CN114172575B - Sampling time offset and channel joint blind estimation method based on direct current offset - Google Patents
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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 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 to the bandwidth limitation of the LED.
Description
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
As an alternative scheme of the traditional radio frequency wireless communication, the visible light communication uses the visible light wave band with large bandwidth for transmission without authorization, so that the problem of crowding and occupation of the communication frequency band can be effectively solved. 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 lead to degradation of system performance. Therefore, the presence of the sampling time offset in the optical OFDM system affects the bit error rate performance of the visible light communication system, which is a problem to be solved. Meanwhile, in most cases, the visible light channel is unknown at the receiving end, and error compensation on the visible light channel can also cause system performance to be reduced.
Sample time offset as part of the synchronization problem, most of the research in the industry is focused on pilot-based estimation algorithms, i.e. acquisition of channel information is performed a priori by pilot, on the basis of which estimation of sample time offset is performed.
However, pilot-based estimation algorithms use pilots to occupy the spectral resources of the system, thus degrading the system spectrum utilization, and most existing estimation algorithms do not have robustness to LED limited bandwidth.
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 visible light channel based on direct current offset, which is used for the most widely used DCO-OFDM system in 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 to the LED limited bandwidth. The invention is realized by the following technical scheme:
a method for joint blind estimation of sampling time offset and channel based on direct current offset, the method being applied to a DCO-OFDM system, the method comprising:
receiving, at a receiving end, an optical signal transmitted through a free space visible light link and from which a cyclic prefix is removed:
y＝G(τ)σ DC 1 N×L h+G(τ)Xh+w
wherein G (τ) σ DC 1 N×L h is a received known direct current bias signal, G (tau) has removed a cyclic prefix part, G (tau) Xh is received useful information needed to be demodulated, w is additive Gaussian white noise, G (tau) represents total equivalent raised cosine roll-off filters of a receiving end and a transmitting end,
w (n) is independent and the mean value of the same distribution is 0 and the variance is sigma 2 Gaussian random variable, sigma DC For DC bias, 1 N×L Representing a full 1 matrix of size nxl, X being the original data signal, h representing a matrix of size lx1, each element of the matrix representing a normalized time domain impulse response size of the visible free link channel;
constructing a receiving end direct current bias estimation signal by using a maximum likelihood method
And->
For the test values, the channel test values are expressed as follows:
wherein,,
test value, t, representing the 3-dB bandwidth limit of an LED s Representing a symbol sampling interval;
since the LoS channel only affects the overall attenuation magnitude, the matrix
The sum of all elements in (1) is represented by the matrix->
To obtain a determined test value, (. Cndot.) by summing the elements of (a) and (b) + Represents the generalized inverse;
constructing a cost function:
wherein,,
representing the Frobenius norm;
when the cost function is minimum, the direct current signal energy is just eliminated, at this time
And->
The values of (2) are as follows:
wherein C represents f b All possible ranges of values.
As a further improvement of the present invention, 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 estimates for the first time, a rough estimated sampling time offset and a channel impulse response estimated initial value are obtained; demodulating the useful signal to obtain a demodulated useful signal X 1 The method comprises the steps of carrying out a first treatment on the surface of the The received signal at the receiving end cancels the demodulated useful signal.
As a further improvement of the invention, the iterations are performed several times, each iteration using the original received signal to cancel the estimated useful signal.
The beneficial effects of the invention are as follows: the invention uses the necessary direct current offset component in the DCO-OFDM system to carry out the joint estimation of sampling time offset and the channel, and does not use pilot signals, thereby improving the frequency spectrum utilization rate of the system. Because the channel estimation is carried out simultaneously in the algorithm process, the channel prior information is not needed, and the 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 of the drawings and detailed description.
The invention is mainly oriented to a DCO-OFDM system, and uses a direct current offset signal which is indispensable in the system and enables a transmitting signal to meet non-negativity to carry out sampling time offset and channel estimation.
First we pairThe DCO-OFDM system models. Defining the number of subcarriers used in each DCO-OFDM block as N, and the system uses M-QAM as the modulation method of effective data, then in each transmission, the total N subcarriers can represent (N-2) log in total 2 M/2 bit binary data. Definition of the definition
In order to make the signal after IFFT be a real signal, the signal after IFFT needs to satisfy the hermite symmetric condition, and the hermite symmetric signal constructed by this method is as formula (1):
s＝[0,x(0),...,x(N/2-2),0,x * (N/2-2),...,x * (0)] T (1)
to replace the signal time domain convolution process with matrix multiplication, the signal needs to be converted into a cyclic matrix form, after which the matrix multiplication operation can be regarded as time domain signal convolution. The hermite symmetric signal is subjected to IFFT and converted into a time domain signal matrix S which is obtained in a cyclic matrix form, and the time domain signal matrix S is shown as formula (2):
S＝F H diag{s}F(1:L) (2)
wherein F represents a DFT matrix of size N, and the (u, v) term is expressed as formula (3):
diag { s } represents a diagonal matrix with rows and columns equal to the length of the vector s, the diagonal element of the diagonal matrix is each element in the vector s, L represents the discrete length of the channel time domain impulse response, F (1:L) is a submatrix of F, the rows of the diagonal matrix are consistent with F, and only the 1 st to the L th columns of F are taken, and the time domain symbol on the nth subcarrier in the time domain signal matrix can be represented as formula (3):
in general, the DC bias sigma DC Is according to the size of the hairThe average energy of the shot signal x (n) is derived as defined by equation (5):
wherein K is the DC bias ratio. In practical use, the transmitter signal transmission power is often constant, and each transmitted signal has the same average energy, so the DC bias sigma is used in the present invention DC Redefined as a constant, the magnitude of which is not discussed in the present disclosure.
In theory, in a DCO-OFDM system which normally operates, the time domain signal added with the direct current offset is mostly changed into a non-negative signal, but when sigma DC At smaller values, a portion of the negative signal may still be present. In the transmitter of DCO-OFDM system, the residual negative signal amplitude will be truncated to zero, so that clipping noise w is introduced clip (n) to represent this process, the clipping noise is defined as formula (6):
at this time, the transmission signal matrix processed by the transmitting end of the DCO-OFDM system may be expressed as formula (7):
wherein 1 is N×L Representing an all 1 matrix of size nxl,
to solve the ISI problem caused by signal tailing due to multipath effect, thereby preventing the ISI problem from affecting the system performance, a cyclic prefix CP is added to the signal to be used as a guardAnd (5) protecting the interval. In order to ensure that the cyclic prefix can effectively improve the reliability of the system, the length of the cyclic prefix is at least set to be L CP > L-1. The signal with the cyclic prefix added can be expressed as formula (8):
in the method, in the process of the invention,
representing a size L CP X L matrix with elements and +.>
Reciprocal L CP The row corresponds to the elements being identical.
In order to convert the digital signal into an analog signal for transmission in an actual channel and reconvert the analog signal into the digital signal at the receiving end, the signals need to be sampled at the transmitting end and the receiving end by using two identical root-mean-square-cosine roll-off filters respectively, and the identical purpose is to enable the receiving and transmitting ends to meet the matched filtering condition. Because both thermal and shot noise belong to the additive white gaussian noise AWGN, the ambient noise is modeled using the additive white gaussian noise. Under the condition of the receiving end complete frame detection, the received sampling signal matrix can be modeled as a formula (9):
where τ represents the sample time offset size normalized to the symbol duration T and satisfies τ ε (-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 free link channel, each adjacent channel has a time delay of T, and the expressions are shown as the following formula (10) and the formula (11):
h(n)＝h LoS *h LED (n) (10)
h＝[h(0),h(1),...,h(L-1)] T (11)
h in LoS Normalizing the gain for the LoS channel, h LED (n) is the gain of the LED at a delay nT due to the limited bandwidth, and represents a linear convolution operation.
Definition of the definition
w (n) is independent and the mean value of the same distribution is 0 and the variance is sigma 2 Is a gaussian random variable of (c); g (τ) represents the total equivalent raised cosine roll-off filter of the raised root cosine roll-off filters of the receiving end and the transmitting end, which are defined as formula (12), (13) and (14):
wherein Q is an oversampling rate for increasing sampling points to ensure the reliability of the system; ts is the oversampling interval, the size of which is ts=t/Q, and α is the filter roll-off coefficient.
An overall flow diagram of the algorithm proposed by the present invention is shown in fig. 1.
At the receiving end, according to the formulas (7) and (9), the optical signal transmitted through the free space visible light link and removed of the cyclic prefix can be decomposed into the form represented by the formula (15):
it can be seen that the signal is mainly composed of three parts: the first part is a received known DC offset signal, where G (τ) has removed the cyclic prefix part; the second part is the 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, the useful information and the noise belong to unknown random signals, and when the known direct current bias information is used for estimation, the useful signal actually exists as an interference signal in the 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 minimum value as the estimated signal matrix. Since channel information can be estimated at the time of trial value determination, each determined trial value corresponds to a determined channel estimate. Is provided with
For the test value of the sampling time offset of the current receiving end, the value range is (-0.5, 0.5), and a receiving end direct current bias estimation signal ++can be constructed through the maximum likelihood method>
And subtracting the received signal from the actual receiver to obtain the formula (16):
it can be seen in equation (16) that the second part of the useful signal and the third part of the additive white gaussian noise are not affected, and their energies are unchanged. When the test signal is introduced into the equation
The first part of the dc bias signal energy is zeroed and +.>
When the direct current bias signal matrix and the channel impulse response matrix both contain non-0 elements, the energy of the direct current bias signal matrix and the channel impulse response matrix is necessarily larger than zero. Therefore, the cost function is constructed as in equation (17):
in the method, in the process of the invention,
the Frobenius norm is represented and is defined as the sum of the squares of the absolute values of the elements in the matrix.
In practice, however, the test channel information is not exactly equal to the actual channel information, so a high accuracy estimate of the channel is required before using this cost function to ensure the accuracy of the cost function, since the maximum likelihood estimate is used as the estimate of the dc offset signal, each test value is taken
When the receiving end receives the ideal signal as the following formula (18):
since the useful signal is calculated as the interference signal at this time, ideally, the signal transmitted by the transmitting end should be all dc offset signal, and the interference is minimal at this time, and the ideal received signal becomes the equation (19):
at this time, the cost function becomes formula (20):
since the channel generally takes the form of an exponential drop, a corresponding test value can be constructed for searching, and the test value of the channel has the element expression as shown in formula (21):
wherein,,
test value, t, representing the 3-dB bandwidth limit of an LED s Representing a symbol sampling interval;
since the LoS channel only affects the overall attenuation magnitude, the matrix
The sum of all elements in (1) can be represented by a matrix
To obtain a determined test value, (. Cndot.) by summing the elements of (a) and (b) + Represents the generalized inverse;
when the cost function is minimum, the direct current signal energy is just eliminated, at this time
And->
Then->
And->
The value of (2) is as shown in the formula (22):
wherein C represents f b All possible value ranges; to this end, the channel and sample time offsets are jointly estimated.
The existence of useful signals can cause excessive energy of interference signals, when the influence of the interference signals on a cost function curve is larger than the size of the cost function changed by searching a sampling time offset test value, the lowest point of the cost function may have larger deviation from the lowest point under the condition that no interference exists, and further, the sampling time offset and the estimation accuracy of a channel are greatly reduced. To solve this problem, an interference iterative cancellation is introduced into the algorithm to minimize the impact of the useful signal on the performance of the synchronization algorithm.
When the algorithm estimates for the first time, a rough estimated sampling time offset and channel impulse response estimated initial value are obtained, in this case, the useful signal is demodulated, and a demodulated useful signal X can be obtained 1 Although the rough estimation can result in a larger error rate, more signals are accurately demodulated and have a certain correlation with the true useful signal, so the received signal at the receiving end eliminates the demodulated useful signal, and the expression is as shown in the following formula (23):
from equation (27), it can be seen that the energy of the useful signal is greatly attenuated and the impact on the performance of the synchronization algorithm is also greatly reduced. At this time, y in the algorithm is replaced with
The obtained sampling time offset and channel estimation are less interfered by the interfered signal, the estimation is more accurate, and compared with the method without using interference iterative elimination, the method can effectively improve the error rate performance of the system by eliminating the interfered signal. On the basis, in order to achieve better algorithm effect, the useful signals can be further eliminated iteratively until the algorithm performance reaches convergence. At the ith iteration, y is used to replace y i Expression is as formula (24):
in the middle of
Sampling time offset estimated for the i-1 th iteration,/th iteration>
Channel impulse response matrix estimated for the i-1 th iteration, X i-1 The demodulated useful signal is estimated from the first two 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 useful signal is cancelled in the previous iteration, otherwise, interference cancellation is disabled.
The foregoing description is only of the preferred embodiments of the present invention and is not intended to limit the scope of the invention, and all equivalent structures or equivalent processes using the descriptions and drawings of the present invention or directly or indirectly applied to other related technical fields are included in the scope of the invention. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and are to be considered as falling within the scope of the invention.
Claims (3)
1. A method for joint blind estimation of sampling time offset and channel based on direct current offset, the method being applied to a DCO-OFDM system, the method comprising:
receiving, at a receiving end, an optical signal transmitted through a free space visible light link and from which a cyclic prefix is removed:
y＝G(τ)σ DC 1 N×L h+G(τ)Xh+w
wherein G (τ) σ DC 1 N×L h is a received known direct current bias signal, τ represents the magnitude of the sampling time offset normalized to the symbol duration T, where G (τ) has removed the cyclic prefix portion, G (τ) Xh is the received useful information that needs to be demodulated, w is additive gaussian white noise, G (τ) represents the total equivalent raised cosine roll-off filter of the root-mean-square raised cosine roll-off filters of the receiving and transmitting ends,
w (n) is independent and the mean value of the same distribution is 0 and the variance is sigma 2 Q represents the oversampling rate, N represents the number of subcarriers used in each DCO-OFDM block, N ε [0, QN-1 ]]Representing the nth subcarrier, σ, used in each DCO-OFDM block DC For DC bias, 1 N×L Representing a full 1 matrix of size nxl, X being the original data signal, h representing a matrix of size lx1, each element of the matrix representing a normalized time domain impulse response size of the visible free link channel;
constructing a receiving end direct current bias estimation signal by using a maximum likelihood method
And->
For the test values, the channel test values are expressed as follows:
wherein h is LoS Indicating the normalized gain of the LoS channel,
test value, t, representing the 3-dB bandwidth limit of an LED s Representing a symbol sampling interval;
since the LoS channel only affects the overall attenuation magnitude, the matrix
The sum of all elements in (1) is represented by the matrix->
To obtain a determined test value, (. Cndot.) by summing the elements of (a) and (b) + Represents the generalized inverse;
constructing a cost function:
wherein,,
representing the Frobenius norm;
when the cost function is minimum, the direct current signal energy is exactly eliminated, and the estimated value of the time offset is sampled
And channel estimation +.>
The values of (2) are as follows:
wherein C is f b Constant in the value range.
2. The method according to claim 1, characterized in that the method introduces interference iterative cancellation for minimizing the effect of the useful signal on the performance of the synchronization algorithm, in particular:
after the algorithm estimates for the first time, a rough estimated sampling time offset and a channel impulse response estimated initial value are obtained; demodulating the useful signal to obtain a demodulated useful signal X 1 The method comprises the steps of carrying out a first treatment on the surface of the The received signal at the receiving end cancels the demodulated useful signal.
3. The method of claim 2, wherein the iterating is performed several times until the synchronization algorithm performance converges, each iteration using the original received signal to cancel the estimated useful signal.
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