KR880001292B1 - Improvements in or relating to data transmission systems - Google Patents

Abstract

A number of k stored vectors is selected from mk expanded vectors, where m is the number of levels of the data signal. Each sample of the received signal is expanded into nk expanded vectors, n being less than m. From the expanded vectors, k vectors are selected and stored with their associated costs. These are used to calculate the most likely level of a received signal. For sequential expansion, n=square root(m) and k vectors are selected after each expansion. When the two expansion processor are performed simultaneously, n is less than square root (m) and the two sets of nk expanded vectors give an effective total of (n) squared (k) vectors.

Description

Multi-level Signal Detection Method for Data Transmission System

1 is a block diagram showing a data transmission system according to the present invention.

2 is a block diagram of a circuit for adaptive adjustment of linear filters and estimators.

Figure 3 (a) is a graph showing the attenuation characteristics of the telephone circuit 1, Figure 3 (b) is a graph showing the group delay characteristics of the telephone circuit 1.

Figure 4 (a) is a graph showing the attenuation characteristics of the telephone circuit 2, Figure 4 (b) is a graph showing the group delay characteristics of the telephone circuit 2.

Figure 5 (a) is a graph showing the attenuation characteristics of the telephone circuit 3, Figure 5 (b) is a graph showing the group delay characteristics of the telephone circuit 3.

Figure 6 (a) is a graph showing the attenuation characteristics of the telephone circuit 4, Figure 6 (b) is a graph showing the group delay characteristics of the telephone circuit 4.

7 (a) is a graph showing the attenuation characteristics of the transmitter and receiver filter combination, Figure 7 (b) is a graph showing the group delay characteristics of the transmitter and receiver filter combination.

8 is a graph showing the variation of the error rate against the signal-to-noise ratio for various systems operating in telephone circuit 1. FIG.

9 is a graph showing the variation of the error rate with respect to the signal-to-noise ratio for various systems operating in telephone circuit 2. FIG.

10 is a graph showing the variation of the error rate against the signal-to-noise ratio for various systems operating in telephone circuit 3. FIG.

FIG. 11 is a graph showing the variation of the error rate against the signal-to-noise ratio for various systems operating in telephone circuit 4. FIG.

FIG. 12 shows the variation of the error rate for the inaccuracy of the estimation by the receiver. FIG. 12 (a) is for the level and FIG. 12 (b) is for the carrier phase of the received signal. Graph showing System E with m = 6 and n = 7 running.

The present invention relates to a data transmission system, and more particularly to a modem for such a system.

The present invention relates to a modem using a Viterbi-algorithm (Forney, GD The Viterbi-algorithm, Proc. IEEE, Vol 61, pp268-278, March 1973) as a method of decoding a data signal. It is about.

An object of the present invention is to reduce the complexity of the reduced-state Viterbi-algorthm operating on multi-level signals, but not to damage the performance. The goal is to be able to detect near maximum possible without costing so much more than an equalizer. The advantage that can be obtained by this system is that the resistance to additive noise is about 6 dB.

The fundamental technique of the present invention is to reduce the complexity of the detector by double-inputting the incoming signal sequentially or simultaneously.

Particularly unique features of the present application include a method for selecting k stored vectors from mk extended vectors (m is the number of levels of the data signal) in the algorithm of the reduced-state Viterbi-algorithm detector.

이고 k개 벡터가 각 확장 이후에 선택된다. 두 확장이 동시적으로 수행될때에는

이고 nk개의 확장된 벡터의 두 집합 이 실효충수가 n²k인 벡터를 발생시키게 되며 이들로 부터 k개의 저정된 벡터가 선택된다. 실효총수 n²k개 벡터중 어느 것이든 그 코스트는 두 별개 벡터의 코스트로 부터 간단히 유도되며 nk개 확장된 벡터의 두 집합 각각으로 부터 하나씩 함께 결과적인 벡터를 만들기 때문에 이에 관련된 총 계산량은 n²k개 벡터가 아니라 2_nk개의 확장된 벡터에 행당하는 것이다.Upon receipt of the received sample, each stored vector is " expanded " into m vectors and the " cost " associated with each of them is calculated. From the mk extended vectors, k vectors are selected according to some criterion. When both m and k are large, mk becomes very large and too much operation is required for the received sample. The basic feature of the present invention is to reduce this extension process to two separate operations, but this operation can be performed sequentially or concurrently, each of which extends k stored vectors to nk vectors (n << m). Since it is included, we select k stored vectors again from these nk vectors. If the two expansion processes are performed sequentially

K vectors are selected after each extension. When both extensions are done concurrently

And two sets of nk extended vectors produce vectors with n ² k effective numbers, from which k stored vectors are selected. The effective total number of any of the n ² k vectors is simply derived from the costs of the two separate vectors, and the total computations associated with it are n ² because the resulting vectors are created together, one from each of the two sets of nk extended vectors. It is per 2 _nk extended vectors rather than k vectors.

The invention applies directly to 9600 bit / second modems for use in public switched telephone networks. Another application is a digital data transmission system in which a multilevel signal is sent across a channel, causing a significant time deviation of the transmission signal-component at a rate of 100,000 bits / second, where it is required to be strong enough against additive noise.

Referring to the present invention in more detail based on the accompanying drawings as follows.

Telephone circuits in switched telephone networks have one of a very wide range of attenuation-frequency characteristics and thus one of a wide range of group-delay frequency characteristics, giving usable bandwidth in the range of about 1500-H _Z -3000H _Z. . Therefore, in order to achieve satisfactory data transmission at a high speed of 9600 bits / second in the switched telephone network, it is clear that the receiver must be adaptive in the sense that the receiver is fully responsible for the distortion of the received data signal. Do. A common approach to solving this problem is to use an adaptive nonlinear (selective-feedback) equalizer, which is adjusted to minimize the squared mean error in the equalized signal. ^2-5 Such systems are known to operate satisfactorily at speeds up to 4800 bits / second in telephone circuits.

At higher speeds, however, they do not always work satisfactorily in low-performance phone circuits.

Another approach recently considered is to use a Viterbi-algorithm detector. ^5-7 This is a possible sequence of transmission data-symbols (signal-component values) that minimizes the squared mean error between the sample of the corresponding received data signal and the sample of the actually received signal when there is no noise for a given signal distortion. sequence as the detected message. If a data signal is received in the presence of constant additive white Gaussian noise, giving a statistically irrelevant Gaussian noise sample to the detector input is the method of maximum possible detection, and the transmitted data-symbol is statistically independent. If the probability of having any of the possible values is the same, the detection method minimizes the probability of error in the detection of the received message. The assumption here is that the received signal is sampled at the Nyquistrate, so the corresponding sample contains all the information of the signal.

Unfortunately, the sampled impulse response of the channel contains a large number of components, which, in the case of the application under consideration, include too much operation and too much storage per data symbol received in the Viterbi-algorithm.

One approach to overcome this difficulty is to use a linear feedforward transversal filter at the detector input to reduce the number of sampled impulse responses of the channel. This filter is adaptively adjusted to give the desired sampled impulse response for the channel and the filter, which has a small number of components and may or may not be fixed. ^8-11 The disadvantages of this device are:

That is, for some telephone circuits, a linear filter equalizes some of the amplitude distortion introduced by the telephone circuit and under these conditions, the maximum possible detection is not achieved and therefore degrades performance. ⁵ Ideally, a linear filter should perform the function of a “whitened match filter” ^6-14 , which ensures the true maximum possible detection by a Viterbi-algorithm detector. In an ideal device, if there is a constant additive white Gaussian noise at the receiver input, the data signal is sent over the channel at the Nygest rate and the receiver filter has the same bandwidth as the received signal, so that once per data symbol at the receiver filter output. By sampling the signal (Nyquist rate), the noise sample at the sampler output becomes a Gaussian random variable with a constant statistically independent variation. The whitened match filter then becomes like a linear feedforward transverse filter that forms the beginning of a conventional nonlinear (selective feedback) equalizer. In this case, a given sampled signal enters and is adjusted to minimize the squared mean error in the output signal (and thus maximize the signal-to-noise ratio), resulting in accurate equalization of the channel. ⁵ The advantages of this are as follows.

In other words, using a simple device essentially the same as that included in a conventional adaptive nonlinear equalizer, the linear filter can be adaptively adjusted to give the channel almost the desired response with a high signal-to-noise ratio. Linear filter output signal ⁵ is sent to a maximum likelihood detector feedback filter juneunde the sample estimate of the impulse response of the channel and linear filter, which is required by the detector. Details of the apparatus will be described later. When properly adjusted, the linear filter is That is, in the transformation of the sampled impulse response of the channel and linear filter, those that lie outside the unit circle of the Z plane of all zeros of the Z transform of the sampled impulse response of the channel (i.e., the absolute value is greater than 1) The inverse is replaced by the conjugate complex number and the remaining zeros remain unchanged. ⁵ Therefore, all zeros of the Z transform of the channel and the linear filter are on or inside the unit circle. Since linear filters are in fact pure phase equalizers (although not always for the channels themselves), they perform orthogonal transformations on the received signal.

In practice, a linear filter can cause some gain or attenuation, but it does not change the statistical relationship between noise and data signals anyway because it has the same effect on noise or data signals. This means that the Viterbi-algorithm detector operating at the filter output is the same as the Viterbi-algorithm detector operating at the input in terms of immunity to Gaussian noise, although the installation is much less complicated. Furthermore, when the level change is allowed, the noise component of the filter output is statistically independent and its variance is constant since it has the same statistical properties as at the input. Therefore, the most cost-effective device for a given application is to use the adaptive linear filter of the type mentioned above, which acts as a whitened matched filter connected between the sampler and the detector. The adaptive filter has the following important properties. That is, it not only removes all phase distortion introduced by the channel, but also adjusts the sampled impulse response of the channel and the filter to an ideally suited form for the quasi-maximum possible detector of the type considered here. ^5,13

The present invention describes the application of a recently developed detection method to the design of quadrature amplitude modulted (QAM) systems of 16-point QAM signals operating at 9600 bits / sec. New detection schemes that avoid the high complexity associated with 16-point signals in the previously described manner will be described in detail herein. A computer simulation test result will then be presented that compares the performance of different systems when operating on different telephone circuits and shows the effect of inaccuracies in estimates of carrier phase and level of the received signal.

A model of a data transfer system is shown in FIG.

This is a synchronous serial 16-point QAM system. The information to be transmitted is carried by data symbol {S ₁ }, where

S ₁ = ± a ± bj (1)

0에서 s₁=0로 가정하면 s₁δ(t-iT)는 송신기 필터로의 입력에서 i번째 신호-성분이 된다. 전송로는 선형 베이스밴드 채널로서 전화회로를 포함하고 있고 또한 송신기측에 선형 QAM 변조기와 수신기측에 선형 QAM 복조기가 함께 존재한다. 변조기 및 복조기의 기본구조는 다른 곳에서 설명되어 있다.¹⁷QAM 시스템의 "정위상(in phase)"채널로 전송되는 신호는 실수치 크기로 표시되고 "직교(quadrature)"채널로 전송되는 신호는 허수치 크기로 표시되어 제 1 도의 전송로 입출력에 결과적으로 복소치 베이스 밴드 신호를 주게되는 것이다. 정위상 및 직교 채널내의 전송신호의 캐리어는 2cos 2πf_ct 및 - 2sin sπf_ct로 각각 취해지며 여기서 f_c=1800이다.¹⁷송신기필터와 전송로 및 수신기 필터는 다같이 선형 베이스 밴드 채널을 구성하는데 이것의 임펄스 응답은 복소치 함수 q(t)로써 그 실효 지연기간 (duration)이 (g+1)T초 이하이며 여기서 g는 임의의 정수이다.And j = -1. a = 1 or 3 and b = 1 or 3. {a ₁ } is statistically irrelevant and will have the same probability of any of the 16 possible values. i

Assuming s ₁ = 0 at s ₁ δ (t-iT) is the i-th signal-component at the input to the transmitter filter. The transmission path includes a telephone circuit as a linear baseband channel, and also includes a linear QAM modulator on the transmitter side and a linear QAM demodulator on the receiver side. The basic structure of the modulator and demodulator is described elsewhere. ¹⁷ Signals transmitted in the "in phase" channel of a QAM system are represented by real magnitudes and signals transmitted by the "quadrature" channel are represented by imaginary magnitudes, resulting in channel I / O in FIG. This gives a complex baseband signal. The carriers of the transmitted signals in the phase and quadrature channels are taken as 2cos 2πf _c t and −2sin sπf _c t, where f _c = 1800. ^{17 The} transmitter filter, the transmission channel, and the receiver filter together form a linear baseband channel whose impulse response is a complex function q (t) whose effective delay is less than (g + 1) T seconds. g is any integer.

For the purposes of the present invention, q (t) is assumed to be time invariant for any transmission. The various forms of additive and multiplier noise coming from the telephone circuit are ignored here, assuming that the only noise is a complex constant white Gaussian noise, which has zero mean and constant (independent of frequency) power spectral density. This is added to the data signal at the channel output, giving the receiver filter output a complex Gaussian noise waveform v (t). Although telephone circuits do not introduce significant amounts of Gaussian noise, the relative immunity of many data transmission systems to white Gaussian noise is a good measure of their relative overall immunity to additive noise actually experienced in telephone circuits. ^One

The waveform at the receiver filter output is a complex signal

은 임의의큰 양의 정수이다. 파형 p(t)는 {iT)의 순간에 데이타 심볼당 한번씩 샘플되어 수신된 샘플{pi}를 주며 이것이 적응성 선형필터(제 1 도)로 보내어진다. 이 필터는 백색화된 정합필터로 동작하므로 앞에 설명된 바처럼 정확히 조절된 것으로 받아 들여지는데, 다만 차이점은 이 필터가 이제는 앞에서 가장했던 실수치 샘플대신 복소치 샘플로 동작한다는 점이다.And

Is any large positive integer. Waveform p (t) is sampled once per data symbol at the instant of {iT) giving a received sample {pi} which is sent to an adaptive linear filter (Figure 1). Since this filter works as a whitened match filter, it is accepted as precisely adjusted as described earlier, except that the filter now works as a complex sample instead of the real sample we simulated earlier.

Thus, the sampled impulse response of the linear baseband channel and the adaptive linear filter (Figure 1) is a (g + 1) -component vector.

Y = y ₀ y ₁ ... y _g (2)

It is a complex component, and all zeros of the Z transform are on or inside the unit circle of the Z plane.

Furthermore, when allowing for a change in level, the noise component {wi} at the filter output has the same statistical properties as the noise component {vi} at the input. Where v ₁ = v (iT).

o이고 y₁=0이다. 따라서 t=iT의 순간 필터 출력에서의 샘플치는 복소치 크기인The delay of transmission across the baseband channel and the adaptive filter is ignored here for convenience, as opposed to related to the time deviation of the received signal, so that y ₀ for i <o and i> g.

o and y ₁ = 0. Thus, the sample value at the instantaneous filter output at t = iT is the complex magnitude

The real and imaginary parts of {wi} are statistically irrelevant Gaussian random variables with an average of zero and a variance of σ ² .

라디안은 코히어런트(coherent)복조기의 위상 오차에 의해 요청되는 캐리어 위상 보정치이다.The adjustment of the adaptive linear filter and the estimation of Y are made by the apparatus shown in FIG. It will be appreciated that this is simply an improvement of the existing adaptive nonlinear (selective-feedback) equalizer if there is a delay in detection (out of two sampling intervals in this embodiment). ⁵ Obviously, if there is no delay in detection, it can be seen that the existing adaptive nonlinear (selective-return) is an improvement over the equalizer. ⁵ obviously. Delay in detection makes this device the same as a normal equalizer. The main tap of the μ-tap adaptive linear feedforward transverse filter is close to the final tap for all channels. The rectangle denoted by T is a storage device having a corresponding sample value, and the stored value is moved by one digit in the direction shown in each sampling interval. The square denoted by Σ is an accumulator that sums the input samples, and * indicates that the elevated sample value has been replaced by its conjugate complex number. a and b are constants of small drugs

Radians are carrier phase correction values required by the phase error of the coherent demodulator.

는 캐리어 위상 제어회로에 의해 결정되는데 이것은 제 1 도 및 제 2 도에 도시되지는 않았다.

의 어댑티브한 조절은 제 2 도의 트랜스버설 필터 탭이득의 조절과 함께 y₀=1이 되도록 조정되며, 각 트랜스버설 필터의 조절방법은 기존의 이쿠얼라이저의 것과 같다.⁵이것과

결정에 대한 상세한 사항은 본 발명의 범주를 벗어나는 것이다.

Is determined by the carrier phase control circuit, which is not shown in FIGS.

The adaptive adjustment of is adjusted so that y ₀ = 1 with the adjustment of the transverse filter tap gain of FIG. 2, and the adjustment method of each transverse filter is the same as that of the conventional equalizer. ⁵ This and

Details of the determination are outside the scope of the present invention.

Unless otherwise noted, the adaptive linear filter is correctly adjusted and is stored in the channel estimator _, y ' _0, y' ₁ ,... … y _'g estimate of the sequence of Y to be also assumed to be the right. The estimate of Y is used by quasi-maximum possible detectors and cancellers with prior knowledge of the possible values of Si.

The detector (FIG. 1) operates on the input sample {r ' ₁ }, giving the final detected data symbol {s' ₁ }, where s ' ₁ is determined after receiving r' _{1 + n} with n <g. There is a delay in the detection of n sampling intervals. The echo canceller removes from the sample {r ₁ } all the estimates (detected values) of all components with respect to the data symbol {s ' ₁ } for which the detected value {s' ₁ } has already been determined. Accordingly, the echo canceling right group is dropped to r _'1 for r _1.

For the time being s ' _1-h ' for all {h}

Since the sampled impulse response of the channel and adaptive filter is reduced from g + 1 to n + 1 components, the detection process is greatly simplified when n << g.

s _k , R ' ₁ and W _K are called k-component row-vectors and the i th component is i = 1,2,... Let k be s ₁ , r ' ₁ and w ₁ , respectively. X _K , Z _K and U _K are also referred to as k-component row-vectors, i = 1,2,... , Let k when each of the i-th component x _1, z ₁ and u _1. Where x ₁ has _one of 16 possible values of s ₁ ,

And u ₁ is a possible value of w ₁ satisfying the following equation.

r ' _{1 =} z ₁ + u ₁ (7)

The square of the "unitauy" distance between vectors R ' _K and Z _K within a k-dimensional complex vector space containing vectors R' _K , Z _K and U _K

U _K | ² = | U ₁ | ² + | U ₂ | ² +. + ｜ U ₄ ｜ ² (8)

And | u ₁ | is the absolute value of u ₁ .

If all real and imaginary components of {w ₁ } are statistically independent and have a constant variance, the maximum possible vector X _K is a possible value that minimizes | U _K | ² . Under the assumed conditions, this X _K is the possible value of S _{K with} the highest probability.

The detection method used here is a variation of the aforementioned system and operates as follows. Just before receiving the sample r _k from the detector input, the detector contains a mn-component vector {Q _K-1 } where m is a multiple of four.

Q _K-1 = x _kn x _{k-1 + n} ... x _k-1 (9)

And x ₁ is as defined above. Each vector Q _I-1 is associated with the corresponding cost | U _I-1 | ² (Equation 8), which is assumed to be s' ₁ = s ₁ for all i. This implies that the echo rain canceller operates in an ideal way, and of course, there is always inaccuracy in | U _K-1 } ² when one or more {s' ₁ } is incorrect.

When r ' _k is received, each stored vector {Q _k-1 } is expanded to four (n + 1) -component vectors {P _k }, where P _k is

P _k = x _kn x _{k-n + 1} ... x _k (10)

The first n components of P _K are the same as the original vector Q _K-1 and the final components x _k have four different values ± 2 ± 2j. The cost associated with each vector P _K is calculated as follows.

개 벡터{P_k}를 선택하여 관련된 코스트와 함께 총 m개의 선택된 벡터를 주게된다. 각 선택된 벡터 P_k가 그 다음에는 4개 벡터{P_k}로 확장되는데 그 첫 x_k성분은 역시 원래 벡터 Q_k-1과 같으며, 최종 성분 x_k과 같으며, 최종 성분 x_k의 주어진 값(±2±2j)에 4가지 다른값 ±1±j가 가산된다. 각 확장된 벡터와 관련된 코스트는 다음과 같이 계산된다.For each of the four possible values of x _k , the detector has a minimum cost, c _k .

Selecting the vector vectors {P _k } gives a total of m selected vectors with associated costs. Each of the selected vector P _k Next, there is extended to four vectors {P _k} The first x _k elements is also original vector the same as Q _k-1, the same as the final component x _k, given the final component x _k Four different values ± 1 ± j are added to the value (± 2 ± 2j). The cost associated with each extended vector is calculated as follows.

The detected data symbol s' _kn is regarded as the value of X _KN within the lowest cost vector P _k and the first symbol x _kn of each vector P _k is discarded to give the corresponding vector Q _k , which of course equals the cost | U _k | ² Related to. Finally, the m vector {Q _k } is selected from the 4m vector {Q _k } as follows.

If m = 32, for each of the 16 possible values of x _k , the detector chooses the two other vectors {Q _k } with the lowest cost and the value of x _k-1 . If m = 16, for each of the 16 possible values of x _k , the detector selects the vector Q _k with the lowest cost. The selected vectors are now stored with the associated cost. Such a device is simply stored with the realized cost. Such a device can be simply realized and ensures that all selected vectors are different, thus avoiding stored vector "merging". ¹³

The technique described is the device of "dual expansion", the following assumptions.

x _k = x _ak + x _bk (13)

Where x _{a, k ㅏ} = ± 2 ± 4j (14)

And x _{b, k} = ± 1 ± j (15)

X _k is thus treated as the sum of two separate four-level data symbols x _{a, k} and x _{b, k} . m one stored vector {Q _k-1} as if x _k x in the expansion of _a, x to be treated as if it were a _{k b, k} is in the extension of one vector is made to zero .m p _{k} These x _k is taken as x _{a, k} + x _{b, k} . Of course _, the value of x _{a, k} for each vector is determined in the expansion and first steps.

This device is based on the following facts: That is, if a complex q _k is _a member whose distance away from a given one of the four possible values of x _{a, k} is less than the distance from the remaining three possible values of x _{a, k} it is also given x _{a, k} and x _b, are separated from the four kinds of one of the possible values of _k that from all x _{a, k} + x _b, the remaining 12 possible values of _k by a small than the distance members. This is for the most to mean that this is the closest x _k possible value can be determined in two successive operations, the first a possible value of q _k and the kkakka cloud x _k is selected, then x _{a, k} value selected for the q _k x _a, The possible values of x _{b, k} are determined such that _{k +} x _{b, k} is closest to q _k .

s'_k-n인 모든 벡터{P_k}가 버려지고 남은 벡터{P_k}의 각각의 첫성분이 생략되어 상응한 n-성분 벡터{Q_K}를 주게된다. 코스트｜U_k}²이 최소인 벡터{P_k}로 부터 유도된 벡터들중 하나는 최초로 선택된 벡터Q_k이다. 그러면 검파기는 나머지 벡터{Q_k}로부터 최소 코스트와 관련된 m-1 벡터를 선택하여, 총m벡터{Q_k} 및 그와 관련된 코스트를 주게 되며 이것들이 저장된다. 주어진 벡터{P_K}를 버림으로써 저장된 벡터의 합성을 막을 수 있는데, 그 이유는 만약 이것들이 전송 시작시에 모두 서로 달랐다면 그중 어는 둘이나 그 이상이라도 그후에 같아질 수 없다는 사실을 보장해 주기때문이다.The following system is also an improvement over the already mentioned system and works as follows. Just before receiving the sample r ' _k from the detector input, the detector stores the mn-component vector {Q _K-1 } with its associated cost {| U _k-1 | ² } (Equations 9 and 12). When r ' _k is received, the detector matches each vector Q _k- ¹ with 16 possible values of x ^k (with a = 1 or 3 and ± a ± bj for b = 1 or 3). _k } (Eq. 10) and calculate the cost | U _k | ² for each 16 vector {P _k }. Then select the vector P _k with the lowest cost and have the detected data symbol s' _kn have the value of x _kn in the selected vector x _kn . x _kn

s' is _kn is discarded, all vectors {P _k} are dropped the remaining vectors {P _k}, each of the first component of this is not a corresponding n- component vectors {Q _K}. One of the vectors derived from the vector {P _k } with the lowest cost | U _k } ² is the first selected vector Q _k . The detector then selects the m-1 vector associated with the minimum cost from the remaining vectors {Q _k }, giving the total m vector {Q _k } and the associated costs and storing them. By discarding a given vector {P _K }, you can prevent the synthesis of stored vectors, because they guarantee that if they were all different at the beginning of transmission, then no two or more of them could ever be the same.

The technique of dual expansion applied in the first system is applied here to the system B to provide a device having less operation and less storage than the system B during the detection process.

Expand m stored vectors {Q _K-1 } to 4 m vectors {P _k } for x _k = ± 2 ± 2j and calculate the associated cost {c _k } and then {x ₁ } as in System A Is any value, the detector chooses the m vector {P _k }, which is the minimum cost.

Expand to 4m vectors {P _K } and calculate its cost {| U _k | ² }, then select the vector P _K with the lowest cost as in System A and select the detected data symbols _kn Let x _{kn be} the vector P _X.

s'_k-n인 모든 벡터{P_K}를 버리고 검파과정은 시스템 B에서와 같이 진행된다.x _kn

discard s' of all _kn vector {P} _K detection process proceeds as in System B.

This is different from that of the third system, reducing the amount of storage and the number of operations associated with the detection of the second system. Upon receiving r ' _k , the detector expands each of the m vectors {Q _K-1 } to the corresponding four vectors {P _k }, where x _k has four values of ± 1 and ± 3, and the detector has a 4m vector Calculate c _k (Eq. 11) for each {P ₄ }. The detector also extends each vector Q _K-1 into four vectors {P _K }, where x _k has four values of ± j and ± 3j (j = -1) and also C _k for each vector P _k . Calculate The detector then removes the vector P _k with the largest cost c _k from each group of four vectors {P _k } (generated from a single vector Q _k-1 through two expansion processes). Leave only the dog vector. _Given that y ₀ = 1, this can be very simple for any vector P _k without actually computing c _k , just the next value in Eq.

You only need to use the real and imaginary parts of. Thus, from the values of d _k for the six vectors {P _K } in the two groups of new vectors resulting from the single vector Q _k-1 , all combinations of the three real and three imaginary values of x _{k in} the six vectors The resulting d _k value for 9 vectors {P _K }, given by, is very easily calculated, giving the corresponding cost of {{U _k | ² }} according to equation (12). Of course, x _k is an imaginary value in each of these vectors. The detector now has a 9m vector {P _K } with its associated cost. The detector then determines s' _kn from the value of x _{kn in} the vector P _k , which is the minimum cost, and the detection process proceeds in the same way as for system B.

The following system is a simple variant of the fourth system, in which m stored vectors {Q _k-1 } are extended to four vectors {P _K } with x _k having four values ± 1 and ± 3 as before. x _k extends into four vectors {P _K } with four values ± j and ± 3, but the detector here finds two vectors with a minimum cost {c _k } from each group of four vectors {P _K }. The basic method of selection is described in system D. In four vectors {P _k } derived from a single vector Q _k-1 , x _k is a real value in two of them and an imaginary value in the other two. From these four vectors {P _k }, All detectors of real and imaginary values of x _k are created, the detector creates four vectors {P _k } with the associated cost {x _k }, and calculates the associated cost {| U _k | ² } . Now the detector has 4 m vectors {P _k } with the associated costs and proceeds just as in the case of system B to _detect s _kn and select m vectors {Q _k }.

Operating in a similar way as a simple variant of the system of claim 5 system, and a fifth system, but only in this case the detector is to elicit only (not a dog 4), three vectors {P _k} of x _k the imaginary value from any single vector Q _k-1 , Vectors {P _k } are those whose cost {| U _k | ² } is minimum in the corresponding group of four vectors of system E. Again, the selection scheme for {P _k } is very simple to realize and does not actually calculate the cost, the cost is determined after the selection process. Thus, the detector generates a 3m vector {P _k } with its associated cost {| U _k | ² } and proceeds just like system B to _detect s _kn and select m vectors {Q _k }.

The immunity to the additive white Gaussian noise of the six systems and the existing nonlinear (selective-feedback) equalizer is applied to models of four telephone circuits using the devices described in Figures 1 and 2, and in Sections 1-8 above. Was determined by computer simulation. In all cases (including the equalizer), it is assumed that the adaptive linear filter has a large number of taps and is precisely adjusted to perform the ideal linear transformation described in Sections 1 and 2.

Figures 3-6 show the attenuation and group-delay characteristics of the four different telephone circuits used in this test, which form part of the transmission path in Figure 1.

FIG. 7 shows the resulting attenuation and group-delay characteristics of the filters, where they operate on transmitted bandpass signals rather than baseband signals at the transmitter and receiver as shown in FIG. Was considered. The filters are adapted to have the filtering required to convert the shock wave sequence at the transmitter input (Figure 1) into the corresponding square wave used in the actual modem.

Table 1 shows the sampled impulse response of the linear base band channel and sampler and adaptive linear filter of FIG. 1 for each of the four telephone circuits tested. Remembering that the first component of an ideal sampled impulse response is 1 and the remainder is 0, this gives some idea of the resulting distortion introduced by each channel.

3 and 7 it can be seen that almost all signal distortions in Table 1 for telephone circuit 1 are actually caused by the filter. While circuits 1 and 2 each produce a negligible level of distortion, respectively, circuits 3 and 4 are close to the typical worst-case circuits typically thought for data transfers of 9600 and 600-1200 bits / sec, respectively. Telephone circuit 3 close to post office network N6 produces severe group-delay distortion, and telephone circuit 4 close to post office network N3 produces very severe attenuation distortion.

dB이며, 단8-11 show the performance of system AF and conventional nonlinear equalizers for telephone circuits 1-4. Where the signal-to-noise ratio

dB, with

=10log₁₀(10/2σ²) (17)

= 10log ₁₀ (10 / 2σ ² ) (17)

The squared mean of the data symbol S ₁ is 10 and 2σ ² is the variance of the Gaussian noise component W ₁ . The 95% confidence limit of the curve is better than ± 1 / 2dB. System A was tested with nM = 16 and 32 and N = 7, where m is the number of stored vectors {Q _k } and n is the number of components of Q _k . System BF was all tested with m-6 and n = 3 and 7. System B was also tested with m = 4 and 8 and n = 7 for telephone circuits 3 and 4.

,3 및 5 1/2dB이다.Figures 8-11 show that the system AFs are all more resistant to additive white Gaussian noise than conventional nonlinear equalizers. System A with m = 32 (32 stored vectors) and n = 7 (delay in the detection of seven sampling intervals) has the best performance of all the systems tested as expected, but with m = 16 and n = 7 At a lower error rate at {S ₁ }, its immunity to noise is inferior to the system BF with m = 6 and n = 7. The latter devices all have similar immunity to noise at lower error rates, which is much better than m = 6 for telephone circuits 4,3 and n = 3. Making m greater than 6 does not seem to have much of an advantage in terms of noise immunity in the system, but decreasing m from 6 to 4 significantly reduces performance. The system BF with m = 6 and n = 7 at an error rate of 1/10 ³ has the advantage of resistance to additive white Gaussian noise over nonlinear equalizers for the telephone circuits 1, 2, 3, and 4 respectively.

, 3 and 5 1/2 dB.

이내로 주는 것을 나타낸다. 따라서, 잘 설계된 모뎀에서 또한 수신 신호 캐리어내의 심한 위상 지터(jitter)의 정정으로써, 수신 신호 레벨이나 캐리어 위상의 부정확한 추정치 때문에 가산성 잡음에 대한 내성이 심하게 나빠져야 하는 것은 아니다.12 shows the effect on the error rate of {S ₁ } of inaccuracy in the carrier phase estimation and the level of the received signal produced by the receiver when system E with m = 6 and n = 7 operates on telephone circuits 1-4. Shows. For telephone circuit 3, the system withstands about 1/4 dB of inaccuracy in the received signal level estimate, otherwise it withstands about 2 degrees of inaccuracy in the estimation of the received signal phase, while the error rate of {S ₁ } doubles. , It is resistant to additive white Gaussian noise

It is given within. Thus, in well-designed modems, as well as correction of severe phase jitter in the received signal carrier, immunity to additive noise should not be severely degraded due to inaccurate estimates of received signal level or carrier phase.

Of the various devices tested, systems E and F with m = 6 and n = 7 were found to be the most cost effective. They make significant advances in addi- tional noise immunity compared to conventional non-linear equalizers without the complexity of the device. Considering that circuit circuit 4 is fundamentally similar to the typical worst-case telephone circuit experienced in a switched telephone network, you can take the appropriate steps to overcome the carrier phase jitter effect in modem design as long as you can bring together the applicable linear filters correctly. As far as possible, the correct operation of the system can be clearly obtained for almost all circuits of the public switched telephone network.

12. References

Clark, A.P., "Principles of Digital Transmission" (Pentech Press, London, 1976).

Monsen, P., "Feedback equalization of fading dispersive channels", IEEE Trans on Information Theory, IT-17, pp. 56-64, January 1971.

3. Westcott, R.J., "An experimental adaptively equalized modem for data transmission over the switched telephone network", The Radio and Electronic Engieer, 42, pp. 499-507, November 1972.

4. Clark, A.P. and Tint, U.S., "Linear and non-linear transversal equalixers for baseband channels", The Radio and Electronic Emgineer, 45, pp. 271-283, June 1975.

5. Clark, A.P., "Advanced Data-Transmission Systems" (Pentech Press, London, 1977).

6. Forney, G.D., "Maximum-likelihood sequence estmation of digital sequences in the presence of intersymbol interference", IEEE Trans., IT-18, pp. 363-378, May 1972.

7. Forney, G.D., "The Viterdipalgorithm", Proc.IEEE, 61, pp.268-278, March 1973.

8. Qureshi, S.U.H. and Newhall, E.E., "An adaptive receiver for data transmission over time-dispersive channels", IEEE Trans., IT-19, pp. 448-457, July 1973.

9. Falconer, D.D. and Magee, F.R., "Adaptive channel memory truncation for maximum-likelihood sequence estmation", Bell Syst. Tech. J., 52, pp. 1541-1562, Novemder 1973.

10. Cantoni, A. and Kwong, K., "Further results on the Viterbi-algorithm dqualizer", IEEE Trans. IT-20, pp. 764-767, Novemder, 1974.

11. Desblache, A.E., "Optimal short desired impulse response for maximum-likelihood sequence estimation", IEEE Trans. on communications, COM-25, pp. 735-738, July 1977.

12. Foschini, G.J., "A reduced state variant of maximum-likelihood sequence detection attaining optimum performance for high signal-to-noise ratios", IT-23, pp. 605-609, September 1977.

13. Clark, A.P., Harvey, J.D. and Driscoll, j.p., "Near-maximum-likelihood detection processes for distorted digital signals", The Radil and Electronic Engineer, 48, pp.301-309, June 1978.

14. Clark, A.P., Kwong.C.P. and Harvey, J.D., "Detection processes for severely distorted digital signlas", Electronic Circuits and Systemn, 3, pp. 27-37, January 1979.

15. Magee, F.R. and Proakis, J.G., "Adaptive maximum-lidelihood sequence estimation for digital signals in the presence of intersymbol interference", IEEE Trans., IT-19, pp. 120-124, Januaury 1973.

16 Clark, A.P., Kwong, C.P. and McVerry, F., "Estimation of the sampled impulse-response of a chammel", Signal Processing, 2, pp. 39-53, January 1980.

17. Clark, A.P. and Harvey, J.D., "Detection of distorted q.a.m. signals", Electronic Circuits and Systiems, 1, pp. 103-109, April 1977.

TABLE 1

For each of the four telephone circuits, the sampled impulse response of the baseband channel and the adaptive linear filter in FIG.

Claims (3)

A method for detecting a multilevel input signal using a Viterbi-algorithm whose incoming signal is m level, the method comprising sampling the incoming signal at predetermined intervals in advance to generate a signal sample, and receiving the received signal. Extend each signal sample of to an nk extension vector (where n is less than m), select a k vector with the lowest cost from the nk extension vector with each cost associated therewith, and select the k vector with the associated cost And calculating an approximate level of the received signal on the basis of the cost. The method of claim 1, wherein the extension is performed in two operations

Where the vector is selected after each expansion process. The method of claim 1, wherein the extension is performed simultaneously in two operations

Then two sets of nk dean vectors are chosen to be the entire n ² k vectors from which k vectors are chosen to be stored.

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