely serial/parallel conversion, CP removal, FFT extraction, data subcarrier extraction, 4QAM demodulation and parallel/serial conversion, are adopted at the receiving end, and the modulated signal is demodulated and restored to the original binary bit stream.
The relative offset of the transmitting and receiving ends of the underwater optical Massive MIMO communication system can be divided into 8 directions, a single right offset is taken as an example, and the algorithm provided in the scene can be also applied to systems in single offset directions such as upward direction, downward direction, leftward direction and the like. The specific comparison of the error rate performance of the OSIC detection method of the present invention with the existing algorithm under the misalignment condition can be seen in FIG. 4 and FIG. 5. Fig. 4 is a simulation diagram of the system bit error rate in the case where the horizontal offset error is small, and fig. 5 is a simulation diagram of the system bit error rate in the case where the horizontal offset error is large. Channel correlation with increasing relative offset error at the transceiving endThe performance is also increased, and at the moment, the SVD pre-coding detection algorithm has limited improvement on the error code performance of the system in a poor channel environment. The ZF detection algorithm amplifies the additive noise weighting. The MMSE detection algorithm is obtained by improving on the basis of the ZF detection algorithm, noise variance estimation is needed, however, the improvement on the system bit error rate is limited, and particularly under the condition of larger offset, the defects also cause that the bit error rate performance of the ZF detection algorithm and the MMSE detection algorithm is inferior to that of the OSIC detection algorithm under the environment with the same signal-to-noise ratio. Compared with the traditional OSIC algorithm (OSIC) based on receiving end power sequencing, the improved OSIC detection algorithm (I-OSIC) based on interference minimum sequencing estimates the light spot offset direction according to the channel gain matrix, selects the first column in the direction opposite to the offset direction as the first column to be detected, so that the interference of other light spots does not exist in the first column to be detected, and detects the column with the interference after subtracting the detected signal, thereby improving the error rate performance under the condition of the same signal to noise ratio. Furthermore, the temporal complexity of the SVD detection algorithm is O (min (m) 2 n,mn 2 ) Time complexity of ZF detection algorithm and MMSE detection algorithm is O (k) 3 ) The time complexity of the conventional OSIC detection algorithm is O (k) 2 ) Where k denotes the number of transmit antennas and m and n denote the number of rows and columns of the matrix, respectively. The invention is improved on the basis of the traditional OSIC detection algorithm, so the time complexity is smaller.
In summary, the method for detecting the OSIC under the misalignment of the transceiving of the underwater optical Massive MIMO communication system provided by the invention combines and applies the technologies of channel estimation, channel coding, signal detection and the like, meets the requirements of improving the communication rate and the error rate index of the UWOC system under the conditions of misalignment of the transceiving end of the underwater imaging optical system, and the enhancement of signal interference and the misalignment of a communication link caused by the deviation and diffusion of an imaging light spot, and avoids the problems of large influence of light source misalignment, poor error rate performance after misalignment and the like in the prior art.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.
Claims (2)
1. An OSIC detection method under misalignment of receiving and transmitting of an underwater optical Massive MIMO communication system is characterized by comprising the following steps:
step 1, estimating the direct current gain of each path of sub-channel of a received electric signal sent by a detector array by using an LS channel estimation method to obtain a channel gain matrix;
step 2, sequentially taking out each column of the current channel gain matrix, and correspondingly comparing the channel gain of each row of sub-channels of the current column with the channel gain of each row of sub-channels of other columns of the current channel gain matrix respectively: if the channel gain of each row of sub-channels of the current column is smaller than the channel gain of each row of sub-channels of all other columns of the current channel gain matrix, deleting the current column from the current channel gain matrix, selecting the current column as a detection column, and turning to the step 3; otherwise, repeating the step 2;
step 3, sorting the channel gains of the sub-channels in each row of the detection column from small to large, thereby obtaining the in-column detection sorting of the sub-channels in each row of the detection column;
step 4, for the detection column selected at the jth time:
if j =1, sequentially sending the original signals of each row of sub-channels into a subsequent signal demodulation process for signal demodulation according to the in-row detection sorting of each row of sub-channels of the j-th selected detection row;
if j is not equal to 1, subtracting the product of the original signal of each sub-channel of each corresponding row of the j-1 th selected detection column from the original signal of each sub-channel of each row of the j-th selected detection column and the channel gain to obtain the residual signal of each sub-channel of each row of the j-th selected detection column; and then sequentially sending the residual signals of the sub-channels in each row into a subsequent signal demodulation process for signal demodulation according to the in-column detection sequencing of the sub-channels in each row of the jth selected detection column.
2. The OSIC detection method under the condition of misalignment of transceiving of the underwater optical Massive MIMO communication system as claimed in claim 1, wherein the LS channel estimation method of step 1 is to insert a pilot signal for each sub-channel signal at an interval of 4 data, and after gain estimation is performed on the pilot positions of the signals, linear interpolation is adopted to obtain the direct current gain of all sub-channels.
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