KR20140067896A - Method and apparatus of iterative detection and decoding of signal in communication systems with mimo channel - Google Patents

Abstract

The present invention relates to a signal reception method of a communication device utilizing a MIMO-based technology. The communication device including a MIMO channel which repeatedly detects or decodes signals according to an embodiment of the present invention includes: a MMSE detector; a QAM demodulator; a first module; a channel decoder; a second module; and a hard-decision estimator.

Description

[0001] The present invention relates to a method and apparatus for repeated detection and decoding of a signal in a communication system having a MIMO channel, and a method and apparatus for iterative detection and decoding of a signal in a communication system having a MIMO channel.

MIMO is a smart antenna technology for improving the capacity of wireless communication. MIMO systems belong to a new direction within the field of wireless communication systems.

MIMO can improve capacity in proportion to the number of used antennas by using multiple antennas at the base station and / or the terminal.

MIMO systems can transmit signals in parallel over a plurality of different channels within the same frequency band. MIMO systems can achieve very high spectral efficiency due to this parallel transmission of preferences.

In one aspect, a communication apparatus having a MIMO channel for repeatedly detecting and decoding a signal, the apparatus comprising: an MMSE detector for estimating QAM symbols based on received signals that have passed through the MIMO channel; A QAM demodulator for demodulating and estimating a first posterior probability of the encoded bits of the QAM symbols, a soft estimate of the encoded bits by removing a first prior probability of the encoded bits from the first posterior probability A channel decoder for decoding the encoded bits based on the soft estimate and obtaining an improved after-probability of the encoded bits, a second decoder for obtaining a second pre-probability based on the improved post- 2 modules, the second prior probability being a first prior probability in a next iteration cycle; And a hard decisions estimator that forms a sequence of hard estimates of information bits based on the improved posterior probabilities.

The first posterior probability may be a log ratio of the posterior probability of the encoded bits.

The first prior probability may be a log ratio of the prior probability of the encoded bits.

The first pre-probability is a value obtained by dividing the probability when the k-th encoded bit in the n-th QAM symbol is 1 and the probability when the k-th encoded bit in the n-th QAM symbol is -1 It can be a value obtained by taking a natural log.

The n may be an integer of 1 or more and N or less.

K may be an integer of 1 or more and K or less.

The N may be the number of QAM symbols.

The K may be the number of bits in the QAM symbol.

The improved posterior probability may be an improved posterior probability log ratio.

And the second prior probability can be obtained by removing the softness estimate from the improved posterior probability.

The first module may use the second pre-probability as the first pre-probability to obtain an improved post-probability in the next iteration if the estimated number of times the improved post-probability is more than once.

The communication device may further comprise a re-modulator to obtain a first expected value and a first variance of the QAM symbols based on the improved posterior probability.

The communication device may further comprise a third module for comparing the first variance with the variance obtained after estimation of the QAM symbols of the previous iteration cycle.

The third module may generate new input parameters for the MMSE detector based on the comparison.

The new input parameters may include a second expected value and a second variance.

The variance obtained after estimation of the QAM symbols of the previous iteration cycle may be a third variance.

The expected value obtained after the estimation of the QAM symbols may be the third expected value.

The third module obtains the second expected value based on the first expectation value, the first variance, the third expectation value and the third variance, if the first variance is less than the third variance, by the comparison can do.

The third module may obtain the second variance based on the first variance and the third variance if the first variance is less than the third variance by the comparison.

Wherein the third module is configured to compare the second expected value and the second variance obtained in the previous iteration cycle to the second expected value and the second variance in the current iterative cycle, respectively, if the first variance is the third variance or more, As shown in FIG.

The MMSE detector may obtain an MMSE estimation estimate and an MMSE estimation variance of the symbol vector by applying an MMSE linear filter to the symbol vector of the QAM symbols received by the MMSE detector.

The MMSE detector may obtain a third expectation to be used in the next iteration cycle based on the second expectation, the second variance, the MMSE estimate estimate and the MMSE estimate variance.

The MMSE detector may obtain a third variance to be used in the next iteration cycle based on the second variance and the MMSE estimate variance.

The QAM symbol in the next iteration cycle can be estimated by obtaining the third expectation and the third variance.

The third expectation and the third variance may be input to the QAM demodulator in the next iteration cycle.

The QAM demodulator may estimate a first posterior probability based on the third expected value and the third variance.

If the MMSE detector first obtains the third expected value and the third variance, the second expected value may be zero and the second variance may be a unit variance.

The communication apparatus may further include a de-interleaver and an interleaver.

The de-interleaver may de-interleave the encoded bits before the encoded bits are input to the channel decoder.

The interleaver may interleave the soft bits output from the channel decoder.

In another aspect, there is provided a method for estimating QAM symbols based on signals received on a MIMO channel, the method comprising the steps of: estimating QAM symbols based on signals received on the MIMO channel performed by a communication device having a MIMO channel that repeatedly detects and decodes the signal; Demodulating and estimating a first posterior probability of the encoded bits of the QAM symbol; obtaining a soft estimate of the encoded bits by removing a first prior probability of the encoded bits from the first posterior probability; , Decoding the encoded bits based on the soft estimate and obtaining an improved after probability of the encoded bits, obtaining a second prior probability based on the improved after probabilities, The prior probability being a first prior probability in a next iteration cycle; And forming a sequence of hard estimates of information bits based on the improved posterior probability. A method for repeatedly detecting and decoding a signal is provided.

The first posterior probability may be a log ratio of the posterior probability of the encoded bits.

The first prior probability may be a log ratio of the prior probability of the encoded bits.

The improved posterior probability may be an improved posterior probability log ratio.

Obtaining the second pre-probability may estimate the second pre-probability by removing the soft estimate from the improved post probability.

Wherein the step of acquiring the improved posterior probability when the estimated number of times of the improved posterior probability is more than once comprises using the second prior probability as the first prior probability to obtain an improved posterior probability in the next iteration cycle Can be obtained.

The method of iteratively detecting and decoding the signal may further comprise obtaining a first expected value and a first variance of the QAM symbols based on the improved posterior probability.

The method for repeatedly detecting and decoding the signal may further comprise comparing the first variance to the variance obtained after the estimation of the QAM symbols of the previous iteration cycle.

The method for repeatedly detecting and decoding the signal may further comprise generating new input parameters for estimating QAM symbols in a next iteration cycle based on the comparison.

The new input parameters may include a second expected value and a second variance.

The variance obtained after estimation of the QAM symbols of the previous iteration cycle may be a third variance.

The expected value obtained after the estimation of the QAM symbols may be the third expected value.

The comparing may obtain the second expected value based on the first expected value, the first variance, the third expected value, and the third variance if the first variance is less than the third variance.

The comparing may obtain the second variance based on the first variance and the third variance if the first variance is less than the third variance.

Wherein the comparing comprises obtaining the second expected value and the second variance obtained in the previous iteration cycle as the second expected value and the second variance respectively in the current iteration cycle if the first variance is the third variance or more have.

Estimating the QAM symbols may comprise obtaining an MMSE estimate estimate of the symbol vector and an MMSE estimate variance by applying an MMSE linear filter to the symbol vector of received QAM symbols.

Wherein estimating the QAM symbols comprises: obtaining a third expectation to be used in a next iteration cycle based on the second expectation value, the second variance, the MMSE estimate estimate and the MMSE estimate variance, And obtain a third variance to be used in the next iteration cycle based on the MMSE estimated variance.

The QAM symbol in the next iteration cycle can be estimated by obtaining the third expectation and the third variance.

The estimating of the first posterior probability may estimate the first posterior probability based on the third expected value and the third variance.

If the third expected value and the third variance are first obtained, the second expected value may be zero.

If the third expected value and the third variance are first obtained, then the second variance may be a unit variance.

1 is a structural diagram of a transmission apparatus having a MIMO channel for generating a signal.
2 is a structural diagram of a receiving apparatus having a MIMO channel.
3 is a structural diagram of a receiving apparatus for performing repetitive detection and decoding.
4 is a flowchart of a method of repeatedly detecting and decoding a signal of a communication apparatus having a MIMO channel according to an embodiment.
5 is a flowchart of QAM symbol estimation according to an example.
6 is a block diagram of a communication device with a MIMO channel that performs repetitive detection and decoding of a signal according to one embodiment.
Figure 7 illustrates the performance of three types of detectors and demodulators according to an example.
Figure 8 shows the performance of three types of detectors and demodulators according to an example.

Various modes of transmission may be used for signals by MIMO. One of the most widely used modes of transmission of signals by MIMO is the Vertical Bell Laboratories Layered Space Time (V-BLAST) architecture.

In a V-blast architecture, known as spatial multiplexing, a signal can be divided into one or more parallel streams. The partitioned parallel streams may be transmitted by a plurality of spatial channels formed between the transmit antennas and the set of receive antennas.

The MIMO system can be described in the frequency domain by the matrix equation of Equation (1) below.

는 복소 잡음의 값들의 벡터일 수 있다. H는 MIMO 채널의 복소 채널 행렬일 수 있다. H의 크기는 M*N일 수 있다. M 및 N은 각각 1 이상의 정수일 수 있다. Y may be an M- dimensional vector of the complex valued signal on the input of the MIMO detector. Y can be regarded as a vector of output samples of the MIMO channel. X may be an N- dimensional vector of transmitted Modulated Quadrature Amplitude Modulation (QAM) symbols in a transmitter. X may be regarded as a vector of input samples of the MIMO channel.

May be a vector of values of the complex noise. H may be a complex channel matrix of a MIMO channel. The size of H may be M * N. M and N may be an integer of 1 or more, respectively.

When a signal is transmitted using the spatial multiplexing scheme, mutual interference between different parallel data streams may occur. Thus, there may be work to design efficient methods of signal detection, modulation, and decoding under conditions of external noise and mutual interference. The most complete method of signal detection may be the Maximum Likelihood (ML) method. The maximum likelihood method can estimate the probability of all possible combinations of symbols. The main drawback of the maximum likelihood method may be the high complexity of the maximum likelihood method, which goes up exponentially with respect to the number of simultaneously transmitted streams. There may be many alternative methods of signal detection due to mutual interference mitigation. The popular methods are the Zero Forcing (ZF) method and the Minimum Mean Square Error (MMSE) method, which are the most popular methods used for interference reduction. The ZF method may be a method of minimizing the average interference power in the receiver. The MMSE method may be a method of minimizing the mean square error of the estimate.

In the case of the MMSE method, Equation (1) can be defined as Equation (2).

는 수학식 3으로 정의될 수 있다.here,

Can be defined by Equation (3).

는 선형 변환(linear transformation)의 MMSE 필터 행렬일 수 있다.

는 잡음 분산일 수 있다.

는 신호 전력의 평균값일 수 있다.

은 N*N의 크기의 항등 행렬일 수 있다. N은 1 이상의 정수일 수 있다.

는 전송된 QAM 심볼들의 MMSE 추정의 벡터일 수 있다.

는 MMSE 해(solution)일 수 있다.

May be an MMSE filter matrix of a linear transformation.

May be a noise variance.

May be an average value of the signal power.

May be an identity matrix of size N * N. N may be an integer of 1 or more.

May be a vector of MMSE estimates of the transmitted QAM symbols.

May be an MMSE solution.

The ZF and MMSE methods have relatively low realization complexity but can exhibit a significant degradation compared to the ML method in terms of the accuracy of received symbol estimates and the probability of eventually receiving incorrect bits in the message (bit error rate).

Modern digital communication systems of the spatial multiplexing scheme can widely suggest other ways of transmitting and receiving signals that improve the efficiency and quality of signal transmission data transmission. In particular, methods of channel encoding of digital data in a transmitting device and corresponding decoding of digital data in the receiver can be widely applied within these methods. In addition, these methods may use data scrambling and interleaving of data, as indicated by the term "interleaving ". Interleaving can lead to a more efficient transmitted signal distribution within a space-time-frequency continuum. A more efficient transmitted signal distribution may ultimately improve the quality of the data transmission.

In methods of repetitive signal detection and decoding, joint detection and decoding may be performed within a common iterative process. These methods may be referred to as Turbo processing methods.

In a communication system, the digital data may be exposed in a coding procedure in a channel coder. In a channel coder, the first input sequence of information bits may be converted to an output sequence. The output sequence may include additional parity-check bits.

There may be various types of channel codes used in digital communication systems. Convolution codes, Turbo codes and Low Density Parity Check Codes (LDPC) codes can be exemplified as widely practicable codes.

After encoding, the data can be interleaved, modulated, spatially de-multiplexed, transformed from a digital signal to an analog signal, frequency converted, Amplified and can be spatially transmitted by the antennas of a plurality of transmitters.

1 is a structural diagram of a transmission apparatus having a MIMO channel for generating a signal.

1 illustrates a design of signal generation in a system with a MIMO channel.

The transmission apparatus 100 may include a channel coder 101, an interleaver 103, a modulator 105, a de-multiplexer 107 and a plurality of transmitters. As N transmitters, a first transmitter 109a and a second transmitter 109b are shown. N may be the number of transmitters, and may be an integer greater than or equal to two.

The input data may be bits. That is, the input data may be input information bits.

The channel coder 101 may generate the encoded bits by transforming the input information bits.

The interleaver 103 may generate interleaved encoded bits by interleaving the encoded bits.

The modulator 105 may generate the modulated data by modulating the interleaved encoded bits. The modulated data may be the result of modulating the interleaved encoded bits. The modulator 105 may be a mapper.

The demultiplexer 107 may demultiplex the modulated data into a plurality of spatial streams.

Each transmitter of the plurality of transmitters may transform each spatial stream of the plurality of spatial streams into an analog signal. Each transmitter can convert the carrier frequency of the analog signal and amplify the analog signal. After the above conversion, conversion and amplification, a plurality of transmitters may each transmit analog signals.

A receiving apparatus corresponding to Fig. 1 will be described below in detail with reference to Fig.

2 is a structural diagram of a receiving apparatus having a MIMO channel.

2 illustrates a design of signal reception in a receiving device with a MIMO channel.

The receiving apparatus 200 may include a plurality of receivers, a MIMO detector 203, a demodulator 205, a de-interleaver 207 and a channel decoder 209. As a plurality of receivers, a first receiver 201a and a second receiver 201b are shown. The number of receivers may be M. M may be an integer of 2 or more.

A plurality of receivers can receive the transmitted signals, respectively. Each receiver of the plurality of receivers can receive each transmitted signal of the transmitted signals, amplify the received signal, convert the received signal by using the carrier frequency, and filter the received signal And can convert the received signal into a digital signal. The above-described reception, amplification, conversion using the carrier frequency, filtering and conversion to digital signals can be performed sequentially for each transmitted signal of the transmitted signals at the corresponding receiver.

The digital signals output from the plurality of receivers may be transmitted to the MIMO detector 203. The MIMO detector 203 can output a digital signal by performing auxiliary MIMO detection on the digital signals. The MIMO detector 203 may detect a multi-dimensional input signal in the digital signals.

The demodulator 205 can generate a demodulated digital signal by demodulating the digital signal processed by the MIMO detector 203. [

The de-interleaver 207 can de-interleave the demodulated digital signal to generate a de-interleaved digital signal.

The channel decoder 209 can generate output data by decoding the de-interleaved digital signal.

The output data may correspond to the input data and input information bits described above with reference to FIG. The de-interleaved digital signal may correspond to the encoded bits described above with reference to FIG. The demodulated digital signal may correspond to the interleaved encoded bits described above with reference to FIG. The digital signal output from the MIMO detector 203 may correspond to the modulated data described above with reference to FIG. The digital signals output from the plurality of receivers may correspond to the plurality of spatial streams described above with reference to FIG. Signals received by the plurality of receivers may correspond to analog signals transmitted from the plurality of transmitters described above with reference to FIG.

3 is a structural diagram of a receiving apparatus for performing repetitive detection and decoding.

3 is a block diagram of a receiving device 300 that performs iterative detection and decoding in a system with a MIMO channel.

The receiving apparatus 300 may correspond to the receiving apparatus 200 described above with reference to Fig. Particularly, in the receiving apparatus 300 and the receiving apparatus 200, components having the same or similar names can perform the same or similar functions.

The receiving apparatus 300 may include a plurality of receivers, a MIMO detector 304, a de-interleaver 307, a channel decoder 309, an interleaver 311 and a hard decisions estimator 313 have. The MIMO detector 304 may include a de-mapper 303 and a demodulator 305. As a plurality of receivers, a first receiver 301a and a second receiver 301b are shown. The number of receivers may be M. M may be an integer of 2 or more.

A plurality of receivers can receive the transmitted signals, respectively. Each receiver of the plurality of receivers can receive each transmitted signal of the transmitted signals, amplify the received signal, convert the received signal by using the carrier frequency, and filter the received signal And can convert the received signal into a digital signal. The above-described reception, amplification, conversion using the carrier frequency, filtering and conversion to digital signals can be performed sequentially for each transmitted signal of the transmitted signals at the corresponding receiver.

The digital signals output from the plurality of receivers may be transmitted to the MIMO detector 304 of the de-mapper 303.

The MIMO detector 304 may detect a multi-dimensional input signal from the digital signals.

The demodulator 305 may generate the encoded bits by demodulating the detected multidimensional input signal. The demodulator 305 may perform a first estimation of the encoded bits probability. The demodulator 305 may perform the first estimation by using a Logarithm Likelihood Ratio (LLR) or a Logarithm Ratio of Posterior Probabilities.

MIMO detector 304 and demodulator 305 may be combined in a de-mapper 303 that is a module of the joint.

The digital signals output from the plurality of receivers may be the input data of the de-mapper 303. The de-mapper 303 may receive prior information about the encoded bits (i.e., the QAM symbols including the encoded bits), along with the input data. The dictionary information may be output from the interleaver 311. The dictionary information for the encoded bits may include a prior probability for the encoded bits. The encoded bits after the probability estimate (i.e., the log ratio of posterior probabilities) may be soft bits.

The soft bits may be input to the de-interleaver 307. The de-interleaver can de-interleave the soft bits and output the de-interleaved soft bits. The de-interleaved soft bits may be input to the channel decoder 309.

The channel decoder 309 may perform estimation of the posterior probability of information bits (i.e., the log ratio of posterior probabilities). The information bits may be formed on the first output (i.e., the main output) of the channel decoder 309 based on the parameters of the code used. The channel decoder 309 may also improve the value of the probabilities of the encoded bits on the second output of the channel decoder 309. [ That is, the channel decoder 309 can form an improved soft estimate of the encoded bits.

The first output of the channel decoder 309 may comprise a soft estimate of the information bits. The hard decision estimator 313 may convert the softness estimates of information bits to hard estimates. Output data can be generated by conversion to hard estimates.

The output of the hard decision estimator 313 may be the common output of a communication device with a MIMO channel.

The second output of the channel decoder 309 may include soft estimates of the improved encoded bits.

After the soft estimates of the improved encoded bits are removed from the information present in the form of soft estimates of the encoded bits at the input of the channel decoder 309, the interleaver 311 calculates the soft estimates of the improved encoded bits Lt; / RTI > The soft estimates of the interleaved improved encoded bits may be output as an auxiliary input of the de-mapper 304 as prior information for the next iteration.

In an embodiment, MIMO detector 304 and demodulator 305 may be tightly integrated. The MIMO detector 304 and the demodulator 305 may be combined in a de-mapper 303, which is a module of a joint.

For example, when a spherical detection method is used, the advance information may be input to the MIMO detector 304 to reduce the number of symbol-candidates participating in the computation of the posterior information. have.

For example, when another method such as an ML detector is used, the prior information may be input to the demodulator 305. [

In the next iteration, the MIMO detector 304 and demodulator 305 may generate a new estimate of the posterior probability of the encoded bits (i.e., the log ratio of posterior probabilities). After the prior information (i. E., The log ratio of prior probabilities) is removed from the new estimate, the de-interleaver 307 may de-interleave the new estimate from which the prior information has been removed. Channel decoder 309 may decode the de-interleaved new estimate. The new estimate can be de-interleaved once more and decoded. Repeating the repeated procedure of detection by the MIMO detector 304 or decoding of the channel decoder 309 can lead to improved reliability of the estimates of the encoded bits. Through the improvement of reliability, the final sequence of hard estimates of information bits can be matched with a higher probability to the transmitted sequence. Here, the final sequence may correspond to the output data of the receiving apparatus 300. The output data of the receiving apparatus 300 may correspond to the input data of the transmitting apparatus 100.

One or more methods may be used to implement repeated detection and decoding of a transmitting device and a receiving device with MIMO. Various methods of iterative detection and decoding can be selected as prototypes of embodiments.

The design of signal reception and processing may correspond to the design of FIG.

 Therefore, after the processing by the MIMO detector 304, the estimation of the posterior probability can be performed according to the ML algorithm of Equation (4).

는 LLR 값일 수 있다. n은 1 이상 N 이하의 값일 수 있다. k는 1 이상 K 이하의 값일 수 있다. K는 성상도(constellation)

에 의해 정의된 QAM 심볼 내의 비트들의 개수일 수 있다. 성상도에 대한 합 계산(summing)은 심볼들의 모든 가능한 조합들을 통해 수행될 수 있다. 성상도는 +1 또는 -1에 동등한 비트를 포함할 수 있다. +1 및 -1은 초기 비트 값들인 0 및 1 에 대응할 수 있다. 수학식 4 내의 두 번째 피가수(summand)는 사전 확률들의 로그비를 정의할 수 있다. 각 수신 안테나에 대한

는 유클리드 거리(Euclidian distance) 값일 수 있다.

May be an LLR value. n may be a value of 1 or more and N or less. k may be a value of 1 or more and K or less. K is a constellation,

Lt; RTI ID = 0.0 > QAM < / RTI > Summing for the constellation may be performed through all possible combinations of symbols. The constellation may include bits equal to +1 or -1. +1 and -1 may correspond to initial bit values of 0 and 1, respectively. The second summand in equation (4) can define the log ratio of prior probabilities. For each receive antenna

May be an Euclidean distance value.

는 하기의 수학식 5에 의해 정의될 수 있다. m은 수신 안테나의 개수로서 1 이상 N 이하의 값일 수 있다.

은 제 m번째 수신 안테나에 대한 유클리드 거리 값일 수 있다

Can be defined by the following equation (5). m may be a value of 1 or more and N or less as the number of receiving antennas.

May be the Euclidean distance value for the m < th > receive antenna

의 계산에 관여하는(engaged in) 가능한 심볼들의 개수는,

개의 전송 안테나들의 개수와 관련하여 기하 급수적으로 증가할 수 있다. 이러한 증가는 전술된 접근법의 실행을 불가능하게 할 수 있다.

The number of possible symbols that are engaged in the calculation of < RTI ID = 0.0 >

Lt; RTI ID = 0.0 > number of transmit antennas. ≪ / RTI > This increase may make it impossible to implement the approach described above.

에 의해 남겨진 벡터 Y를 곱하는 것이 제안될 수 있다. 남겨진 벡터 Y를 곱하는 것은 하나를 제외한 모든 전송된 심볼들(말하자면, 모든 전송 안테나들로부터의 심볼들)을 0으로 만들 수 있다.MIMO detection can use a procedure of interference mitigation. A simplified procedure of MIMO detection using conventional interference cancellation can be used. ( M - N + 1) * N matrix of size

It may be proposed to multiply the left Y by the vector Y. Multiplying the remaining vector Y can make all transmitted symbols (i.e., the symbols from all transmit antennas) to be zero except for one.

As a result of the LLR calculation, it may only be required to calculate ( M - N + 1) * K Euclidian distances. If the value of M and the value of N are equal (say, the number of transmit antennas and the number of receive antennas are equal), the proposed approach can match the ZF method. In addition, the ZF method can exhibit significant performance degradation compared to the approach using an ML detector and can seriously lose another somewhat simpler way of linear filtering of MMSE input signals.

The embodiments described below can repeatedly detect and decode signals within communication devices with a MIMO channel.

A communication device with a MIMO channel may have improved reception characteristics. A communication device with a MIMO channel may provide lower bit error rate values for the decoded information bits in embodiments. The complexity of a communication device with a MIMO channel may have a complexity that is closer to the mere sum of the complexity of channel decoding and the complexity of MIMO detection of the MMSE used separately. The complexity of a communication device with a MIMO channel may be complex without feedback, used in repetitive processing,

In the following, a communication apparatus having a MIMO channel capable of achieving the above-described technical result will be described in detail.

4 is a flowchart of a method of repeatedly detecting and decoding a signal of a communication apparatus having a MIMO channel according to an embodiment.

In step 410, a plurality of receive antennas may receive the signals, respectively. The received signals may each be a signal modulated by transmitted QAM symbols.

In step 420, the plurality of receive antennas may each perform down-conversion of the received signals. The down-conversion performed may be a down-conversion to a zero carrier frequency. The plurality of receive antennas may generate down-converted signals through performing down-conversion.

In step 430, the MMSE detector may form samples of the down-converted signals. The MMSE detector, through quantization and digitization, can construct samples of the received down-converted signals.

Samples of down-converted signals may be considered as signals that pass through the MIMO channel.

The samples of the down-converted signals may be defined based on Equation (6) below.

는 잡음 샘플들의 M 차원의 벡터이고, H는 MIMO 채널 행렬일 수 있다. H의 크기는 M*N일 수 있다. 샘플링 주파수는 QAM 심볼들의 되풀이(repetition) 주파수와 같다고 가정될 수 있다. 따라서 MIMO 채널으로 입력된 신호의 벡터는 전송된 QAM 심볼들의 벡터일 수 있다. Y may be an M-dimensional vector of the signal that has passed through the MIMO channel. X may be an N-dimensional vector of the signal input to the MIMO channel.

Is an M-dimensional vector of noise samples, and H may be a MIMO channel matrix. The size of H may be M * N. The sampling frequency can be assumed to be equal to the repetition frequency of the QAM symbols. Thus, the vector of the signal input to the MIMO channel may be a vector of transmitted QAM symbols.

및 평균 신호 전력

를 추정할 수 있다.At step 435, the MMSE detector uses the received signals that have passed through the MIMO channel to generate a MIMO channel matrix H ,

And average signal power

Can be estimated.

In step 440, the MMSE detector may estimate the QAM symbols based on the received signals that have passed the MIMO channel. Estimation of QAM symbols may be to detect QAM symbols. The method of estimating QAM symbols will be described in more detail with reference to FIG. 5 to be described later.

At step 445, the QAM demodulator can demodulate the detected QAM symbols from the MMSE detector.

및

에 기반하여 제1 사후 확률

를 추정할 수 있다.

및

는 각각 후술될 제3 기대치 및 제3 분산일 수 있다. 제3 기대치 및 제3 분산에 대해서는 후술될 수학식 13 및 도 5를 참조하여 더 자세하게 설명된다. 제1 사후 확률

는 하기의 수학식 7에 의해 계산될 수 있다.The QAM demodulator may estimate the first posterior probability of the encoded bits of the QAM symbols. The QAM demodulator

And

Based on the first posterior probability

Can be estimated.

And

May be a third expected value and a third variance, respectively, which will be described later. The third expectation value and the third variance will be described in more detail with reference to Equation (13) and FIG. 5 to be described later. First posterior probability

Can be calculated by the following equation (7).

는 n 번째 QAM 심볼의, k 번째 인코드된 비트의 사후 확률일 수 있다.

는

개의 조건(condition)들을 갖는 테이블 함수일 수 있고, 인코드된 비트들

(

)의 조합에 의존할 수 있다.

는 전송된 QAM 심볼의 성상도를 나타낼 수 있다.

는, 이전의 반복 사이클에서 획득된, 제n 번째 QAM 심볼 내의 제k 번째 인코드된 비트의 사전 확률일 수 있다. K는 하나의 QAM 심볼 내의 인코드된 비트들의 개수일 수 있다.

May be the posterior probability of the kth encoded bit of the nth QAM symbol.

The

Lt; / RTI > may be a table function with a number of conditions,

(

). ≪ / RTI >

May represent the constellation of the transmitted QAM symbol.

May be the prior probability of the kth encoded bit in the nth QAM symbol obtained in the previous iteration cycle. K may be the number of encoded bits in a QAM symbol.

을 획득할 수 있다.At step 450, the QAM demodulator may obtain the prior probability of the received QAM symbols. The QAM demodulator includes a first prior probability

Can be obtained.

은 이전의 반복 사이클에서 획득된 사전 확률로서 후술될 제2 모듈로부터 입력될 수 있다. 최초의 반복 사이클이 수행되는 경우, 제1 사전 확률

은 하기의 수학식 8과 같이 정의될 수 있다.The first prior probability

May be input from the second module to be described later as the prior probability obtained in the previous iteration cycle. When the first iteration cycle is performed, the first prior probability

Can be defined as Equation (8) below.

은 제n 번째 QAM 심볼 내의 제k 번째 인코드된 비트가 1일 경우의 확률에 제n 번째 QAM 심볼 내의 제k 번째 인코드된 비트가 -1일 경우의 확률을 나눈 값에 자연로그를 취한 값일 수 있다. n은 1 이상 N 이하의 정수일 수 있고, k는 1 이상 K 이하의 정수일 수 있다. N은 QAM 심볼의 개수일 수 있고, K는 QAM 심볼 내의 비트들의 개수일 수 있다.The first prior probability

Is a value obtained by dividing the probability when the k-th encoded bit in the n-th QAM symbol is 1 and the probability obtained when the k-th encoded bit in the n-th QAM symbol is -1, . n may be an integer of 1 or more and N or less, and k may be an integer of 1 or more and K or less. N may be the number of QAM symbols, and K may be the number of bits in the QAM symbol.

은 인코드된 비트들의 사전 확률의 로그비일 수 있다.The first prior probability

May be the logarithmic ratio of the prior probability of the encoded bits.

로부터 제1 사전 확률

을 제거함으로써 인코드된 비트들의 연성 추정

을 획득할 수 있다. 말하자면, 제1 모듈은 제1 사후 확률

로부터 각 인코드된 비트에 대한 사전 정보

를 제거함으로써 인코드된 비트들의 연성 추정

를 계산할 수 있다. 연성 추정

은 하기의 수학식 9와 같이 정의될 수 있다. 제1 모듈은 외부의 정보를 구별할 수 있다. 말하자면, 제1 사후 확률로부터 제1 사전 확률이 제거됨으로써 외부의 정보가 획득될 수 있다. 획득된 연성 추정은 외부의 정보로서 외부의 확률일 수 있다.At step 455, the first module compares the first posterior probability of the encoded bits

Lt; RTI ID = 0.0 >

Lt; RTI ID = 0.0 >

Can be obtained. In other words, the first module has a first posterior probability

Lt; RTI ID = 0.0 >

Lt; RTI ID = 0.0 >

Can be calculated. Ductility estimation

Can be defined as: " (9) " The first module can distinguish external information. That is, external information can be obtained by removing the first prior probability from the first posterior probability. The obtained ductility estimate may be an external probability as external information.

는 사후 확률들의 연성 추정일 수 있다. 다음의 반복 사이클에서의 제1 사전 확률

는 채널 코드 파라미터들에 따른 인코드된 비트들(또는, 정보 비트들)의 디코딩이 수행됨에 기반하여 획득될 수 있다. 다음의 반복 사이클에서의 제1 사전 확률

가 획득되는 방법은 하기에서 더 자세하게 설명된다.

May be a ductility estimate of posterior probabilities. The first prior probability < RTI ID = 0.0 >

May be obtained based on the decoding of the encoded bits (or information bits) according to the channel code parameters. The first prior probability < RTI ID = 0.0 >

Lt; / RTI > is described in more detail below.

에 기반하여 인코드된 비트들을 디코딩하고 인코드된 비트들의 개선된 사후 확률

을 획득할 수 있다. 개선된 사후 확률

은 사후 확률의 추정에 의해 획득될 수 있다. 개선된 사후 확률

은 개선된 사후 확률들의 로그비일 수 있다. 개선된 사후 확률

은 연성 추정

의 개선된 연성 추정일 수 있다. 채널 디코더의 출력은 인코드된 비트에 대한 개선된 사후 확률을 포함할 수 있다. 채널 디코더는 인코드된 비트들에 대한 사후 확률의 추정을 사용하여 정보 비트들을 디코딩할 수 있다. 인코드된 비트들은 QAM 복조기로부터 전송될 수 있다. 채널 디코더는 채널 코드의 파라미터들에 따라 정보 비트들에 대한 사후 확률의 추정을 수행할 수 있다. 정보 비트들에 대한 사후 확률의 추정은 인코드된 비트들이 채널 디코더에 의해 디코드됨으로써 수행될 수 있다. 정보 비트들에 대한 개선된 사후 확률은 인코드된 비트들의 개선된 사후 확률일 수 있다. 또한, 채널 디코더는 정확도가 개선된 인코드된 비트들의 사후 확률의 추정을 획득할 수 있다. 채널 디코더는 연성 비트들을 출력할 수 있다. 개선된 사후 확률

은 출력된 연성 비트들의 연성 추청일 수 있다.At step 460, the channel decoder estimates the softness of the encoded bits

And decodes the encoded posterior probability of the encoded bits < RTI ID = 0.0 >

Can be obtained. Improved posterior probability

Can be obtained by estimating the posterior probability. Improved posterior probability

May be a log ratio of improved posterior probabilities. Improved posterior probability

Ductility estimation

Lt; / RTI > The output of the channel decoder may include an improved posterior probability for the encoded bits. The channel decoder may use the estimation of the posterior probability for the encoded bits to decode the information bits. The encoded bits may be transmitted from a QAM demodulator. The channel decoder may perform an estimation of the posterior probability for the information bits according to the parameters of the channel code. Estimation of the posterior probability for the information bits can be performed by decoding the encoded bits by the channel decoder. The improved posterior probability for the information bits may be an improved posterior probability of the encoded bits. The channel decoder may also obtain an estimate of the posterior probability of the encoded bits with improved accuracy. The channel decoder may output the soft bits. Improved posterior probability

Lt; / RTI > may be a soft sequence of output soft bits.

은 개선된 사후 확률의 로그비일 수 있다. 디-인터리버는 인코드된 비트들이 채널 디코더로 입력되기 전에 인코드된 비트들을 디-인터리브할 수 있다. 인터리버는 채널 디코더로부터 출력된 연성 비트들을 인터리빙할 수 있다. 인터리빙된 연성 비트들은 제2 모듈 및 재-변조기로 입력될 수 있다.Improved posterior probability

May be the log ratio of the improved posterior probability. The de-interleaver may de-interleave the encoded bits before the encoded bits are input to the channel decoder. The interleaver may interleave the soft bits output from the channel decoder. The interleaved soft bits may be input to a second module and a re-modulator.

에 기반하여 제2 사전 확률

을 획득할 수 있다. 제2 모듈은 외부의 정보를 구별할 수 있다. 말하자면, 개선된 사후 확률로부터 연성 추정

이 제거됨으로써 외부의 정보가 획득될 수 있다. 제2 사전 확률은 외부의 정보로서 외부의 확률일 수 있다. 제2 모듈에 의해 획득된 제2 사전 확률

는 다음의 반복 사이클에서의 제1 사전 확률일 수 있다.In step 465, the second module determines the improved posterior probability of the encoded bits

The second prior probability < RTI ID = 0.0 >

Can be obtained. The second module can distinguish external information. From the improved posterior probabilities,

The external information can be obtained. The second prior probability may be an external probability as external information. A second prior probability < RTI ID = 0.0 >

May be the first prior probability in the next iteration cycle.

는 하기의 수학식 10과 같이 정의될 수 있다.

Can be defined as shown in Equation (10) below.

에 기반하여 제2 사전 확률

을 획득할 수 있다. 제2 사전 확률

은 다음의 반복 사이클에서의 제1 사전 확률일 수 있다. 제2 모듈은 개선된 사후 확률

로부터 연성 추정

을 제거함으로써 제2 사전 확률

을 획득할 수 있다.The second module has an improved posterior probability

The second prior probability < RTI ID = 0.0 >

Can be obtained. The second prior probability

May be the first prior probability in the next iteration cycle. The second module has an improved posterior probability

Ductility estimation from

The second prior probability

Can be obtained.

에 기반하여 다음 반복 사이클에서의 사후 확률의 추정을 정의할 수 있다. 제2 사전 확률

은 다음 반복 사이클에서 QAM 복조기 및 제1 모듈로 입력될 수 있다. 제1 모듈은 개선된 사후 확률이 추정된 횟수가 한 번 이상인 경우, 입력된 제2 사전 확률을 제1 사전 확률로 사용하여 다음의 반복 사이클에서 개선된 사후 확률을 획득할 수 있다.The second module has a second prior probability

, It is possible to define the estimation of the posterior probability in the next iteration cycle. The second prior probability

May be input to the QAM demodulator and the first module in the next iteration cycle. The first module may use the inputted second pre-probability as the first pre-probability to obtain an improved post-probability in the next iterative cycle if the estimated number of times the improved post-probability is more than once is obtained.

및 제1 분산

을 획득할 수 있다. 제1 기대치

은 QAM 성상도의 값들의 가중치가 부여된 합(weighted sum)이 획득됨으로써, 획득될 수 있다. 제1 기대치

는 재-변조기로 입력된 QAM 심볼의 심볼 벡터의 기대치일 수 있다. 인코드된 비트들의 사후 확률의 개선된 추정들은 채널 디코더로부터 출력될 수 있다.At step 470, a remodulator, based on the improved posterior probability of the encoded bits,

And first dispersion

Can be obtained. First expectation

Can be obtained by obtaining a weighted sum of the values of the QAM constellation. First expectation

May be the expected value of the symbol vector of the QAM symbol input to the re-modulator. Improved estimates of the posterior probability of the encoded bits can be output from the channel decoder.

는 하기의 수학식 11과 같이 정의될 수 있다. First expectation

Can be defined as Equation (11) below.

는 가중치들을 나타낼 수 있다.

는 하기의 수학식 12와 같이 정의될 수 있다.

는 인코드된 비트들의 개선된 사후 확률에 의해 정의될 수 있다.

Can represent weights.

Can be defined as: < EMI ID = 12.0 >

May be defined by an improved posterior probability of the encoded bits.

은 하기의 수학식 13과 같이 정의될 수 있다. First dispersion

Can be defined as Equation (13) below.

및 제2 분산

을 포함할 수 있다.The third module of the communication device of the embodiment may output the prior information to the auxiliary input of the MMSE detector. The prio information output from the third module may be the information required to form a new estimate of the posterior probabilities of encoded bits and information bits to be used on the next iteration cycle. The dictionary information output from the third module is the second expected value

And the second dispersion

. ≪ / RTI >

을 이전의 반복 사이클의 QAM 심볼들의 추정 후 획득된 분산

과 비교할 수 있다. 제3 모듈은 상기 비교에 기반하여, 사전 정보를 교정할 수 있다. 사전 정보는 MMSE 검출기로 입력될 수 있다. 사전 정보는 후술될 제2 기대치

및 제2 분산

일 수 있다.In a step 475,

Lt; RTI ID = 0.0 > QAM < / RTI > symbols of the previous iteration cycle

. The third module may correct the prior information based on the comparison. The dictionary information can be input to the MMSE detector. The dictionary information includes a second expectation value

And the second dispersion

Lt; / RTI >

은 제3 분산일 수 있다. 이전의 반복 사이클의 QAM 심볼들의 추정 후 획득된 기대치

는 제3 기대치일 수 있다.After the estimation of the QAM symbols of the previous iteration cycle,

May be a third variance. After the estimation of the QAM symbols of the previous iteration cycle,

May be the third expected value.

및 제3 분산 간의 비교에 의해 제1 분산

이 제3 분산

미만이면, 수학식 14의 교정을 수행함으로써 제2 기대치

및 제2 분산

을 획득할 수 있다.The third module is a first distributed

And the third dispersion,

This third dispersion

, The second expectation value < RTI ID = 0.0 >

And the second dispersion

Can be obtained.

, 제1 분산

, 제3 기대치

및 제3 분산

에 기반하여, 제2 기대치

를 획득할 수 있다. 또한, 제3 모듈은 제1 분산

및 제3 분산

에 기반하여 제2 분산

을 획득할 수 있다.That is to say, the third module,

, First dispersion

, The third expected value

And third dispersion

The second expectation value < RTI ID = 0.0 >

Can be obtained. In addition, the third module may include a first distributed

And third dispersion

Lt; RTI ID = 0.0 >

Can be obtained.

이 제3 분산

이상이면 수학식 15의 교정을 수행함으로써 제2 기대치

및 제2 분산

을 획득할 수 있다. The third module is a first distributed

This third dispersion

(15), the second expectation value < RTI ID = 0.0 >

And the second dispersion

Can be obtained.

및

는 각각 이전의 반복 사이클에서 획득된 제2 기대치 및 제2 분산일 수 있다. 말하자면, 제3 모듈은 이전의 반복 사이클에서 획득된 제2 기대치

및 제2 분산

을 각각 이번 반복 사이클에서의 제2 기대치

및 제2 분산

으로서 획득할 수 있다.

And

May each be the second expected value and the second variance obtained in the previous iteration cycle. That is to say, the third module compares the second expected value obtained in the previous iteration cycle

And the second dispersion

Lt; RTI ID = 0.0 >

And the second dispersion

As shown in FIG.

및 제2 분산

을 포함할 수 있다.In step 480, the third module may generate new input parameters for the MMSE detector based on the comparison between the first variance and the variance after detection of the QAM symbols obtained in the previous iteration cycle. The third module may generate new input parameters for estimation of the QAM symbols in the next iteration cycle based on the comparison between the first variance and the variance after detection of the QAM symbols obtained in the previous iteration cycle. The new input parameters generated by the third module are the second expected value

And the second dispersion

. ≪ / RTI >

및 새로운 사전 대각 상관 행렬

을 포함할 수 있다. 새로운 기대치들

은 제2 기대치

에 기반하여 생성될 수 있다. 새로운 사전 대각 상관 행렬

은 제2 분산

에 기반하여 생성될 수 있다. 모든 n에 대한 제2 기대치

및 제2 분산

은 각각

및

을 구성하는 벡터일 수 있다. n은 1 이상 N 이하의 정수일 수 있다. 말하자면,

는 모든 n에 대한 사전 기대치들

이 벡터로서 결합된 것일 수 있다.

는 모든 n에 대한 사전 분산들

이 벡터로서 결합된 것일 수 있다.The new input parameters are the new expectations

And a new pre-diagonal correlation matrix

. ≪ / RTI > New expectations

Lt; RTI ID = 0.0 >

Lt; / RTI > A new pre-diagonal correlation matrix

The second dispersion

Lt; / RTI > The second expectation for all n

And the second dispersion

Respectively

And

May be used. n may be an integer of 1 or more and N or less. as it were,

Lt; RTI ID = 0.0 > n < / RTI &

May be combined as a vector.

Lt; RTI ID = 0.0 > n < / RTI &

May be combined as a vector.

및 제2 분산

은 사전 정보로서, 다음의 반복 사이클에서의 QAM 심볼들의 추정에 사용될 수 있다. MMSE 검출기는 사전 정보로서의 제2 기대치

및 제2 분산

에 기반하여 제3 기대치

및 제3 분산

을 획득함으로써 QAM 심볼을 추정할 수 있다. QAM 심볼들을 추정하는 방법에 대해서는 후술될 도 5를 참조하여 더 자세하게 설명된다.Second expectation

And the second dispersion

As prior information, can be used to estimate QAM symbols in the next iteration cycle. The MMSE detector detects the second expected value < RTI ID = 0.0 >

And the second dispersion

Lt; RTI ID = 0.0 >

And third dispersion

The QAM symbol can be estimated. The method of estimating QAM symbols will be described in more detail with reference to FIG. 5 to be described later.

In step 485, the hard decision estimator may form a sequence of hard decisions of information bits based on the improved posterior probability obtained from the channel decoder. The resulting final sequence may be output data. Step 480 may be performed after all iteration cycles have been completed, and the sequence of hardness estimates formed by the hard decision estimator may be the final sequence of hard decisions of information bits. Through the formation of the final sequence, the hard decision estimator can recover the original data. The estimation of the posterior probability of the information bits may be on the main output of the channel decoder.

The method of repetitive detection and decoding of the signals of the above-described embodiments can be used in a communication device having a MIMO channel.

A transmitting apparatus and a receiving apparatus having a MIMO channel have been described with reference to Figs. 1 to 3, and a method of repeatedly detecting and decoding a signal in the transmitting apparatus and the receiving apparatus described above can be applied.

5 is a flowchart of QAM symbol estimation according to an example.

A method of estimating the QAM symbols of step 440 is described in detail with reference to FIG. The MMSE detector may estimate the QAM symbol through steps 510 and 520 described below. Step 440 may include steps 510 and 520 described below.

In a first step 510, the MMSE detector may obtain an MMSE estimate estimate and an MMSE estimate variance of the symbol vector by applying an MMSE linear filter to the symbol vector of received QAM symbols with an MMSE detector.

The MMSE linear filter can be defined as Equation (16) below.

은 대각 행렬일 수 있다.

은 신호 전력의 평균 값

에 의해 정규화된 전송된 QAM 심볼들의 사전 분산일 수 있다.

May be a diagonal matrix.

Is the average value of the signal power

Lt; RTI ID = 0.0 > QAM < / RTI >

는 하기의 수학식 17에 의해 정의될 수 있다.By the MMSE linear filter, the MMSE estimation vector

Can be defined by the following equation (17).

은 전송된 QAM 심볼들의 N 차원의 벡터일 수 있다.

은 전송된 QAM 심볼들의 사전 기대치(mathematical expectation)들의 N 차원의 벡터일 수 있다. MMSE 추정 벡터

의 각 구성 요소

(n=1,2,..N)에 대해, MMSE 추정 분산

이 획득될 수 있다.

는 QAM 심볼들의 각 심볼 벡터의 MMSE 추정 기대치일 수 있다.

는 MMSE 추정 오류의 분산일 수 있다.

은 상관 행렬(correlation matrix)

의 대응하는 대각의 요소들과 동일할 수 있다.

는 하기의 수학식 18에 의해 정의될 수 있다.

May be an N- dimensional vector of transmitted QAM symbols.

May be an N- dimensional vector of mathematical expectations of the transmitted QAM symbols. MMSE estimation vector

Each component of

(n = 1,2, ... N ), the MMSE estimation variance

Can be obtained.

May be an MMSE estimate estimate of each symbol vector of QAM symbols.

May be a variance of the MMSE estimation error.

A correlation matrix < RTI ID = 0.0 >

May be the same as the corresponding diagonal elements of FIG.

Can be defined by the following equation (18).

및 제3 분산

을 획득할 수 있다.In step 520, the MMSE detector computes a third expected value < RTI ID = 0.0 >

And third dispersion

Can be obtained.

의 n 번째 구성요소

및 2) 상기의

에 대응하는 사전 기대치(mathematical expectation)

의 선형 변환을 수행할 수 있다. n은 1 이상 N 이하의 정수일 수 있다.The MMSE detector includes 1) an MMSE estimation vector

The nth component of

And 2)

A mathematical expectation corresponding to < RTI ID = 0.0 >

Can be performed. n may be an integer of 1 or more and N or less.

을 생성할 수 있고, 새로운 선형 추정에 대한 오류의 분산

을 생성할 수 있다. 새로운 선형 추정

은 다음의 반복 사이클에서 사용될 제3 기대치일 수 있고, 새로운 선형 추정에 대한 오류의 분산

은 다음의 반복 사이클에서 사용될 제3 분산일 수 있다.The MMSE detector may perform a new linear estimation of the transmitted QAM symbol by performing a correction on the linear transformation

And the variance of the error for new linear estimates

Can be generated. New Linear Estimation

May be the third expected value to be used in the next iteration cycle, and the variance of the error for the new linear estimate

May be the third variance to be used in the next iteration cycle.

및

는 하기의 수학식 19에 의해 획득될 수 있다.

및

는 각각 제3 기대치 및 제3 분산일 수 있다.

And

Can be obtained by the following equation (19).

And

May be the third expected value and the third variance, respectively.

는 제n 번째로 전송된 QAM 심볼의 기대치의 사전 추정일 수 있다.

는 제n 번째로 전송된 QAM 심볼의 분산의 사전 추정일 수 있다.

및

는 각각 이전의 반복 사이클에서 획득된 도 4를 참조하여 전술된 제2 기대치 및 제2 분산일 수 있다. 말하자면, MMSE 검출기는 이전의 반복 사이클에서의 제2 기대치

, 이전의 반복 사이클에서의 제2 분산

, MMSE 추정 기대치

및 MMSE 추정 분산

에 기반하여 다음의 반복 사이클에서 사용될 제3 기대치

을 획득할 수 있고, 제2 분산

및 MMSE 추정 분산

에 기반하여 상기 다음의 반복 사이클에서 사용될 제3 분산을 획득할 수 있다.

May be a prior estimate of the expectation of the nth transmitted QAM symbol.

May be a prior estimate of the variance of the nth transmitted QAM symbol.

And

May be the second expected value and the second variance described above with reference to Figure 4, respectively, obtained in the previous iteration cycle. That is to say, the MMSE detector determines the second expected value < RTI ID = 0.0 >

, The second variance in the previous iteration cycle

, MMSE Estimated Expected Value

And MMSE estimation variance

The third expected value to be used in the next iteration cycle

, And the second variance

And MMSE estimation variance

To obtain a third variance to be used in the next iteration cycle.

및

이 획득됨으로써 다음의 반복 사이클에서의 QAM 심볼이 추정될 수 있다. 획득된

및

은 다음의 반복 사이클에서 QAM 복조기로 입력될 수 있다. 도 4를 참조하여 전술된 것처럼, QAM 복조기는 입력된

및

에 기반하여 제1 사후 확률

를 추정할 수 있다. MMSE 검출기가 제3 기대치

및 제3 분산

을 최초로 획득하는 경우, 이전의 반복 사이클에서의 제2 기대치

는 0이고, 이전의 반복 사이클에서의 제2 분산

은 단위 분산일 수 있다. 말하자면 최초의 반복 사이클에서, 0의 기대치 및 단위 분산(unit variance)을 갖는 벡터가 수신된 QAM 심볼의 벡터의 사전 추정으로서 이용될 수 있다.

And

The QAM symbol in the next iteration cycle can be estimated. Obtained

And

May be input to the QAM demodulator in the next iteration cycle. As described above with reference to FIG. 4, the QAM demodulator receives

And

Based on the first posterior probability

Can be estimated. If the MMSE detector detects the third expected value

And third dispersion

The second expectation value in the previous iteration cycle < RTI ID = 0.0 >

Is 0, and the second variance < RTI ID = 0.0 >

May be a unit variance. That is to say, in the first iteration cycle, a vector with an expected value of zero and a unit variance can be used as a prior estimate of the vector of received QAM symbols.

The technical contents described above with reference to Figs. 1 to 4 can be applied as they are, so that a more detailed description will be omitted below.

6 is a block diagram of a communication device that performs repetitive detection and decoding of a signal according to one embodiment.

The communication apparatus 600 having a MIMO channel includes an MMSE detector 601, a QAM demodulator 603, a first module 605, a de-interleaver 607, a channel decoder 609, an interleaver 611, Module 613, a re-modulator 615, a third module 617, and a hard decision estimator 619.

A QAM demodulator 603, a first module 605, a de-interleaver 607, a channel decoder 609, an interleaver 611, a second module 613, a re-modulator 615, an MMSE detector 601, a QAM demodulator 603, The third module 617 and the hard decision estimator 619, a configuration performed by a subject having the same name among the configurations described with reference to Figs. 4 and 5 is a communication device 600 having a MIMO channel ). ≪ / RTI > For example, the steps 410 to 485 described above with reference to FIG. 4 may be performed by the communication device 600. FIG.

The communication device 600 having a MIMO channel may further include a plurality of reception antennas (not shown).

The plurality of receive antennas may receive the signals, respectively. The received signals may each be a signal modulated by transmitted QAM symbols. The plurality of receive antennas may each perform down-conversion of the received signals. The down-conversion performed may be a down-conversion to a zero carrier frequency. The plurality of receive antennas may generate down-converted signals through performing down-conversion.

및

가 입력될 수 있다. H는 채널 행렬의 구성 요소들일 수 있다.The signals received, amplified and converted by the plurality of receive antennas may be input to the MMSE detector 601. The MMSE detector 601 may also receive H ,

And

Can be input. H may be components of the channel matrix.

,

및

일 수 있다. 변환된 신호들은 Y일 수 있다. Y는 복수의 안테나들에 의해 수신된 신호들의 벡터일 수 있다.In Figure 6, the converted signals

,

And

Lt; / RTI > The converted signals may be Y. Y may be a vector of signals received by the plurality of antennas.

The MMSE detector 601 may estimate the received QAM symbols through the steps 510 and 520 described above with reference to FIG. For estimation of the QAM symbols, the MMSE linear filter defined by equation (16) can be applied.

및 분산

을 포함할 수 있다. 추정된 심볼 벡터의 기대치는

일 수 있다. 기대치는

의 오류의 분산은

일 수 있다.

및

은 도 4 및 도 5를 참조하여 전술된 제3 기대치 및 제3 분산일 수 있다. 기대치

및 분산

은 제3 모듈(617)로부터 출력된 제2 기대치

및 제2 분산

에 기반하여 생성될 수 있다.Prior information related to the symbol vector of the received QAM symbol may also be input to the MMSE detector 601. [ The dictionary information associated with the symbol vector is the expected value of the components of the symbol vector received in the previous iteration

And dispersion

. ≪ / RTI > The expected value of the estimated symbol vector is

Lt; / RTI > Expectation

The variance of the error is

Lt; / RTI >

And

May be the third expected value and the third variance described above with reference to Figures 4 and 5. Expectation

And dispersion

Lt; RTI ID = 0.0 > 617 < / RTI >

And the second dispersion

Lt; / RTI >

및 추정의 오류의 분산

은 QAM 복조기(603)로 입력될 수 있다. 또한,

및

은 제3 모듈(617)로 입력될 수 있다. 제3 모듈(617)은

및

에 기반하여 제2 기대치

및 제2 분산

을 획득할 수 있다.

및

은 전술된 수학식 19에 의해 정의될 수 있다.The expected value of the symbol vector of the estimated QAM symbol

And variance of error of estimation

Can be input to the QAM demodulator 603. Also,

And

May be input to the third module 617. The third module 617

And

Lt; RTI ID = 0.0 >

And the second dispersion

Can be obtained.

And

Can be defined by the above-described equation (19).

일 수 있다.

는 전술된 수학식 7에 의해 정의될 수 있다.A QAM demodulator 603 can demodulate the estimated QAM symbols and estimate a first posterior probability for the encoded bits of the QAM symbols. The first posterior probability is

Lt; / RTI >

Can be defined by the above-described equation (7).

은 이전의 반복 사이클에서 획득된 사전 확률로서 제2 모듈(410)로부터 입력되거나, 전술된 수학식 8에 의해 정의될 수 있다.The QAM demodulator may also obtain a first prior probability of received QAM symbols. The first prior probability

May be input from the second module 410 as the prior probability obtained in the previous iteration cycle, or may be defined by the above-described equation (8).

로부터 인코드된 비트들의 제1 사전 확률

을 제거함으로써 인코드된 비트들의 연성 추정

을 획득할 수 있다. 따라서, MMSE 검출기(601) 내에서 획득된 외부 정보가 생성될 수 있다.The first module 605 includes a first posteriori probability

Lt; RTI ID = 0.0 > 1 < / RTI &

Lt; RTI ID = 0.0 >

Can be obtained. Thus, the external information obtained in the MMSE detector 601 can be generated.

The de-interleaver 607 may de-interleave the encoded bits before the encoded bits are input to the channel decoder 609. [

The channel decoder 609 may perform the decoding described above according to the channel code parameters. The channel decoder 609 may use a plurality of decoding methods. For example, the channel decoder 609 may use a Viterbi method, a maximum posterior probability method, a turbo-decoding method, and / or a belief propagation method. MAP and / or Log-MAP decoders may be used for estimation of posterior probabilities. The decoding method may be selected by one or more factors. For example, 1) the type of code used and / or 2) the efficiency of the applied algorithms can be considered. Efficiency can be proportional to the degree of noise immunity within acceptable implementation complexity.

The decoding method selected in the above embodiments may not be necessary. In the above-described embodiments, various decoding methods that make a predetermined estimation more accurate, for example, can be applied. Some estimates may include 1) estimation of the probability of information and / or 2) estimation of the probability of encoded bits.

The channel decoder 609 may generate an estimate of the posterior probability of information bits. The channel decoder 609 may perform decoding and then estimate the probability of the encoded bits based on the posterior probability of the information bits. After decoding, the estimation of the post-information of the encoded bits may also be completed through an alternative scheme of re-encoding.

에 기반하여 인코드된 비트들을 디코딩하고 인코드된 비트들의 개선된 사후 확률

을 획득할 수 있다. 채널 디코더(609)의 제1 출력은 획득된 개선된 사후 확률

을 포함할 수 있다. 제1 출력은 인코드된 비트들의 개선된 연성 추정일 수 있다. 인터리버(611)는 제1 출력에 포함된 연성 비트들을 인터리빙할 수 있다. 제1 출력의 개선된 사후 확률

은 제2 모듈(613)로 입력될 수 있다. 제2 모듈(613)은 개선된 사후 확률

및 연성 추정

에 기반하여 소정의 정보를 획득할 수 있다. 획득된 소정의 정보는 제2 사전 확률

을 포함할 수 있다. 제2 사전 확률

은 QAM 복조기(603) 및 제1 모듈(605)로 입력될 수 있다. 제1 모듈(605)은 개선된 사후 확률이 추정된 횟수가 한 번 이상인 경우, 입력된 제2 사전 확률을 제1 사전 확률로 사용할 수 있다. QAM 복조기(603)로 입력된 제2 사전 확률

은 다음의 반복 사이클에서 QAM 복조기(603)에 의해 사용될 수 있다.The channel decoder 609 may obtain an improved posterior probability of the encoded bits. The channel decoder 609 receives a soft-estimate

And decodes the encoded posterior probability of the encoded bits < RTI ID = 0.0 >

Can be obtained. The first output of the channel decoder 609 is the improved posterior probability

. ≪ / RTI > The first output may be an improved soft estimate of the encoded bits. The interleaver 611 may interleave the soft bits included in the first output. Improved posterior probability of first output

May be input to the second module 613. The second module 613 may have an improved posterior probability

And ductility estimation

It is possible to obtain predetermined information. The obtained predetermined information includes a second prior probability

. ≪ / RTI > The second prior probability

May be input to the QAM demodulator 603 and the first module 605. The first module 605 may use the inputted second pre-probability as the first pre-probability when the estimated number of times that the improved post-probability is estimated is one or more times. The QAM demodulator 603 receives the second prior probability

May be used by the QAM demodulator 603 in the next iterative cycle.

The first output passed through the interleaver 611 may be input to the re-modulator 615.

에 기반하여 수신된 QAM 심볼의 벡터에 대한 추정을 수행할 수 있다. 재-변조기(615)는 QAM 심볼들의 제1 기대치

및 제1 분산

을 획득할 수 있다. 제1 기대치

및 제1 분산

은 수학식 11 내지 13에 의해 정의될 수 있다.

는 QAM 심볼들의 각 벡터의 기대치일 수 있고,

는

의 오류의 분산일 수 있다. 제1 기대치

및 제1 분산

은 제3 모듈(617)로 입력될 수 있다. 제3 모듈(617)은 사전 정보의 교정을 수행할 수 있다. 제3 모듈(617)은 이전의 반복 사이클에서 MMSE 검출기(601)에 의해 획득된 QAM 심볼의 벡터에 대한 추정들을 수신할 수 있다. 제3 모듈(617)은 MMSE 검출기(601)로부터 이전의 반복 사이클의

및

을 수신할 수 있다. 제3 모듈(617)은 제1 분산

을 이전의 반복 사이클의

과 비교할 수 있다. 제3 모듈은 상기 비교에 기반하여 MMSE 검출기(601)에 대한 새로운 입력 파라미터들을 생성할 수 있다. 생성된 새로운 입력 파라미터들은 제2 기대치

및 제2 분산

을 포함할 수 있다.The re-modulator 615 has an improved posterior probability

Lt; RTI ID = 0.0 > QAM < / RTI > The re-modulator 615 receives the first expectation of the QAM symbols

And first dispersion

Can be obtained. First expectation

And first dispersion

Can be defined by Equations (11) to (13).

May be the expectation of each vector of QAM symbols,

The

Of the error. First expectation

And first dispersion

May be input to the third module 617. The third module 617 may perform calibration of the prior information. The third module 617 may receive estimates for the vector of QAM symbols obtained by the MMSE detector 601 in the previous iteration cycle. The third module 617 receives from the MMSE detector 601 the

And

Lt; / RTI > The third module (617)

Of the previous iteration cycle

. The third module may generate new input parameters for the MMSE detector 601 based on the comparison. The generated new input parameters are the second expected value

And the second dispersion

. ≪ / RTI >

및

을 포함할 수 있다. MMSE 검출기(601)는 출력된 사전 추정을 다음의 반복 사이클에서 사전 정보(추정)로서 사용할 수 있다.The third module 617 may perform a calibration of the vector of QAM symbols and then output a prior estimate. The pre-estimation

And

. ≪ / RTI > The MMSE detector 601 may use the output pre-estimation as the prior information (estimation) in the next iteration cycle.

The second output of the channel decoder 609 may comprise an improved soft estimate of the encoded bits. The improved softness estimate may be soft bits. The soft bits may be input to the hard decision estimator 619. [ Hard decision estimator 619 may perform hard decisions on soft bits. That is to say, the hard decision estimator 619 can form a sequence of hard decisions of information bits based on the improved posterior probability obtained from the channel decoder 609. After the iterative cycles are performed a plurality of times, the second output may be input to the hard decision estimator 619. [ The sequence formed from hard decision estimator 619 may be the final sequence. Through the formation of the final sequence, the hard decision estimator 619 can recover the original data.

The reliability of the data received by the communication device 600 can be improved by repeating cycles a plurality of times. That is to say, the iterative estimation of the information bits can be matched to the transmitted sequence with a higher probability by the repetition cycles being performed a plurality of times.

In an iterative process of decoding or detecting a received signal, the conversion of the digital representation of the above process can be described by the above-described equations (1) to (19).

In the embodiments described above, channel decoding may be satisfied by repetition of one or more cycles. One outer iteration cycle may include joint detection and decoding. The detection and decoding of the joint may include one or more internal cycles of operation of the channel decoder 609. [

Further, in the above-described embodiment, the bit interleaving procedure can be applied after channel encoding at the time of initial signal generation. That is to say, the QAM symbols for the encoded bits on which the interleaving has been performed can be demodulated by the QAM demodulator 603. The bit interleaving procedure by interleaver 611 may be applied after channel decoding performed by channel decoder 609 upon receipt of a sequence of probability estimates of demodulated bits. The sequence of probability estimates of demodulated bits may be de-interleaved by passing through the de-interleaver 607 before being input to the channel decoder 609. [ The sequence of probability estimates of encoded bits after decoding by the channel decoder 609 may be used in a feedback line. The sequence of probability estimates of encoded bits may be interleaved by passing the interleaver 611 by turns. The interleaving procedure may be for generation of prior estimates. The sequence that has passed through the interleaver 611 may be input to the MMSE detector 601 and the QAM demodulator 603 in the next iteration cycle.

The encoded bits may be separated into bits of the system and parity check bits in the initial signal generation. Thus, the sequence of estimates of the probabilities of bits generated by the decoding procedure by channel decoder 409 may include only bits of the system. The re-modulator 615 may process a re-encoding procedure for a sequence of estimates of the probability of bits of the system after decoding. Through the re-encoding procedure, re-modulator 615 can add parity-check bits to the estimates and recover a full sequence of encoded bits. The recovered full sequence may be used by the MMSE detector 601 and the QAM demodulator 603 in the next iteration.

In re-encoding, the probabilities of the verifying bits may be based on 1) the probabilities of the bits of the system, and 2) according to the parameters of the channel code. The bits to be verified may be parity-check bits.

The re-encoding procedure by re-modulator 615 may be to add to the estimates the values of the probability of parity-check bits that are characterized by the 0 LLR.

Figure 7 illustrates the performance of three types of detectors and demodulators according to an example.

The results of FIG. 7 may be for an LTE standard model. In FIG. 7, the MIMO configuration may be 4x4. The modulation may be 16QAM. The channel may be EPA-5. In addition, the code rate may be 1/2. The code rate may be 3640000 bits.

In the graph, the x-axis can represent the signal-to-noise ratio (SNR). The unit of x-axis can be dB. and the y-axis may indicate a bit error rate performance (BER).

The results for three types of detector and modulator are shown. "MMSE" represents the result of a conventional MMSE detector. "ML" represents the result of a conventional ML detector. "TP FB" represents the result of the iterative detector and demodulator according to the embodiment described above.

As shown in the graph, the above-described embodiments can yield a better effect than other methods or devices with MMSE detectors.

Figure 8 shows the performance of three types of detectors and demodulators according to an example.

The results of FIG. 8 may be for an LTE standard model. In FIG. 7, the MIMO configuration may be 4x4. The modulation may be 16QAM. The channel may be EPA-5. In addition, the code rate may be 3/4. The code rate may be 5432000 bits.

In the graph, the x-axis can represent the SNR. The unit of x-axis can be dB. The y-axis can represent the BER.

The results for three types of detector and modulator are shown. "MMSE" represents the result of a conventional MMSE detector. "ML" represents the result of a conventional ML detector. "TP FB" represents the result of the iterative detector and demodulator according to the embodiment described above.

As shown in the graph, the above-described embodiments can yield a better effect than other methods or devices with MMSE detectors.

For joint repetitive detection and decoding, only two external cycles of iterative detection and decoding may be used while the channel decoder fulfills the decoding using the internal iterative cycles. In the course of decoding using internal cycles, the turbo code can be decoded. Thus, after the first cycle of operation of the MMSE detector, the channel decoder can perform two internal cycles in the decoding process. After completion of the first cycle, another cycle of detection may be performed using the prior information obtained by the channel decoder. After completion of the second cycle, the channel decoder may further perform four internal decoding cycles. Thus, the total number of internal cycles of operation of the channel decoder may be six. Cycles of operation of the same number of channel decoders may be used in different detection and decoding results designs. That is to say, the complexity and delay can only increase by one additional cycle of the MIMO detection operation. The increase in complexity and additional cycles of delay may not be significant given the relative simplicity of the MIMO detection method based on the MMSE filter.

The method according to an embodiment may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

Claims (17)

A communication apparatus having a MIMO channel for repeatedly detecting and decoding a signal,
An MMSE detector for estimating QAM symbols based on received signals that have passed through the MIMO channel;
A QAM demodulator for demodulating the estimated QAM symbols and estimating a first posteriori probability of the encoded bits of the QAM symbols;
A first module for obtaining a soft estimate of encoded bits by removing a first prior probability of the encoded bits from the first posterior probability;
A channel decoder for decoding the encoded bits based on the softness estimate and obtaining an improved posterior probability of the encoded bits;
A second module for obtaining a second prior probability based on the improved after probabilities, the second prior probability being a first prior probability in a next iteration cycle; And
A hard decisions estimator that forms a sequence of hard estimates of information bits based on the improved posterior probabilities;
And a MIMO channel. The method according to claim 1,
Wherein the first posterior probability is a log of a posterior probability of the encoded bits,
Wherein the first prior probability is a log probability of the prior probability of the encoded bits. The method according to claim 1,
The first prior probability is calculated by dividing the probability when the k-th encoded bit in the n-th QAM symbol is 1 and the probability when the k-th encoded bit in the n-th QAM symbol is -1 Is a value obtained by taking a natural logarithm,
N is an integer of 1 or more and N or less,
K is an integer of 1 or more and K or less,
Wherein the N is a number of QAM symbols and the K is a number of bits in a QAM symbol. The method according to claim 1,
Wherein the improved posterior probability is a log ratio of an improved posterior probability,
Wherein the second module comprises:
Obtaining the second prior probability by removing the softness estimate from the improved posterior probability,
The first module includes:
If the estimated number of times of the improved posterior probability is more than once,
And using the second pre-probability as the first pre-probability to obtain an improved post-probability in the next iterative cycle. The method according to claim 1,
The communication device comprising:
A re-modulator to obtain a first expected value and a first variance of the QAM symbols based on the improved posterior probability; And
And a third module for comparing the first variance with the variance obtained after estimating the QAM symbols of the previous iteration cycle
Further comprising:
And the third module generates new input parameters for the MMSE detector based on the comparison. 6. The method of claim 5,
The new input parameters including a second expected value and a second variance,
Wherein the variance obtained after estimation of the QAM symbols of the previous iteration cycle is a third variance, the expected value obtained after estimation of the QAM symbols is a third expected value,
The third module, by comparison,
Acquiring the second expected value based on the first expected value, the first variance, the third expected value, and the third variance if the first variance is less than the third variance, Obtaining the second variance based on the variance,
Acquiring a second expected value and a second variance obtained in the previous iteration cycle as a second expected value and a second variance respectively in the current iteration cycle if the first variance is the third variance or more, Device. The method according to claim 6,
Wherein the MMSE detector comprises:
Obtaining an MMSE estimation expectation value and an MMSE estimation variance of the symbol vector by applying an MMSE linear filter to the symbol vector of the QAM symbols received by the MMSE detector,
Obtain a third expected value to be used in the next iteration cycle based on the second expectation value, the second variance, the MMSE estimation expectation and the MMSE estimation variance, and based on the second variance and the MMSE estimation variance, Obtaining a third variance to be used in the iterative cycle,
The third expectation and the third variance are obtained so that the QAM symbol in the next iteration cycle is estimated,
Wherein the third expectation and the third variance are input to the QAM demodulator in the next iteration cycle. 8. The method of claim 7,
And the QAM demodulator estimates a first posterior probability based on the third expected value and the third variance. 8. The method of claim 7,
When the MMSE detector first acquires the third expected value and the third variance,
Wherein the second expected value is zero and the second variance is a unit variance. The method according to claim 1,
De-interleaver; And
Interleaver
Further comprising:
Wherein the de-interleaver de-interleaves the encoded bits before the encoded bits are input to the channel decoder,
Wherein the interleaver interleaves the soft bits output from the channel decoder. A communication apparatus having a MIMO channel for repeatedly detecting and decoding a signal,
Estimating QAM symbols based on signals received on the MIMO channel;
Demodulating the estimated QAM symbol and estimating a first posterior probability of the encoded bits of the QAM symbol;
Obtaining a soft estimate of encoded bits by removing a first prior probability of the encoded bits from the first posterior probability;
Decoding the encoded bits based on the soft estimate and obtaining an improved after probability of the encoded bits;
Obtaining a second prior probability based on the improved post probability, the second prior probability being a first prior probability in a next iteration cycle; And
Forming a sequence of hardness estimates of information bits based on the improved posterior probability;
Gt; a < / RTI > repeatedly detecting and decoding a signal. 12. The method of claim 11,
Wherein the first posterior probability is a log of a posterior probability of the encoded bits,
Wherein the first prior probability is a log of a prior probability of the encoded bits,
Wherein the improved posterior probability is a log ratio of an improved posterior probability,
Wherein the step of acquiring the second pre-
Estimate the second prior probability by removing the soft estimate from the improved after probability,
If the estimated number of times of the improved posterior probability is more than once,
Wherein the step of obtaining the improved posterior probability comprises:
And using the second pre-probability as the first pre-probability to obtain an improved post-probability in the next iterative cycle. 12. The method of claim 11,
Obtaining a first expected value and a first variance of the QAM symbols based on the improved posterior probability;
Comparing the first variance to an obtained variance after estimation of QAM symbols of a previous iteration cycle; And
Generating new input parameters for estimating QAM symbols in a next iteration cycle based on the comparison;
Further comprising the step of detecting and decoding the signal repeatedly. 14. The method of claim 13,
The new input parameters including a second expected value and a second variance,
Wherein the variance obtained after estimation of the QAM symbols of the previous iteration cycle is a third variance, the expected value obtained after estimation of the QAM symbols is a third expected value,
Wherein the comparing comprises:
Acquiring the second expected value based on the first expected value, the first variance, the third expected value, and the third variance if the first variance is less than the third variance, Obtaining the second variance based on the variance,
And obtaining a second expected value and a second variance obtained in the previous iteration cycle as a second expected value and a second variance, respectively, in the current iteration cycle when the first variance is the third variance or more, Lt; / RTI > 15. The method of claim 14,
Wherein estimating the QAM symbols comprises:
Obtaining an MMSE estimate estimate of the symbol vector and an MMSE estimate variance by applying an MMSE linear filter to the symbol vector of received QAM symbols; And
Obtain a third expected value to be used in the next iteration cycle based on the second expectation value, the second variance, the MMSE estimation expectation and the MMSE estimation variance, and based on the second variance and the MMSE estimation variance, Obtaining a third variance to be used in the iterative cycle
Lt; / RTI >
Wherein the third expected value and the third variance are obtained so that the QAM symbol in the next iteration cycle is estimated. 16. The method of claim 15,
Estimating the first posterior probability comprises:
And estimating the first posterior probability based on the third expected value and the third variance. 16. The method of claim 15,
When the third expected value and the third variance are first obtained,
Wherein the second expected value is zero and the second variance is a unit variance.

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