CN114172575A - Sampling time offset and channel joint blind estimation method based on direct current offset - Google Patents

Sampling time offset and channel joint blind estimation method based on direct current offset Download PDF

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CN114172575A
CN114172575A CN202111458317.6A CN202111458317A CN114172575A CN 114172575 A CN114172575 A CN 114172575A CN 202111458317 A CN202111458317 A CN 202111458317A CN 114172575 A CN114172575 A CN 114172575A
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蒋宇飞
高翔
朱旭
王同
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Shenzhen Graduate School Harbin Institute of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/11—Arrangements specific to free-space transmission, i.e. transmission through air or vacuum
    • H04B10/114—Indoor or close-range type systems
    • H04B10/116—Visible light communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/60—Receivers
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0238—Channel estimation using blind estimation
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Abstract

The invention provides a sampling time offset and channel joint blind estimation method based on direct current offset, which is applied to a DCO-OFDM system. The method of the invention obtains more accurate sampling time offset and visible light channel impulse response under the condition of not using pilot frequency, has higher frequency spectrum utilization rate and has robustness for LED limited bandwidth.

Description

Sampling time offset and channel joint blind estimation method based on direct current offset
Technical Field
The invention relates to the technical field of wireless communication, in particular to a sampling time offset and channel joint blind estimation method based on direct current offset.
Background
Visible light communication is used as an alternative scheme of traditional radio frequency wireless communication, and a visible light wave band free of authorization and large in bandwidth is used for transmission, so that the problem of crowded occupation of a communication frequency band can be effectively solved. The DCO-OFDM technology is widely used in the field of visible light communication for ISI resistance. However, DCO-OFDM systems are extremely sensitive to synchronization and any minor synchronization error may cause system performance degradation. Therefore, the existence of the sampling time offset in the optical OFDM system may affect the error rate performance of the visible light communication system, which is a problem to be solved at present. Meanwhile, in most cases, the visible light channel is also unknown at the receiving end, and the error compensation thereof also causes the system performance to be degraded.
As part of the synchronization problem, most studies in the industry currently focus on pilot-based estimation algorithms, that is, estimation of the sampling time offset is performed on the basis of acquisition of channel information by using pilot apriori.
However, the pilot-based estimation algorithm uses the pilot to occupy the spectrum resources of the system, so that the spectrum utilization rate of the system is reduced, and most of the existing estimation algorithms do not have the robustness for limiting the bandwidth of the LED.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a combined blind estimation algorithm of sampling time offset and a visible light channel based on direct current offset for a DCO-OFDM system which is most widely used in the industry, obtains more accurate sampling time offset and visible light channel impulse response under the condition of not using pilot frequency, has higher frequency spectrum utilization rate, and has robustness for limiting bandwidth of an LED. The invention is realized by the following technical scheme:
a direct current offset-based sampling time offset and channel joint blind estimation method is applied to a DCO-OFDM system, and is characterized by comprising the following steps:
receiving the optical signal transmitted by the free space visible light link and removed with the cyclic prefix at a receiving end:
y＝G(τ)σDC1N×Lh+G(τ)Xh+w
wherein G (τ) σDC1N×Lh is the received known DC bias signal, in the formula, G (tau) has removed the cyclic prefix part, G (tau) Xh is the received useful information to be demodulated, w is additive white Gaussian noise, G (tau) represents the total equivalent raised cosine roll-off filter of the root mean square raised cosine roll-off filter of the receiving end and the transmitting end,
Figure BDA0003387241270000021
w (n) is an independent homodistribution with mean 0 and variance σ2Of a Gaussian random variable, [ sigma ]DCFor direct current bias, 1N×LRepresenting a full 1 matrix with the size of NxL, wherein X is an original data signal, h represents a matrix with the size of Lx1, and each element of the matrix represents the normalized time domain impulse response size of a visible light free link channel;
constructing a receiving end DC offset estimation signal by utilizing a maximum likelihood method
Figure BDA0003387241270000022
Figure BDA0003387241270000023
And
Figure BDA0003387241270000024
for the test values, the expressions of the elements of the channel test values are as follows:
Figure BDA0003387241270000025
wherein the content of the first and second substances,
Figure BDA0003387241270000026
test value, t, representing the 3-dB limiting bandwidth of an LEDsRepresents a symbol sampling interval;
since the LoS channel only affects the overall attenuation magnitude, the matrix
Figure BDA0003387241270000027
The sum of all the elements in the matrix
Figure BDA0003387241270000028
To obtain a determined test value, (-)+Represents a generalized inverse;
constructing a cost function:
Figure BDA0003387241270000029
wherein the content of the first and second substances,
Figure BDA00033872412700000210
represents the Frobenius norm;
when the cost function is minimum, the energy of the direct current signal is just eliminated, and the direct current signal is used for eliminating the energy of the direct current signal
Figure BDA00033872412700000211
And
Figure BDA00033872412700000212
the values of (A) are as follows:
Figure BDA00033872412700000213
wherein C represents fbAll possible value ranges.
As a further improvement of the present invention, the method introduces interference iterative cancellation for reducing the influence of the useful signal on the performance of the synchronization algorithm to the maximum extent, specifically:
after the algorithm carries out estimation for the first time, a roughly estimated sampling time offset and a channel impulse response estimation initial value are obtained; demodulating the useful signal to obtain a demodulated useful signal X1(ii) a The received signal at the receiving end cancels the demodulated useful signal.
As a further improvement of the invention, the iteration is performed several times, and each iteration cancels the estimated useful signal by using the original received signal.
The invention has the beneficial effects that: the invention uses the necessary direct current offset component in the DCO-OFDM system to carry out the joint estimation of the sampling time offset and the channel, and does not use a pilot signal, thereby improving the frequency spectrum utilization rate of the system. Because the estimation of the channel is carried out simultaneously in the algorithm process, the prior information of the channel is not needed, and blind estimation can be realized. The influence of the low-pass characteristic of the LED limited bandwidth on the performance of the algorithm is considered, so that the algorithm has robustness on the LED limited bandwidth.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.
The invention is mainly oriented to a DCO-OFDM system, and carries out sampling time offset and channel estimation by using an indispensable direct current bias signal which enables a transmission signal to meet non-negativity in the system.
First we model a DCO-OFDM system. Defining the number of sub-carriers used in each DCO-OFDM block as N and the system using M-QAM as the modulation method of the effective data, all N sub-carriers can represent (N-2) log in total in each transmission2M/2 bit binary data. Definition of
Figure BDA0003387241270000031
For the signal modulated by the constellation diagram, in order to make the signal after IFFT be a real signal, the signal subjected to IFFT needs to satisfy the hermitian symmetry condition, and the hermitian symmetric signal constructed for this purpose is as follows:
s＝[0,x(0),...,x(N/2-2),0,x*(N/2-2),...,x*(0)]T (1)
in order to replace the signal time domain convolution process by matrix multiplication, the signal needs to be converted into a circular matrix form, and the matrix multiplication operation can be regarded as time domain signal convolution. A time domain signal matrix S obtained by IFFT and conversion of the hermitian symmetric signal into a cyclic matrix form is as shown in formula (2):
S＝FHdiag{s}F(1:L) (2)
where F denotes a DFT matrix of size N × N, whose (u, v) term is expressed by equation (3):
Figure BDA0003387241270000032
diag { s } represents a diagonal matrix with rows and columns equal to the length of the vector s, the diagonal elements of the diagonal matrix are each element in the vector s, L represents the discrete length of the channel time-domain impulse response, F (1: L) is a sub-matrix of F, the rows of the sub-matrix are consistent with F, only the 1 st column to the L th column of F are taken, and the time-domain symbol on the nth sub-carrier in the time-domain signal matrix can be represented by the following formula (3):
Figure BDA0003387241270000033
normally, the DC bias σDCIs derived from the average energy of the transmitted signal x (n), and is defined as formula (5):
Figure BDA0003387241270000041
wherein K is a DC bias ratio. In practical use, the signal transmitting power of the transmitter is always constant, and the signal transmitted each time has the same average energy, so that the DC bias voltage sigma is used in the inventionDCRedefined as a constant, the magnitude settings of which are not discussed in the present invention.
Theoretically, in a DCO-OFDM system which normally operates, most of time domain signals added with direct current offset become nonnegative signals, but when sigma is equal toDCWhen the value is small, a part of the negative signal may still exist. In the transmitter of the DCO-OFDM system, the remaining negative signal amplitude is truncated to zero, thereby introducing clipping noise wclip(n) is used to represent this process, and clipping noise is defined as equation (6):
Figure BDA0003387241270000042
at this time, the transmit signal matrix after being processed by the transmitting end of the DCO-OFDM system can be represented by equation (7):
Figure BDA0003387241270000043
wherein 1 isN×LRepresenting an all 1 matrix of size nxl,
Figure BDA0003387241270000044
Figure BDA0003387241270000045
in order to solve the ISI problem caused by the signal tail due to the multipath effect and thus prevent the ISI from affecting the system performance, a cyclic prefix CP is usually added to the signal to be used as a guard interval. In order to ensure that the cyclic prefix can effectively improve the system reliability, the length of the cyclic prefix is set to be at least LCPIs greater than L-1. The cyclic prefix added signal can be expressed as equation (8):
Figure BDA0003387241270000046
in the formula (I), the compound is shown in the specification,
Figure BDA0003387241270000047
indicates a size of LCPX L matrix of elements and
Figure BDA0003387241270000048
reciprocal LCPThe row corresponding elements are identical.
In order to convert a digital signal into an analog signal for transmission in an actual channel and convert the analog signal into the digital signal again at a receiving end, the signals need to be sampled by two identical root-mean-square raised cosine roll-off filters at a transmitting end and the receiving end respectively, and the identical purpose is to enable the transmitting end and the receiving end to meet matched filtering conditions. Since both thermal noise and shot noise belong to additive white gaussian noise AWGN, the environmental noise is modeled using the additive white gaussian noise. Under the condition of receiving-end full frame detection, the received sampling signal matrix can be modeled as formula (9):
Figure BDA0003387241270000051
where τ represents the sample time offset size normalized for the symbol duration T and satisfies τ e (-0.5, 0.5); h represents a matrix with the size of L multiplied by 1, each element of the matrix represents the normalized time domain impulse response size of a visible light free link channel, the time delay of each adjacent channel is T, and the expression is as shown in formula (10) and formula (11):
h(n)＝hLoS*hLED(n) (10)
h＝[h(0),h(1),...,h(L-1)]T (11)
in the formula hLoSFor LoS channel normalized gain, hLED(n) is the gain at time delay nT due to LED limited bandwidth, representing a linear convolution operation.
Definition of
Figure BDA0003387241270000052
w (n) is an independent homodistribution with mean 0 and variance σ2(ii) a gaussian random variable; g (τ) represents the total equivalent raised cosine roll-off filter of the root-mean-square raised cosine roll-off filters of the receiving end and the transmitting end, which is defined as equations (12), (13) and (14):
Figure BDA0003387241270000053
Figure BDA0003387241270000054
Figure BDA0003387241270000055
q is an oversampling rate and is used for increasing the number of sampling points to ensure the reliability of the system; and Ts is an oversampling interval, the size of the oversampling interval is T/Q, and alpha is a roll-off coefficient of the filter.
The overall flow diagram of the algorithm proposed by the present invention is shown in fig. 1.
At the receiving end, according to equation (7) and equation (9), the optical signal transmitted through the free space visible light link and with the cyclic prefix removed can be decomposed into a form represented by equation (15):
Figure BDA0003387241270000056
as can be seen, the signal is composed of three parts: the first part is a received known direct current offset signal, wherein G (tau) has a cyclic prefix part removed; the second part is received useful information which needs to be demodulated; the third part is additive white gaussian noise. The direct current bias signal is a known signal, useful information and noise belong to unknown random signals, and when the known direct current bias signal is used for estimation, the useful signal actually exists as an interference signal in a synchronization process.
The basic principle of maximum likelihood detection is to calculate the square of the euclidean distance between the received signal matrix and the test signal matrix and select the corresponding test signal matrix with the smallest value as the estimated signal matrix. Since the channel information can be estimated at the time of tentative value determination, each determined tentative value corresponds to a determined channel estimate. Is provided with
Figure BDA0003387241270000061
The value range of the test value of the sampling time offset of the current receiving end is (-0.5,0.5), and a receiving end direct current offset estimation signal can be constructed by a maximum likelihood method
Figure BDA0003387241270000062
And subtracting the signal received by the actual receiving end from the actual receiving end to obtain equation (16):
Figure BDA0003387241270000063
as can be seen from equation (16), neither the second part of the useful signal nor the third part of the additive white gaussian noise is affected, and the energy thereof is unchanged. When a test signal is introduced into the formula, if
Figure BDA0003387241270000064
The first part of the dc bias signal energy is zeroed and
Figure BDA0003387241270000065
in time, since both the dc bias signal matrix and the channel impulse response matrix contain non-0 elements, their energy must be greater than zero. Therefore, the cost function is constructed as shown in formula (17):
Figure BDA0003387241270000066
in the formula (I), the compound is shown in the specification,
Figure BDA0003387241270000067
represents the Frobenius norm, which is defined as the sum of the squares of the absolute values of the elements in the matrix.
In practice, however, the experimental channel information is not completely equal to the actual channel information, so that a high-precision estimation needs to be performed on the channel before using the cost function to ensure the accuracy of the cost function
Figure BDA00033872412700000611
In time, the ideal receiving signal of the receiving end is as follows (18):
Figure BDA0003387241270000068
since the useful signal is calculated as the interference signal, ideally, the signals transmitted by the transmitting end should be all dc offset signals, and the interference is the minimum, and the ideal received signal now becomes equation (19):
Figure BDA0003387241270000069
at this time, the cost function becomes equation (20):
Figure BDA00033872412700000610
because the channel usually presents an exponential descent form, a corresponding experimental value can be constructed for searching, and each element of the channel experimental value is expressed as formula (21):
Figure BDA0003387241270000071
wherein the content of the first and second substances,
Figure BDA0003387241270000072
test value, t, representing the 3-dB limiting bandwidth of an LEDsRepresents a symbol sampling interval;
since the LoS channel only affects the overall attenuation magnitude, the matrix
Figure BDA0003387241270000073
The sum of all the elements in the matrix
Figure BDA0003387241270000074
To obtain a determined test value, (-)+Represents a generalized inverse;
when the cost function is minimum, the energy of the direct current signal is just eliminated, and the direct current signal is used for eliminating the energy of the direct current signal
Figure BDA0003387241270000075
And is
Figure BDA0003387241270000076
Then
Figure BDA0003387241270000077
And
Figure BDA0003387241270000078
the value of (A) is as follows (22):
Figure BDA0003387241270000079
wherein C represents fbAll possible value ranges; to this end, the channel and sample time offsets are jointly estimated.
The existence of the useful signal can cause the energy of the interference signal to be overlarge, and when the influence of the interference signal on the cost function curve is larger than the size of the cost function of the search change of the sampling time offset test value, the lowest point of the cost function can have larger deviation with the lowest point under the condition of no interference, thereby causing the estimation precision of the sampling time offset and the channel to be greatly reduced. To solve the problem, interference iterative cancellation is introduced into the algorithm to reduce the influence of the useful signal on the performance of the synchronization algorithm to the maximum extent.
After the algorithm is estimated for the first time, a roughly estimated sampling time offset and an initial value of channel impulse response estimation are obtained, and the useful signal is demodulated under the condition, so that a demodulated useful signal X can be obtained1Although the rough estimation results in a larger error rate, more signals are still accurately demodulated, and have a certain correlation with the real useful signal, so that the received signal at the receiving end cancels the demodulated useful signal, which is expressed as formula (23):
Figure BDA00033872412700000710
as can be seen from the equation (27),the energy of the useful signal is greatly weakened, and the influence on the performance of the synchronization algorithm is greatly reduced. At this time, y in the algorithm is replaced by
Figure BDA00033872412700000711
The obtained sampling time offset and channel estimation are less interfered by interference signals, the estimation is more accurate, and compared with the method without interference iterative elimination, the method for eliminating the interference signals can effectively improve the system error rate performance. On the basis, in order to achieve better algorithm effect, the useful signals can be further iteratively eliminated until the performance of the algorithm converges. Y for y replacement at i-th iterationiThe expression is as in formula (24):
Figure BDA0003387241270000081
in the formula
Figure BDA0003387241270000082
The estimated sample time offset for the i-1 st iteration,
Figure BDA0003387241270000083
channel impulse response matrix, X, estimated for the i-1 th iterationi-1The demodulated useful signal is estimated from the first two terms for the i-1 th iteration.
It should be noted that each iteration uses the original received signal to cancel the useful signal, and does not use the signal after the previous iteration to cancel the useful signal, which would otherwise cause the interference cancellation to fail.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention. For those skilled in the art, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (3)

1. A direct current offset-based sampling time offset and channel joint blind estimation method is applied to a DCO-OFDM system, and is characterized by comprising the following steps:
receiving the optical signal transmitted by the free space visible light link and removed with the cyclic prefix at a receiving end:
y＝G(τ)σDC1N×Lh+G(τ)Xh+w
wherein G (τ) σDC1N×Lh is the received known DC bias signal, in the formula, G (tau) has removed the cyclic prefix part, G (tau) Xh is the received useful information to be demodulated, w is additive white Gaussian noise, G (tau) represents the total equivalent raised cosine roll-off filter of the root mean square raised cosine roll-off filter of the receiving end and the transmitting end,
Figure FDA0003387241260000011
w (n) is an independent homodistribution with mean 0 and variance σ2Of a Gaussian random variable, [ sigma ]DCFor direct current bias, 1N×LRepresenting a full 1 matrix with the size of NxL, wherein X is an original data signal, h represents a matrix with the size of Lx1, and each element of the matrix represents the normalized time domain impulse response size of a visible light free link channel;
constructing a receiving end DC offset estimation signal by utilizing a maximum likelihood method
Figure FDA0003387241260000012
Figure FDA0003387241260000013
And
Figure FDA0003387241260000014
for the test values, the expressions of the elements of the channel test values are as follows:
Figure FDA0003387241260000015
wherein the content of the first and second substances,
Figure FDA0003387241260000016
test value, t, representing the 3-dB limiting bandwidth of an LEDsRepresents a symbol sampling interval;
since the LoS channel only affects the overall attenuation magnitude, the matrix
Figure FDA0003387241260000017
The sum of all the elements in the matrix
Figure FDA0003387241260000018
To obtain a determined test value, (-)+Represents a generalized inverse;
constructing a cost function:
Figure FDA0003387241260000019
wherein the content of the first and second substances,
Figure FDA00033872412600000110
represents the Frobenius norm;
when the cost function is minimum, the DC signal energy is just eliminated, and the estimated value of the sampling time offset is obtained
Figure FDA00033872412600000111
And channel estimation
Figure FDA00033872412600000112
The values of (A) are as follows:
Figure FDA00033872412600000113
wherein, C tableShow (f)bAll possible value ranges.
2. The method according to claim 1, characterized in that the method introduces interference iterative cancellation for minimizing the impact of the useful signal on the performance of the synchronization algorithm, in particular: after the algorithm carries out estimation for the first time, a roughly estimated sampling time offset and a channel impulse response estimation initial value are obtained; demodulating the useful signal to obtain a demodulated useful signal X1(ii) a The received signal at the receiving end cancels the demodulated useful signal.
3. The method of claim 2, wherein the iteration is performed a plurality of times, each iteration using the original received signal to cancel the estimated useful signal.
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