CN117749579A - Single carrier frequency domain iterative equalization receiver based on expected propagation - Google Patents
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Abstract
The invention provides a single carrier frequency domain iterative equalization receiver based on expected propagation, and belongs to the technical field of wireless communication. The invention realizes equalizer and demodulator based on FPGA, the equalizer outputs external information to the demodulator, the demodulator feeds back soft information to the equalizer, and external iterative processing is formed between the equalizer and the demodulator; the equalizer comprises a detector and a moment matcher, and inner iteration processing is formed between the detector and the moment matcher; when each external iteration is performed, the demodulator transmits a set of probability values to the equalizer, the equalizer calculates the mean value and the variance of the set of probability values, the mean value and the variance are used as initial prior information, and internal iteration is started; when the preset inner iteration times are reached, the detector outputs corresponding corrected mean and variance to the demodulator, and one outer iteration is completed. According to the invention, on the basis of inner iteration, the equalizer and the channel decoder are cascaded, and information interaction is generated between the outer layer iteration combined with the decoder and the decoder, so that an effect better than that of the traditional equalization method is obtained.
Description
Technical Field
The invention relates to the technical field of wireless communication, in particular to a single carrier frequency domain iterative equalization receiver based on expected propagation.
Background
The main design idea of iterative equalization is to output demodulated soft information, and feed the soft information back to an equalizer at the front end for reconstructing an interference component, thereby eliminating interference caused by multipath transmission and improving the reliability of a receiver. The mature single carrier frequency domain equalization consists of two parts, equalizer and demodulator, as shown in fig. 1, the main implementation of single carrier frequency domain equalization is as follows:
1. the transmitting end designs a data block with a cyclic prefix form and transmits the data block into a channel;
2. the receiving end receives the data block, and obtains the channel response and the characteristic value of the soft information through the equalizer;
3. the soft information characteristic value of the equalizer is input to the demodulator, the demodulator recovers soft information through the characteristic value, and after calculation, the information after signal processing is fed back to the equalizer;
4. the equalizer and the demodulator obtain final decoding information after multiple iterative computations.
In inter-symbol interference channel equalization techniques, the equalizer typically uses a frequency domain equalization algorithm that can achieve low complexity and the same performance by a fast fourier transform.
The traditional single-carrier frequency domain equalization algorithm has strong applicability in multipath fading channels, but when the multipath interference of the channel is serious, the iterative convergence speed of the traditional algorithm is slow and the obtained channel response result is poor.
The desired propagation (Expectation Propagation, EP) is an algorithm that approximately solves the probability distribution, which works well in a linear measurement model. The frequency domain equalization calculation based on the expected propagation algorithm can process severe multipath interference channels, and more accurate channel response can be obtained through a small number of iterations. This feature makes the desired propagation algorithm more advantageous than conventional algorithms under severe multipath interference.
Disclosure of Invention
The invention provides a single carrier frequency domain iterative equalization receiver based on expected propagation. The invention introduces an expected propagation algorithm in the frequency domain equalization process, and extracts likelihood probability information of the modulation symbol to the greatest extent through multiple internal iterative processes.
The invention adopts the technical scheme that:
the single carrier frequency domain iterative equalization receiver based on expected propagation comprises an FPGA, wherein the FPGA is used for realizing an equalizer and a demodulator, the equalizer outputs external information to the demodulator, the demodulator feeds back soft information to the equalizer, and external iterative processing is formed between the equalizer and the demodulator.
The equalizer comprises a detector and a moment matcher, and inner iteration processing is formed between the detector and the moment matcher; the feedback soft information of the demodulator is a set of probability values, and the information outside the symbol output by the equalizer is the mean value and the variance of the input probability values.
And when each external iteration is performed, the demodulator transmits a set of probability values to the equalizer, the equalizer calculates the mean value and the variance of the set of probability values, the mean value and the variance are used as initial prior information, and the internal iteration is started.
And when each inner iteration is performed, the moment matcher calculates the mean value and the variance of the inner iteration according to the following steps:
wherein,and->Respectively representing the mean value and the variance of the s-th inner iteration in the t-th outer iteration, wherein the mean value and the variance when s=1 are the mean value and the variance of the initial prior information; />And->The mean and variance are calculated according to the expected variance formula of Gaussian distribution; the damping factor beta is a function of the outer iteration number t and the modulation order M:
min (,) represents a small value.
The moment matcher will iterate the mean value in this timeSum of variances->Transmitting to a detector, and calculating corrected mean value ++by the detector by adopting an unbiased detection estimation method>Sum of variances->And the input mean +.>Sum of variances->Returning to the moment matcher for the next iteration.
When the preset inner iteration times are reached, the detector outputs the corrected mean value and variance to the demodulator, and one outer iteration is completed.
Further, in each outer iteration, the demodulator processes the corrected mean and variance of the equalizer output, obtains log-likelihood ratios (Log Likelihood Ratio, LLR) through a full probability formula and a Gaussian distribution probability formula, obtains soft information according to LLR values through soft demodulation, de-interleaving, decoding, interleaving and soft modulation, and transmits the soft information to the equalizer.
When the preset outer iteration times are reached, the demodulator judges according to the corresponding LLR values, obtains decoding information and outputs the decoding information.
The invention has the beneficial effects that:
1. the invention introduces an expected propagation algorithm in the frequency domain equalization process, and extracts likelihood probability information of the modulation symbol to the greatest extent through multiple internal iterative processes.
2. The invention is cascaded with the demodulator based on the EP algorithm, and improves the decision accuracy of the equalizer by utilizing the soft information fed back by the demodulator.
3. The joint iteration equalizer scheme provided by the invention obtains better effect compared with the traditional equalization method through the outer layer iteration combined with the demodulator and the inner iteration of the equalizer.
Drawings
Fig. 1 is a schematic diagram of single carrier frequency domain equalization;
fig. 2 is a schematic diagram of single carrier frequency domain equalization based on iteration of a desired propagation algorithm in accordance with the present invention;
FIG. 3 is a flow chart of the operation of the present invention;
FIG. 4 is a graph of BER simulation results under the use of QPSK modulation in the Proakis C channel according to the present invention;
fig. 5 is a graph of BER simulation results for the present invention using 16QAM modulation on the Proakis C channel.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
A single carrier frequency domain iterative equalization receiver based on expected propagation, as shown in figure 2, comprises an FPGA, wherein the FPGA is used for realizing an equalizer and a demodulator, the equalizer outputs external information to the demodulator, the demodulator feeds back soft information to the equalizer, and external iterative processing is formed between the equalizer and the demodulator.
The equalizer comprises a detector and a moment matcher, and inner iteration processing is formed between the detector and the moment matcher; the feedback soft information of the demodulator is a set of probability values, and the external information output by the equalizer is the mean value and variance of the input probability values.
And when each external iteration is performed, the demodulator transmits a set of probability values to the equalizer, the equalizer calculates the mean value and the variance of the set of probability values, the mean value and the variance are used as initial prior information, and the internal iteration is started.
And when each inner iteration is performed, the moment matcher calculates the mean value and the variance of the inner iteration according to the following steps:
wherein,and->Respectively representing the mean value and the variance of the s-th inner iteration in the t-th outer iteration, wherein the mean value and the variance when s=1 are the mean value and the variance of the initial prior information; />And->Is based on the expected variance of the Gaussian distributionThe mean and variance pairs obtained by formula calculation; the damping factor beta is a function of the outer iteration number t and the modulation order M:
β＝min(0.35,exp(t/log 2 (M))/20) (6)
min (,) represents a small value.
The moment matcher will iterate the mean value in this timeSum of variances->Transmitting to a detector, and calculating corrected mean value ++by the detector by adopting an unbiased detection estimation method>Sum of variances->And the input mean +.>Sum of variances->Returning to the moment matcher for the next iteration.
When the preset inner iteration times are reached, the detector outputs the corrected mean value and variance to the demodulator, and one outer iteration is completed.
In each outer iteration, the demodulator processes the outer information output by the equalizer, obtains LLR through a full probability formula and a Gaussian distribution probability formula, then obtains soft information through soft demodulation, de-interleaving, decoding, interleaving and soft modulation, and transmits the soft information to the equalizer.
When the preset outer iteration times are reached, the demodulator judges according to the corresponding LLR, obtains decoding information and outputs the decoding information.
The receiver comprises an outer layer iteration and an inner layer iteration during operation, wherein the inner layer iteration refers to an EP equalizerThe inner iterative computation and the outer iterative computation refer to the information interaction iterative computation performed after the cascade connection of the EP equalizer and the demodulator. Next, the superscript sequence numbers [ t, s ] are used]The s-th inner iteration representing the t-th outer iteration. Wherein the method comprises the steps ofRepresenting the mean and variance of the information outside the symbol output by the detector in the s-th inner iteration of the t-th outer iteration. />Representing that in the s-th inner iteration process of the t-th outer iteration, the mean value of the sub-block prior soft information or feedback soft information of the EP detector is +.>Variance is->
As shown in fig. 3, the specific working procedure is as follows:
step 1: the demodulator outputs feedback information to the EP equalizer in the outer iteration.
According to the log-likelihood ratio fed back by the decoder, the demodulator calculates soft feedback information of the feedback sub-block through soft modulation. The initial prior information at the first inner iteration of the first outer iteration of the algorithm is equal.
Step 2: the detector in the inner iteration outputs the mean and variance of the outer information to the moment matching module.
The specific deduction flow is as follows:
based on the mean of soft informationInterference cancellation may be performed; s represents a transmission data block, wherein the nth symbol is s n The j-th symbol is s j Y represents the received data block, with the aid of soft information, in the t-th iteration, for s n Detection result of->Can be expressed as:
in the above formula, let us letWherein (1)>Is an N-dimensional received symbol vector, ">Representing an equivalent channel response matrix in the time domain corresponding to a data block, h n An nth column vector representing an H vector, H j An nth column vector representing an H vector. Noise vectors obey complex gaussian distribution +.>Wherein (1)>Is the variance of Gaussian distribution, I N Representing an N-dimensional unit vector.
According to the minimum mean square error criterion, the biased estimation detection result with the assistance of the feedback symbol can be written as follows:
detector matrix according to minimum mean square error criterionCan be expressed as:
in the above, a feedback variance matrix V is used [t,s] Sum of sign variance
At the t-th outer iteration, when s=1, the feedback soft information comes from the soft information fed back by the t-1 st outer iteration demodulator.
Where N is the dimension of the received symbol vector,representing the variance of the nth symbol calculated from the feedback soft information of the t-1 th outer iteration decoder in the 1 st inner iteration of the t-1 st outer iteration. At the same time, feed back the variance matrix V [t,1] Has diagonal characteristics:
at the t-th outer iteration, when s>1, symbol varianceObtained through a moment matching process, and simultaneously feeds back a variance matrix V [t,s] The form of the diagonal matrix is still maintained.
In the formula, the matrix is requiredInversion, here->To simplify the inversion process of (a), firstly, letThus, a formula can be obtained.
The two terms to the right of the last equal sign are analyzed separately, with the expression for the first term simplified as follows:
the expression of the second term is simplified as follows:
by taking the formula and the formula into the formula, the equalization result can be written as follows:
when calculating the equalization result of the expression, adopting a vectorization expression method to reflect the processing result of the whole data block through one expression. Meanwhile, due to the effect of the cyclic prefix, the equivalent channel matrix H has cyclic translation characteristics, namely, each column of the matrix can be obtained by carrying out cyclic translation on the first column; for cyclic shift matrices, the frequency domain channel response matrix has a diagonal form, i.e
G＝FHF H ＝diag{g 0 ,g 1 ,…,g N-1 } (16)
Therefore, the formula can be simplified continuously, and the calculation complexity is further reduced.
First the following matrix is defined:
in the above formula, G is a diagonal matrix,also diagonal matrix, F and F H Representing the FFT and IFFT matrices, respectively. Therefore, the FFT transform result of the diagonal matrix +.>Is a cyclic shift matrix. D according to the characteristics of the cyclic shift matrix [t,s] Is a diagonal matrix with equal diagonal sign, i.eAt the same time (I)>The frequency domain channel response calculation may be used to obtain:
wherein, |g n And I represents the modulus value of the nth element on the diagonal of the G matrix.
Thus, the equalization process characterized by the formula is written in vectorized form as:
V [t,s] ,D [t,s] all are diagonal matrices, the simplification of the computational complexity is mainly focused onIs calculated by the computer. The following equivalent operation is performed using the diagonal characteristics of the frequency domain channel response.
In the aboveA received signal representing the s-th inner layer iteration of the t-th outer iteration in the frequency domain,/v>Can be written in the following form:
and synthesizing the analysis results, and finally writing the vectorized equalization result into the following form:
in the formula, the matrices G, V [t,s] ,D [t,s] Are diagonal matrices, which means that all matrix inversion operations are performed on the diagonal matrices, and the calculation complexity is O (N); meanwhile, the operation of FFT and IFFT is included in the formula, so that the computational complexity of the formula is of the order of O (N log N).
In the s inner layer iteration of the t outer iteration, the unbiased detection result after normalization of the signal coefficient can be written as follows:
wherein the effective signal coefficientThe expression of (2) is:
in the s inner layer iteration of the t outer iteration, the unbiased detection result normalized by the signal coefficient can be written as follows
The variance of the superposition result of the noise and the interference after detection corresponding to the result of unbiased estimation is
In an inner layer iteration of the EP algorithm,and->Representing the mean and variance of the outer information obtained after the s-th inner iteration of the t-th outer iteration passed the detector.
Step 3: the moment matching module in the inner iteration updates based on the soft feedback of the EP criteria.
In soft feedback updating based on the EP criterion, the posterior probability of the modulation constellation point is calculated according to the mean value and the variance of the external information and in combination with the prior information provided by the channel decoder, and then the mean value and the variance of the discrete constellation point are calculated.
In the t outer layer iteration, the outer information output result of the s inner layer iteration is thatI.e. comprising mean and variance. Meanwhile, in the t outer layer iteration, the prior information provided by the demodulator is assumed to be discrete probability distributionAnd (3) representing the probability that the nth modulation symbol in the calculated data block takes the value of the mth constellation point according to the feedback of the demodulator in the t-th outer iteration.
According to the result, based on prior information and external information, mapping to discrete constellation points, and obtaining a posterior probability expression as follows:
therefore, the formula is LLR value after the inner iteration is output to the outer iteration. Meanwhile, according to the probability calculation result of the formula, the posterior mean value is further obtainedSum of variances->Is calculated as the result of:
in order to achieve moment matching, the variance result calculated based on posterior probability is considered as the mean of the variances of the N symbols in the data block:
according to the above analysisAnd in the s-th inner layer iteration marked as the t-th outer layer iteration, calculating the obtained mean and variance pairs based on posterior probability distribution.
According to the moment matching criterion of the EP algorithm, the following expression can be obtained according to the calculation criterion of the mean and variance of the Gaussian random variables, when the variance isWhen the formula and the formula are selected
When variance isWhen the method is used, a formula sum is selected.
The mean and variance pairs of the "extrinsic information" after moment matching can be obtained by the above calculation.
In the calculation of the formula sum, the calculation of the subtraction is included, negative calculation results are likely to appear in numerical value, in order to solve the problem, a standard-quantity variance transmission mode is adopted, and since the standard-quantity variance transmission mode averages the results of all N symbol variance calculations, the variance after mean calculation is relatively stable, that is, the large probability can meet the expression of the formula, and in the case of unsatisfied, that is, the variance is negative, the method adoptsDirectly replace->
The input mean and variance for the next iteration, i.e., the (s+1) th linear iteration, can be written as follows
The process of one inner layer iteration based on the EP is completed. The damping factor is set as a function of the number of outer iterations t and the modulation order M
β＝min(0.35,exp(t/log 2 (M))/20) (36)
Wherein 0.35 is taken as the maximum value of the damping factor, and the convergence speed of the algorithm is limited. In the high-order modulation, the smaller convergence speed is used to ensure the convergence accuracy, and in the outer iteration process, the confidence of the updating parameter of the EP process is increased along with the increase of the outer iteration times, so that the convergence speed is increased. And (3) feeding back the updated result in the step (3) to the step (2) before the internal iteration times are reached, and outputting the updated result to the step (4) after the internal iteration times are reached.
Step 4: the EP equalizer outputs external information to the demodulator in an external iteration.
External information mean and variance pairs obtained by demodulator pair internal iterationAnd performing soft demodulation to calculate LLR corresponding to the extrinsic information, and performing decoding operation by a decoder according to the LLR to finish one extrinsic iteration.
After finishing one outer iteration, feeding back the demodulator calculation result of the outer iteration to the EP equalizer of the outer iteration, and continuing the next outer iteration from the step 1.
Step 5: and when the outer iteration times are reached, outputting decoding information to judge.
Finally, the Matlab tool is used for simulating an Expected Propagation (EP) equalization algorithm under the Proakis C channel, and the simulation is compared with a traditional MMSE algorithm. Firstly, setting the data block length of a single carrier transmission as 512, adopting QPSK as a modulation mode, setting the code length of channel coding as 1024 and setting the code rate as 1/2, namely, setting the single carrier data block to exactly contain a channel coding code block.
In the BER simulation result of fig. 4, MMSE equalizationBoth the algorithm and the Expected Propagation (EP) equalization algorithm were iterated 5 times. Under the same iteration times, the EP equalization algorithm has obvious performance gain relative to the MMSE equalization algorithm. As can be seen from fig. 4, in the case of the iteration number of 5, when the Bit Error Rate (BER) is equal to 10 -4 When compared to the MMSE equalization algorithm, the EP equalization algorithm has a performance gain of 0.9 dB.
Fig. 5 shows simulation results under 16QAM modulation. The simulation channel uses a proapic C channel. The number of FFT points is still 512, the adopted channel coding rate is 1/2, and the length of the coded data block is 2048 bits.
As can be seen from fig. 5, the EP equalization algorithm has a more significant performance advantage under 16QAM high order modulation. Under the condition that the bit error rate reaches 1e-5, the EP equalization algorithm iterates 5 times, and the performance advantage obtained is about 5dB relative to the MMSE equalization algorithm iterates 5 times.
In the inter-symbol interference channel equalization technology, the equalization method based on expected propagation efficiently extracts likelihood probability information of a modulation symbol through 5 outer iterative computations and 2 inner iterative computations by assuming that prior information is Gaussian distribution, and improves detection performance of an equalizer.
In short, the equalizer and the channel decoder are cascaded on the basis of inner iteration, and information interaction is generated between the outer layer iteration combined with the decoder and the decoder, so that an effect better than that of the traditional equalizing method is obtained. The invention approximates the discrete prior probability distribution with Gaussian distribution through the expected propagation algorithm to reduce the complexity of the EP algorithm. The invention adopts a standard variance transmission mode to maintain the characteristic of low complexity characteristic calculation, and averages the results of all N symbol variance calculation so as to avoid that the subtraction operation in the updating process can cause the calculation result that the variance is negative when the prior parameter is updated in the moment matching. The damping factor beta is introduced to balance the reliability of the moment matching result and the priori result, namely, the damping factor is weighted by a linear method, so that the robustness of the EP soft information feedback process is enhanced.
Claims (2)
1. The single carrier frequency domain iterative equalization receiver based on expected propagation comprises an FPGA, wherein the FPGA is used for realizing an equalizer and a demodulator, the equalizer outputs external information to the demodulator, the demodulator feeds back soft information to the equalizer, and external iterative processing is formed between the equalizer and the demodulator;
the equalizer is characterized by comprising a detector and a moment matcher, wherein inner iteration processing is formed between the detector and the moment matcher; the feedback soft information of the demodulator is a set of probability values, and the external information output by the equalizer is the mean value and variance of the input probability values;
when each external iteration is performed, the demodulator transmits a set of probability values to the equalizer, the equalizer calculates the mean value and the variance of the set of probability values, the mean value and the variance are used as initial prior information, and internal iteration is started;
and when each inner iteration is performed, the moment matcher calculates the mean value and the variance of the inner iteration according to the following steps:
wherein,and->Respectively representing the mean value and the variance of the s-th inner iteration in the t-th outer iteration, wherein the mean value and the variance when s=1 are the mean value and the variance of the initial prior information; />And->Is based on the period of Gaussian distributionThe mean value and variance pair obtained by calculating the telescope variance formula; the damping factor beta is a function of the outer iteration number t and the modulation order M:
β＝min(0.35,exp(t/log 2 (M))/20) (3)
min (,) represents a small value;
the moment matcher will iterate the mean value in this timeSum of variances->Transmitting to a detector, and calculating corrected mean value ++by the detector by adopting an unbiased detection estimation method>Sum of variances->And the input mean +.>Sum of variances->Returning to the moment matcher for the next iteration;
when the preset inner iteration times are reached, the detector outputs corresponding corrected mean and variance to the demodulator, and one outer iteration is completed.
2. The single carrier frequency domain iterative equalization receiver of claim 1, wherein in each outer iteration, the demodulator processes the outer information output from the equalizer, obtains log likelihood ratios by a full probability formula and a gaussian distribution probability formula, and obtains soft information by soft demodulation, deinterleaving, decoding, interleaving and soft modulation according to the log likelihood ratios, and transmits the soft information to the equalizer.
When the preset outer iteration times are reached, the demodulator judges according to the corresponding log-likelihood ratio, obtains decoding information and outputs the decoding information.
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