CN113630120A - Zero-time-delay communication method combined with 1-bit analog-to-digital converter and application thereof - Google Patents
Zero-time-delay communication method combined with 1-bit analog-to-digital converter and application thereof Download PDFInfo
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Abstract
The invention relates to the field of wireless communication, in particular to a zero-delay communication method combined with a 1-bit analog-to-digital converter and application thereof. The method comprises the following steps: the method comprises the following steps: initializing coding mapping; step two: and updating the coding mapping. Compared with the existing coding scheme of separating the information source and the information channel, the invention combines the information source coding and the information channel coding, and adopts the coding scheme of combining the information source and the information channel to realize the transmission of the related information source on the broadcasting channel. And consider an extreme case where a single signal sample is transmitted over one channel transmission to achieve the requirement of a zero-delay transmission. The invention considers zero time delay transmission of a related Gaussian source on a broadcast channel combined with the front end of a 1-bit analog-to-digital converter, combines a broadcast channel model of the front end of the 1-bit analog-to-digital converter, and optimizes initial coding mapping in a non-parametric mapping mode under a determined distortion standard, so that the method can improve the distortion performance of a system.
Description
Technical Field
The invention relates to the field of wireless communication, in particular to a zero-delay communication method combined with a 1-bit analog-to-digital converter and application thereof.
Background
Modern wireless communication systems achieve reliable transmission of certain high-rate content types, such as Joint Photographic Experts Group (JPEG) and Moving Picture Experts Group (MPEG), by utilizing channel coding and highly optimized compression algorithms that approach channel capacity. However, many emerging applications, such as internet of things (IOT) or machine-to-machine communication (M2M), further limit the cost and complexity of the communication device, or place higher requirements on available energy and end-to-end delay, which makes many known coding methods and modulation techniques unsuitable.
Broadcast communication is a communication means of transmitting information from a central node to a plurality of devices using a common channel. Broadcast communication is applied in many scenarios, such as the downlink of cellular systems, or Wireless Sensor Networks (WSNs), whereby communication between a control node and a large number of sensors is controlled. One solution for reliably transmitting information over a broadcast channel is based on a mechanism of source-channel separation, i.e. source coding and channel coding are separately optimized.
Generally, a coding scheme based on source-channel separation can provide near-optimal performance, but at the same time, the scheme has certain disadvantages. On one hand, coding schemes based on source-channel separation require the use of long codewords at the encoding end to approach the theoretical optimum, but this results in increased coding complexity and higher latency. On the other hand, since the coding rate depends on the channel condition, the system needs to be redesigned in a time-varying environment so as to match the encoder to the channel condition. Therefore, coding schemes based on source-channel separation are generally not optimal in a multi-user environment.
Nowadays, a large-scale multi-antenna system is considered as a very valuable technology for next-generation communication systems. As the size of the antenna increases, the design of the receiver becomes more complex and the power consumption becomes higher. One key component of a digital receiver front-end is an analog-to-digital converter connected to each receive antenna. The power consumed by an analog-to-digital converter increases linearly with the number of bits. The resolution of the analog-to-digital converter is limited when the available power is limited, such as for a sensor node or a mobile device where battery power is limited. In one extreme case, 1-bit analog-to-digital converters are of interest due to their low hardware complexity: can be realized by a simple threshold comparator, and does not need automatic gain control. Therefore, it is an important research content to research a communication method combined with a 1-bit analog-to-digital converter, reduce time delay and improve distortion performance of a system.
Disclosure of Invention
In order to solve the above problem, a first aspect of the present invention provides a zero-delay communication method in combination with a 1-bit analog-to-digital converter, including:
the method comprises the following steps: code mapping initialization: two sources x1And x2After being coded by a coder, the x is obtained by noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated signal
Obtaining a cost function J, where J is 1 or 2, as shown in equation (1):
α is the coding map of the coder, β1As a source x1Of the decoder, beta2As a source x2A (x) of the decoder, alpha (x)1,x2) As a source x1And x2The encoder output after the encoder encoding mapping, wherein lambda is a Lagrange multiplier;
step two: and (3) updating the coding mapping: preserving transcoding map beta1And beta2Unchanged, updating the code mapping
Mu is the step size and is the length of the step,
for the gradient, k is an element {0, R }, and the coding mapping is obtained as alphak+1Estimate a signal of
Cost function of time Jk+1。
As a preferred technical solution of the present invention, the step twoIn (1) when Jk+1>JkRepeating the second step, when Jk+1≤JkAnd then, the process is ended.
As a preferred embodiment of the present invention, the estimation signal is
Is represented by formula (2):
p(x1,x2) Representing a joint probability density function, p (z)i|α(x1,x2) Represents a known alpha (x)1,x2) Conditional probability density function ofiIs the output of a 1-bit analog-to-digital converter.
As a preferable embodiment of the present invention, z isiIs represented by formula (3):
Yiand outputting the channel after the noise is superposed.
As a preferred technical solution of the present invention, the gradient is
Is represented by formula (4):
σn1as a source x1Variance of superimposed noise, σn2As a source x2Variance of the superimposed noise, β1(0) Decoding the mapping beta for an input 0 time1Output of (b), beta2(0) Decoding the mapping beta for an input 0 time2Output of (b), beta1(1) Decoding a mapping beta for an input 1 time1Output of (b), beta2(1) Decoding a mapping beta for an input 1 time2To output of (c).
As a preferred embodiment of the present invention, when step two Jk+1≤JkThen, the third step is carried out: updating the cost function: preserving coding mapping alphak+1Obtaining two information sources x according to the step one without changing1And x2Encoding alpha via an encoderk+1Then, x is obtained through noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated as
Obtaining a code mapping as alphak+1Estimate a signal of
Cost function J ofk+2。
As a preferable technical scheme of the invention, in the third step, when J isk+2>Jk+1Repeating the second step and the third step, when J isk+2≤Jk+1And then, the process is ended.
As a preferable technical scheme of the invention, in the third step, when J isk+2≤Jk+1And calculating the average Mean Square Error (MSE).
As a preferred technical solution of the present invention, the decoder uses a minimum mean square error estimator to obtain x1And x2Is estimated signal
In a second aspect, the invention provides an application of the zero-delay communication method in combination with a 1-bit analog-to-digital converter, which is used for broadcast communication.
Compared with the prior art, the invention has the following beneficial effects:
(1) compared with the existing coding scheme of separating the information source and the information channel, the invention combines the information source coding and the information channel coding, and adopts the coding scheme of combining the information source and the information channel to realize the transmission of the related information source on the broadcasting channel. And consider an extreme case where a single signal sample is transmitted over one channel transmission to achieve the requirement of a zero-delay transmission.
(2) The invention considers zero time delay transmission of a related Gaussian source on a broadcast channel combined with the front end of a 1-bit analog-to-digital converter, combines a broadcast channel model of the front end of the 1-bit analog-to-digital converter, and optimizes initial coding mapping in a non-parametric mapping mode under a determined distortion standard, so that the method can improve the distortion performance of a system.
(3) According to the method, the Lagrange cost function is constructed, the power limited average distortion minimization problem of the communication system is converted into the unlimited minimization problem, the implicit equation met by the optimal encoder under the model is obtained, and therefore the gradient formula of the cost function J relative to the optimal encoding alpha is obtained
And performing iterative optimization from the initialized coding mapping by using a gradient descent method to realize optimized coding mapping close to the optimal condition.
(4) Compared with parametric mapping, such AS a variable symbol scalar quantizer linear encoder (AS-SQLC), the non-parametric mapping method can find nearly optimal coding mapping under the condition of giving prior distribution of source symbols, and the average distortion of a user end can basically obtain 0.2dB gain under different channel signal-to-noise ratios (CSNR).
Drawings
Fig. 1 is a flowchart of the zero-delay communication method.
Fig. 2 is a block diagram of the zero-delay communication method.
Fig. 3 is a diagram of the channel signal-to-noise ratio and the signal-to-noise ratio obtained by performing simulation comparison tests on the zero-delay communication method and the linear encoder of the variable-sign scalar quantizer provided by the present invention.
Detailed Description
The disclosure may be understood more readily by reference to the following detailed description of preferred embodiments of the invention and the examples included therein. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. In case of conflict, the present specification, including definitions, will control.
When a parameter is expressed as a range, preferred range, or as a range defined by a list of upper preferable values and lower preferable values, this is to be understood as specifically disclosing all ranges formed from any pair of any upper range limit or preferred value and any lower range limit or preferred value, regardless of whether ranges are separately disclosed. For example, when a range of "1 to 5" is disclosed, the described range should be interpreted to include the ranges "1 to 4", "1 to 3", "1 to 2 and 4 to 5", "1 to 3 and 5", and the like. When a range of values is described herein, unless otherwise stated, the range is intended to include the endpoints thereof and all integers and fractions within the range.
The singular forms "a", "an" and "the" include plural referents unless the context clearly dictates otherwise. "optional" or "any" means that the subsequently described event or events may or may not occur, and that the description includes instances where the event occurs and instances where it does not.
Approximating language, as used herein throughout the specification and claims, is intended to modify a quantity, such that the invention is not limited to the specific quantity, but includes portions that are literally received for modification without substantial change in the basic function to which the invention is related. Accordingly, the use of "about" to modify a numerical value means that the invention is not limited to the precise value. In some instances, the approximating language may correspond to the precision of an instrument for measuring the value. In the present description and claims, range limitations may be combined and/or interchanged, including all sub-ranges contained therein if not otherwise stated.
In addition, the indefinite articles "a" and "an" preceding an element or component of the invention are not intended to limit the number requirement (i.e., the number of occurrences) of the element or component. Thus, "a" or "an" should be read to include one or at least one, and the singular form of an element or component also includes the plural unless the stated number clearly indicates that the singular form is intended.
The present invention is illustrated by the following specific embodiments, but is not limited to the specific examples given below.
The invention provides a zero-time delay communication method combined with a 1-bit analog-to-digital converter in a first aspect, which comprises the following steps:
the method comprises the following steps: initializing coding mapping;
step two: and updating the coding mapping.
Step one
In one embodiment, the method of the present invention comprises the following steps: code mapping initialization: two sources x1And x2After being coded by a coder, the x is obtained by noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated signal
And i is 1 or 2, and obtaining a cost function J.
As shown in fig. 2, the associated source x1And x2The coded output is transmitted to a broadcast channel through a coder, and Gaussian white noise is respectively superposed through a channel 1 and a channel 2, wherein the noise N of the channel 11Noise N stronger than channel 22Numerically expressed as N1Is greater than N2The variance of (a) is determined,
the noise signals of the two channels respectively pass through a 1-bit analog-to-digital converter. The 1-bit analog-to-digital converter output is denoted as Zi. Zi reconstructs the information source information at the user end through a decoder, wherein the user 1 only focuses on the information source x1 User 2 is only interested in the source x2And (4) reconstructing. System performance is represented by the mean squared error of the two users. Preferably, the source x of the invention1And x2Is a gaussian source. Gaussian source, continuous amplitude source. And random variables for representing the information source, wherein the probability distribution of the random variables is subjected to normal distribution.
As shown in FIG. 2, the encoder receives a pair of WoodsMemoried and stationary Gaussian correlation source x1And x2Mean of the sources is zero and variance is σX 2The encoder output is V. The encoder α receives a pair of source symbols and maps one channel symbol as output, implementing 2:1 compression coding. The encoder output must meet the power constraint as follows: e [ | | α (X)1,X2)||21 ≦ pP is the defined power, E is the mathematical expectation.
As shown in FIG. 2, at the front end of the decoder, a 1-bit analog-to-digital converter outputs Y to the channeliQuantization is carried out to obtain the output z of the 1-bit analog-to-digital converteriPreferably, z is as defined in the present inventioniIs represented by formula (3):
Yiand outputting the channel after the noise is superposed.
The method aims to minimize the total average mean square error of the estimated signal values and the source signal values of two user ends, and a decoder beta i obtains x by adopting a Minimum Mean Square Error (MMSE) estimator1And x2Is estimated signal
More preferably, the estimation signal of the present invention
Is represented by formula (2):
p(x1,x2) Representing a joint probability density function, p (z)i|α(x1,x2) Represents a known alpha (x)1,x2) Conditional probability density function ofiIs the output of a 1-bit analog-to-digital converter.
p(x1,x2) Presentation coupletAnd (4) combining probability density functions. According to Bayes' principle, p (x)1,x2)＝p(x1)p(x2|x1)。p(x1) Representing a source component x1P (x) as a function of the probability density2|x1) Representing a known source component x1Conditional probability density function of (a). The p (x), p (x)1,x2)、p(x2|x1) The formula of (a) is as follows:
further preferably, according to the present invention, the cost function J is shown in formula (1):
α is the coding map of the coder, β1As a source x1Of the decoder, beta2As a source x2A (x) of the decoder, alpha (x)1,x2) As a source x1And x2And the output of the encoder after the encoding and mapping of the encoder, wherein lambda is a Lagrange multiplier and is a constant value.
Step two
The signal source obtains the initialization parameter through coding and decoding, and the minimum problem of the power limited average distortion of the communication system is converted into the unlimited minimum problem through constructing the Lagrange cost function. The distortion term is deformed, and a deformation form of the distortion term is obtained according to the orthogonality of the minimum mean square error, and is as follows:
after removing the constant terms that are not related to the encoding map α, the minimization objective is converted into:
and (3) obtaining an optimal coding implicit equation formula of the zero-delay related information source broadcast communication system combined with the 1-bit analog-to-digital converter through calculus operation expansion:
and obtaining a gradient formula of the cost function J about the optimal coding alpha according to the implicit equation. More preferably, the gradient of the invention
Is represented by formula (4):
σn1as a source x1Variance of superimposed noise, σn2As a source x2Variance of the superimposed noise, β1(0) Decoding the mapping beta for an input 0 time1Output of (b), beta2(0) Decoding the mapping beta for an input 0 time2Output of (b), beta1(1) Decoding a mapping beta for an input 1 time1Output of (b), beta2(1) Decoding a mapping beta for an input 1 time2To output of (c).
The invention designs the following gradient descent-based algorithm by utilizing the deduced gradient expression, performs iterative optimization from initialized coding mapping, and realizes optimized coding close to the optimal conditionAnd (6) code mapping. Further preferably, the second step of the present invention: and (3) updating the coding mapping: preserving transcoding map beta1And beta2Unchanged, updating the code mapping
Mu is the step size and is the length of the step,
for the gradient, k is an element {0, R }, and the coding mapping is obtained as alphak+1Estimate a signal of
Cost function of time Jk+1. μ is a defined parameter, representing the step size of the gradient descent, determining the amount by which each iteration is to be incremented along the gradient direction.
Still more preferably, in step two of the present invention, when J isk+1>JkRepeating the second step, when Jk+1≤JkAnd then, the process is ended.
λ is used to tie the constraint function and the objective function together. For a given λ, a certain code mapping α can be obtained. If the solution that minimizes the cost function also satisfies the power constraint, the solution will also be a solution to the constraint problem. Still more preferably, in step two of the present invention, when J isk+1≤JkComputing a coding mapping alphak+1Actual power E [ | | α (x)1,x2)||2]When E [ | | α (x)1,x2)||2]>Limiting power P, increasing the value of lambda, repeating the first step and the second step, when E [ | | alpha (x)1,x2)||2]And (4) stopping or performing the third step. In addition, to make the actual power larger, closer to the limit power, when E [ | | | α (x)1,x2)||2]<When limiting the power P, the lambda can be reduced to repeat the first step and the second step until E [ | | alpha (x)1,x2)||2]Is close to or equal to P.
In one embodiment, when step two Jk+1≤JkAnd (5) carrying out the third step.
Step three
In one embodiment, the present invention comprises the following step three: updating the cost function: preserving coding mapping alphak+1Obtaining two information sources x according to the step one without changing1And x2Encoding alpha via an encoderk+1Then, x is obtained through noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated as
Obtaining a code mapping as alphak+1Estimate a signal of
Cost function J ofk+2。
Preferably, in step three of the present invention, when Jk+2>Jk+1Repeating the second step and the third step, when J isk+2≤Jk+1And then, the process is ended. When J isk+2≤Jk+1Corresponding to alphak+1And, and
corresponding beta1And beta2To optimize encoding and decoding mapping.
The distortion performance of the method provided by the invention is represented by the mean square error of two users. More preferably, in step three of the present invention, when Jk+2≤Jk+1And calculating the average Mean Square Error (MSE). The mean square error MSE is formulated as
As shown in fig. 1, the algorithm flow of the present invention is: in the first step, the initial stage uses an existing scheme, such AS a variable sign scalar quantizer linear encoder (AS-SQLC), to initialize the encoding mapping. Using minimum mean square error decoder to obtain estimated signals of two users under initial coding
And calculating a cost function value J of the system in the initial state.
Second, keeping the decoding mapping beta1And beta2The gradient of the cost function J with respect to the coding map alpha is obtained according to equation 16, unchanged, and is decreased by the gradient
And updating the coding mapping, updating the cost function value, comparing the sizes of the cost function before and after updating, repeating the operation of the second step if the updated cost function value is still larger than the value before updating, and otherwise, entering the third step.
Thirdly, keeping the coding mapping alpha unchanged, and updating the decoding mapping beta of the two users1And beta2Is estimated signal
And updating the cost function value, comparing the sizes of the cost function before and after updating, returning to the second step if the updated cost function value is still larger than the value before updating, and otherwise, entering the fourth step.
The fourth step, saving the coding mapping alpha and the decoding mapping beta1And beta2The mean square error value is recorded.
The symbol-variant scalar quantizer linear encoder scheme is a parameterized zero-delay encoding scheme, which is proposed and applied in a zero-delay correlation source broadcast communication system. The parametric mapping scheme has the advantage that the structure of the code mapping is fixed and any point in the source space can be directly mapped into the corresponding channel input symbols. The parameterized map may update the map by adjusting parameters of the map according to signal properties and channel conditions.
The invention realizes the optimization of the linear encoder of the variable symbol scalar quantizer by applying the non-parametric mapping algorithm. The advantage of non-parametric mapping is that a near-optimal coding mapping can be found given the a-priori distribution of source symbols. But the complexity of non-parametric mapping is higher relative to parametric mapping.
A second aspect of the invention provides the use of a zero-delay communication method as described above in combination with a 1-bit analog-to-digital converter for broadcast communication.
Examples
The present invention will be specifically described below by way of examples. It should be noted that the following examples are only for illustrating the present invention and should not be construed as limiting the scope of the present invention, and that the insubstantial modifications and adaptations of the present invention by those skilled in the art based on the above disclosure are still within the scope of the present invention.
Example 1
As shown in fig. 1 and 2, the present example provides a zero-delay communication method in combination with a 1-bit analog-to-digital converter, including:
the method comprises the following steps: code mapping initialization: two sources x1And x2After being coded by a coder, the x is obtained by noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated signal
i is 1 or 2, the estimation signal
Is represented by formula (2):
p(x1,x2) Representing a joint probability density function, p (z)i|α(x1,x2) Represents a known alpha (x)1,x2) Conditional probability density function ofiIs the output of a 1-bit analog-to-digital converter; z isiIs represented by formula (3):
Yiand outputting the channel after the noise is superposed.
And obtaining a cost function J, wherein J is shown as formula (1):
α is the coding map of the coder, β1As a source x1Of the decoder, beta2As a source x2A (x) of the decoder, alpha (x)1,x2) As a source x1And x2The encoder output after the encoder encoding mapping, wherein lambda is a Lagrange multiplier;
step two: and (3) updating the coding mapping: preserving transcoding map beta1And beta2Unchanged, updating the code mapping
Mu is the step size and is the length of the step,
is the gradient, k ∈ {0, R }, the gradient
Is represented by formula (4):
σn1as a source x1Variance of superimposed noise, σn2As a source x2Variance of the superimposed noise, β1(0) Decoding the mapping beta for an input 0 time1Output of (b), beta2(0) Decoding the mapping beta for an input 0 time2Output of (b), beta1(1) Decoding a mapping beta for an input 1 time1Output of (b), beta2(1) Decoding a mapping beta for an input 1 time2And obtaining a code mapping as alphak+1Estimate a signal of
Cost function of time Jk +1When J isk+1>JkAnd repeating the step two.
Step three: updating the cost function: preserving coding mapping alphak+1Obtaining two information sources x according to the step one without changing1And x2Encoding alpha via an encoderk+1Then, x is obtained through noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated as
Obtaining a code mapping as alphak+1Estimate a signal of
Cost function J ofk+2When J isk+2>Jk+1Repeating the second step and the third step, when J isk+2≤Jk+1And then, the process is ended.
Evaluation of Performance
The method provided in example 1 and the linear encoder with a variable symbol scalar quantizer are respectively subjected to simulation comparison tests to obtain graphs of the channel signal-to-noise ratio and the signal-to-noise ratio, as shown in fig. 3.
The invention is directed to a zero delay correlated source broadcast communication system incorporating a 1-bit analog-to-digital converter, which has not been investigated within the scope of the inventors' investigation. The invention realizes that the power requirement of a communication system is reduced by using the 1-bit analog-to-digital converter on the basis of broadcast communication. The inventor researches the distortion performance achieved by the optimized code mapping under the system, and according to simulation comparison tests, as shown in fig. 3, the non-parametric mapping scheme, the comparison parametric mapping scheme, namely the variable sign scalar quantizer linear encoder scheme, provided by the invention can basically obtain a gain of 0.2dB for the average distortion of the user terminal under different channel signal-to-noise ratios (CSNR).
The foregoing examples are merely illustrative and serve to explain some of the features of the method of the present invention. The appended claims are intended to claim as broad a scope as is contemplated, and the examples presented herein are merely illustrative of selected implementations in accordance with all possible combinations of examples. Accordingly, it is applicants' intention that the appended claims are not to be limited by the choice of examples illustrating features of the invention. Also, where numerical ranges are used in the claims, subranges therein are included, and variations in these ranges are also to be construed as possible being covered by the appended claims.
Claims (10)
1. A zero-delay communication method in conjunction with a 1-bit analog-to-digital converter, comprising:
the method comprises the following steps: code mapping initialization: two sources x1And x2After being coded by a coder, the x is obtained by noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated signal
Obtaining a cost function J, where J is 1 or 2, as shown in equation (1):
α is the coding map of the coder, β1As a source x1Of the decoder, beta2As a source x2A (x) of the decoder, alpha (x)1,x2) As a source x1And x2The encoder output after the encoder encoding mapping, wherein lambda is a Lagrange multiplier;
step two: and (3) updating the coding mapping: preserving transcoding map beta1And beta2Unchanged, updating the code mapping
Mu is the step size and is the length of the step,
for the gradient, k is an element {0, R }, and the coding mapping is obtained as alphak+1Estimate a signal of
Cost function of time Jk+1。
2. The zero-delay communication method in combination with a 1-bit analog-to-digital converter according to claim 1, wherein in the second step, when J is reachedk+1>JkRepeating the second step, when Jk+1≤JkAnd then, the process is ended.
3. The method of zero-delay communication in combination with a 1-bit analog-to-digital converter according to claim 1, wherein the estimated signal is a signal
Is represented by formula (2):
p(x1,x2) Representing a joint probability density function, p (z)i|α(x1,x2) Represents a known alpha (x)1,x2) Conditional probability density function ofiIs the output of a 1-bit analog-to-digital converter.
4. The method of zero-latency communication in conjunction with a 1-bit analog-to-digital converter of claim 3, wherein z isiIs represented by formula (3):
Yiand outputting the channel after the noise is superposed.
5. A combination 1-bit analog-to-digital converter as claimed in claim 1The zero-delay communication method of (1), characterized in that the gradient is
Is represented by formula (4):
σn1as a source x1Variance of superimposed noise, σn2As a source x2Variance of the superimposed noise, β1(0) Decoding the mapping beta for an input 0 time1Output of (b), beta2(0) Decoding the mapping beta for an input 0 time2Output of (b), beta1(1) Decoding a mapping beta for an input 1 time1Output of (b), beta2(1) Decoding a mapping beta for an input 1 time2To output of (c).
6. The zero-delay communication method in combination with a 1-bit analog-to-digital converter according to claim 2, wherein when step two J is performedk+1≤JkThen, the third step is carried out: updating the cost function: preserving coding mapping alphak+1Obtaining two information sources x according to the step one without changing1And x2Encoding alpha via an encoderk+1Then, x is obtained through noise superposition, a 1-bit analog-to-digital converter and a decoder respectively1And x2Is estimated as
Obtaining a code mapping as alphak+1Estimate a signal of
Cost function J ofk+2。
7. The method of claim 6, wherein in step three, when J isk+2>Jk+1Repeating the stepsStep two and step three, when Jk+2≤Jk+1And then, the process is ended.
8. The method of claim 7, wherein in step three, when J isk+2≤Jk+1And calculating the average Mean Square Error (MSE).
9. The zero-delay communication method in combination with a 1-bit ADC of any one of claims 1 to 8, wherein the decoder uses a minimum mean square error estimator to obtain x1And x2Is estimated signal
10. Use of a zero-delay communication method in combination with a 1-bit analog-to-digital converter according to any of claims 1 to 9 for broadcast communication.
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