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CN110300409B - Finite block length concealed communication realizing method based on channel estimation - Google Patents

Finite block length concealed communication realizing method based on channel estimation Download PDF

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CN110300409B
CN110300409B CN201910419695.XA CN201910419695A CN110300409B CN 110300409 B CN110300409 B CN 110300409B CN 201910419695 A CN201910419695 A CN 201910419695A CN 110300409 B CN110300409 B CN 110300409B
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block length
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channel estimation
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CN110300409A (en
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束锋
徐婷珍
唐钰城
胡锦松
颜世豪
桂林卿
徐玲
刘笑语
陆造宇
钱玉文
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Nanjing University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0256—Channel estimation using minimum mean square error criteria
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/02—Protecting privacy or anonymity, e.g. protecting personally identifiable information [PII]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

本发明提供了一种基于信道估计的有限块长隐蔽通信实现方法。以往对于衰落信道中隐蔽通信的研究都是假设信道是已知的，或者通过信道反转功率控制方法来避免信道的估计。然而实际中，由于信道互易性假设的理想性，在衰落信道中不可避免地要进行信道估计。在传统的信道估计中，最优导频数等于发送天线数，但是在隐蔽通信中，该结论可能不再成立。为了提高隐蔽通信的可靠性，我们利用最小均方误差估计方法对信道进行估计，在隐蔽约束条件下设计最优的导频数目和发射功率、数据数目和发射功率以最大化有效速率。与此同时，由于以前的研究一般都是集中于无限块长的分析，但实际中通常要发送有限块长的符号，因此本发明研究有限块长下的隐蔽通信。

Figure 201910419695

The invention provides a method for realizing covert communication with limited block length based on channel estimation. Previous studies on covert communication in fading channels all assume that the channel is known, or avoid channel estimation through channel inversion power control methods. However, in practice, channel estimation is unavoidable in fading channels due to the ideality of the channel reciprocity assumption. In traditional channel estimation, the optimal number of pilots is equal to the number of transmitting antennas, but in covert communication, this conclusion may no longer hold true. In order to improve the reliability of covert communication, we use the minimum mean square error estimation method to estimate the channel, and design the optimal pilot number, transmission power, data number and transmission power under the covert constraints to maximize the effective rate. At the same time, because the previous studies generally focus on the analysis of infinite block length, but in practice, symbols with finite block length are usually sent, so the present invention studies covert communication under finite block length.

Figure 201910419695

Description

基于信道估计的有限块长隐蔽通信实现方法Implementation method of finite block length covert communication based on channel estimation

技术领域technical field

本发明涉及无线通信技术领域，特别涉及基于信道估计的有限块长隐蔽通信实现方法。The invention relates to the technical field of wireless communication, in particular to a method for realizing covert communication with limited block length based on channel estimation.

背景技术Background technique

随着移动通信的迅速发展，保护信息传输的隐私性变得越来越重要。然而传统的保证信息安全性的方法中，往往是对信息内容本身进行保护，比如加密。但这样很容易让窃听者知道此时正在传输隐秘信息，会更容易激发窃听者解密的兴趣。With the rapid development of mobile communications, it is becoming more and more important to protect the privacy of information transmission. However, in the traditional method of ensuring information security, the information content itself is often protected, such as encryption. But in this way, it is easy for the eavesdropper to know that the secret information is being transmitted at this time, and it will be easier to arouse the eavesdropper's interest in deciphering.

隐蔽通信的目的就是隐藏信息传输的过程，让看守者不知道有信息传输行为的发生，即确保看守者以很低的检测概率探测到信息正在传输。以往对于隐蔽通信在衰落信道中的研究都是假设信道是已知的，或者利用信道的互易性，用信道反转功率控制方法来避免对信道的估计。然而实际中，信道互易性的假设过于理想，这就避免不了对信道进行估计。与此同时，大多数对于隐蔽通信的研究都是假设无限块长，但在实际中往往需要发送有限块长的符号。因此，针对这些问题，本发明研究基于信道估计的有限块长隐蔽通信，在隐蔽约束下优化导频数目和导频与数据之间的功率分配因子以最大化有效速率，具有非常深远的意义和重要的理论研究价值和应用前景。The purpose of covert communication is to hide the process of information transmission, so that the watchman does not know that there is information transmission, that is, to ensure that the watchman detects that the information is being transmitted with a very low detection probability. Previous studies on covert communication in fading channels all assume that the channel is known, or use channel reciprocity, and use channel inversion power control method to avoid channel estimation. However, in practice, the assumption of channel reciprocity is too ideal, which makes it inevitable to estimate the channel. At the same time, most of the research on covert communication assumes infinite block length, but in practice it is often necessary to send symbols with finite block length. Therefore, in response to these problems, the present invention studies the finite block length covert communication based on channel estimation, and optimizes the number of pilots and the power allocation factor between pilots and data under covert constraints to maximize the effective rate, which has very far-reaching significance and Important theoretical research value and application prospects.

发明内容Contents of the invention

本发明所要解决的技术问题是针对含有信道估计误差的有限块长隐蔽通信系统，提供了一种基于信道估计的如何优化发送导频数和功率分配因子以最大化有效速率的方法，有效提高系统的可靠性和隐蔽性。The technical problem to be solved by the present invention is to provide a channel estimation-based method of how to optimize the number of transmission pilots and power allocation factors to maximize the effective rate for a finite block length covert communication system with channel estimation errors, effectively improving the system performance. reliability and concealment.

本发明为解决上述技术问题采用以下技术方案：一种基于信道估计的有限块长隐蔽通信实现方法，包括：In order to solve the above technical problems, the present invention adopts the following technical solutions: a method for realizing covert communication with limited block length based on channel estimation, comprising:

由于信道增益是通过估计得到的，并且包含估计误差，于是我们需要根据估计得到的信道求得有效速率的表达式；Since the channel gain is estimated and contains estimation errors, we need to obtain the expression of the effective rate based on the estimated channel;

考虑第一种情况为发送端和接收者之间为瑞利衰落信道，而发送端和看守者之间为高斯信道，即从发送端考虑最坏的情况。考虑第二种更一般性的情况，即发送端和接收端、发送端和看守者之间都是衰落信道。分别计算两种情况下看守者的虚警和漏检概率；Consider the first case where there is a Rayleigh fading channel between the sender and the receiver, and a Gaussian channel between the sender and the watcher, that is, consider the worst case from the sender. Consider the second, more general case, where there are fading channels between the sender and the receiver, and between the sender and the caretaker. Calculate the false alarm and missed detection probability of the watchman in the two cases respectively;

要获得最优的功率分配因子η和导频数np，一般要通过二维搜索，但是我们根据优化问题的特征提出了一种与二维搜索高度匹配的一维搜索方法；In order to obtain the optimal power allocation factor η and the number of pilots n p , two-dimensional search is generally required, but we propose a one-dimensional search method that is highly compatible with two-dimensional search according to the characteristics of the optimization problem;

作为一种实施例，所述考虑根据信道估计求得有效速率表达式，包括：As an embodiment, the consideration is to obtain an effective rate expression based on channel estimation, including:

步骤11)，首先假设利用MMSE估计器，则发送端Alice和接收端Bob之间的信道可以表示为

Figure BDA0002065613000000021
Step 11), first assuming that the MMSE estimator is used, the channel between Alice at the sending end and Bob at the receiving end can be expressed as
Figure BDA0002065613000000021

其中

Figure BDA0002065613000000022
为估计信道，
Figure BDA0002065613000000023
为估计误差，E[|hab|2]＝λab，np和ρp分别表示导频数和平均导频符号功率，
Figure BDA0002065613000000024
为Bob端的噪声功率，
Figure BDA0002065613000000025
和
Figure BDA0002065613000000026
的功率分别记为
Figure BDA0002065613000000027
和
Figure BDA0002065613000000028
in
Figure BDA0002065613000000022
To estimate the channel,
Figure BDA0002065613000000023
To estimate the error, E[|h ab | 2 ]=λ ab , n p and ρ p represent the number of pilots and the average power of pilot symbols respectively,
Figure BDA0002065613000000024
is the noise power at Bob’s end,
Figure BDA0002065613000000025
and
Figure BDA0002065613000000026
The power of
Figure BDA0002065613000000027
and
Figure BDA0002065613000000028

步骤12)，Bob在解码阶段，接收数据可以表示为

Figure BDA0002065613000000029
其中xd表示数据符号，ρd表示平均数据符号功率，nb为Bob的加性高斯噪声。将估计误差和噪声同时视为干扰nb'，于是Bob的有效信噪比为
Figure BDA00020656130000000210
Step 12), Bob is in the decoding stage, the received data can be expressed as
Figure BDA0002065613000000029
Where x d represents the data symbol, ρ d represents the average data symbol power, and n b is Bob's additive Gaussian noise. The estimation error and noise are regarded as interference n b' at the same time, so Bob's effective SNR is
Figure BDA00020656130000000210

步骤13)，为了简化分析，把从总功率中分配给数据的功率占比记为η，剩余1-η部分分配给导频，即ρdnd＝ηρn，ρpnp＝(1-η)ρn，0<η<1，其中ρ表示平均符号功率，n表示总符号数，即np+nd＝n，nd为数据符号数。于是Bob的有效信噪比可以化简为

Figure BDA00020656130000000211
有效速率为
Figure BDA00020656130000000212
Step 13), in order to simplify the analysis, the power ratio allocated to the data from the total power is recorded as η, and the remaining 1-η part is allocated to the pilot frequency, that is, ρ d n d = η ρn, ρ p n p = (1- η) ρn, 0<η<1, where ρ represents the average symbol power, n represents the total number of symbols, that is, n p + nd =n, and n d is the number of data symbols. So Bob's effective SNR can be simplified as
Figure BDA00020656130000000211
The effective rate is
Figure BDA00020656130000000212

作为一种实施例，所述在两种情况下分别计算看守者的虚警和漏检概率，包括：As an embodiment, the false alarm and missed detection probability of the watchman are calculated respectively in two cases, including:

步骤21)，在Alice-Willie的信道服从高斯分布情况下，当ρp＝ρd＝ρ时，虚警概率为

Figure BDA00020656130000000213
漏检概率为
Figure BDA00020656130000000214
其中τ为看守者Willie的检测门限。令错误概率ξ＝α+β最小化，于是得到看守者的最优检测门限为
Figure BDA00020656130000000215
对应的最优错误概率为ξ*，把ξ*≥1-∈作为隐蔽约束条件。Step 21), when Alice-Willie's channel obeys Gaussian distribution, when ρ p = ρ d = ρ, the false alarm probability is
Figure BDA00020656130000000213
The probability of missed detection is
Figure BDA00020656130000000214
Among them, τ is the detection threshold of the watchman Willie. Minimize the error probability ξ=α+β, so the optimal detection threshold of the guard is obtained as
Figure BDA00020656130000000215
The corresponding optimal error probability is ξ * , and ξ * ≥ 1-∈ is used as the hidden constraint.

步骤22)，在高斯信道中，当ρp≠ρd时，根据强大数定律并当导频数较小时，Willie的平均接收符号功率可以近似为

Figure BDA00020656130000000216
于是漏检概率为
Figure BDA0002065613000000031
虚警概率不变，得到最优检测门限为
Figure BDA0002065613000000032
得到最优错误概率ξ*。Step 22), in the Gaussian channel, when ρ p ≠ ρ d , according to the strong law of large numbers and when the number of pilots is small, the average received symbol power of Willie can be approximated as
Figure BDA00020656130000000216
Then the probability of miss detection is
Figure BDA0002065613000000031
The false alarm probability remains unchanged, and the optimal detection threshold is obtained as
Figure BDA0002065613000000032
Get the optimal error probability ξ * .

步骤23)，在Alice-Willie的信道服从瑞利分布情况下，当ρp＝ρd＝ρ时，易得该情况下的最优错误概率ξ*与高斯信道中ρp＝ρd＝ρ情况下的表达式相同。Step 23), in the case that the Alice-Willie channel obeys the Rayleigh distribution, when ρ p = ρ d = ρ, it is easy to obtain the optimal error probability ξ * in this case and ρ p = ρ d = ρ in the Gaussian channel The expressions in the case are the same.

步骤24)，在瑞利信道中，当ρp≠ρd时，根据马尔科夫不等式，求得漏检的近似表达式为

Figure BDA0002065613000000033
于是得到最优检测门限为
Figure BDA0002065613000000034
Step 24), in the Rayleigh channel, when ρ p ≠ ρ d , according to the Markov inequality, the approximate expression of missing detection is obtained as
Figure BDA0002065613000000033
Then the optimal detection threshold is obtained as
Figure BDA0002065613000000034

作为一种实施例，所述根据优化问题提出一种高精确度的一维搜索方法，包括：As an embodiment, according to the optimization problem, a high-precision one-dimensional search method is proposed, including:

步骤31)，初始化参数n,ρ,

Figure BDA0002065613000000035
∈,λab。Step 31), initialization parameters n, ρ,
Figure BDA0002065613000000035
∈,λ ab .

步骤32)，对于每个η，求解ξ*＝1-∈，得到固定η下最优的np，记为

Figure BDA0002065613000000036
Step 32), for each η, solve ξ * = 1-∈ to obtain the optimal n p under fixed η, denoted as
Figure BDA0002065613000000036

步骤33)，取距

Figure BDA0002065613000000037
最近的两个整数，记为
Figure BDA0002065613000000038
和
Figure BDA0002065613000000039
分别代入ξ*的表达式得到
Figure BDA00020656130000000310
和
Figure BDA00020656130000000311
若
Figure BDA00020656130000000312
令
Figure BDA00020656130000000313
否则令
Figure BDA00020656130000000314
把
Figure BDA00020656130000000315
代入有效速率表达式得到
Figure BDA00020656130000000316
Step 33), taking the distance
Figure BDA0002065613000000037
The nearest two integers, denoted as
Figure BDA0002065613000000038
and
Figure BDA0002065613000000039
Substituting into the expressions of ξ * respectively, we get
Figure BDA00020656130000000310
and
Figure BDA00020656130000000311
like
Figure BDA00020656130000000312
make
Figure BDA00020656130000000313
Otherwise order
Figure BDA00020656130000000314
Bundle
Figure BDA00020656130000000315
Substituting into the effective rate expression we get
Figure BDA00020656130000000316

步骤34)，比较所有的

Figure BDA00020656130000000317
搜索最大值，得到全局最优的
Figure BDA00020656130000000318
和C*。Step 34), compare all
Figure BDA00020656130000000317
Search for the maximum value to get the global optimal
Figure BDA00020656130000000318
and C * .

本发明采用以上技术方案与现有技术相比，具有以下技术效果：Compared with the prior art, the present invention adopts the above technical scheme and has the following technical effects:

提出的基于信道估计的有限块长隐蔽通信实现方法，将包含误差的信道估计考虑在内，根据估计得到的信道对导频数和功率分配因子进行优化，比一般的衰落信道中直接假设信道是已知的隐蔽通信的研究更具有实际意义，性能也得到了提高。而且本发明所提的一维搜索算法大大降低了算法的复杂度。The proposed finite block length covert communication implementation method based on channel estimation takes the channel estimation including errors into account, optimizes the number of pilots and power allocation factors according to the estimated channel, and directly assumes that the channel is already The research on the covert communication of knowing has more practical significance, and the performance has also been improved. Moreover, the one-dimensional search algorithm proposed by the present invention greatly reduces the complexity of the algorithm.

本发明附加的方面和优点将在下面的描述中部分给出，这些将从下面的描述中变得明显，或通过本发明的实践了解到。Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description, or may be learned by practice of the invention.

附图说明Description of drawings

图1示出了基于信道估计的有限块长隐蔽通信实现方法流程图。Fig. 1 shows a flowchart of a method for implementing covert communication with a limited block length based on channel estimation.

图2示出了一维搜索算法和二维算法仿真结果。Figure 2 shows the simulation results of the one-dimensional search algorithm and the two-dimensional algorithm.

图3示出了本发明方法得到的最优有效速率和现有的信道反转功率控制(CIPC)方法的仿真结果。Fig. 3 shows the optimal effective rate obtained by the method of the present invention and the simulation result of the existing Channel Inversion Power Control (CIPC) method.

具体实施方式Detailed ways

下面结合附图和具体实施例，进一步阐明本发明，应理解这些实施例仅用于说明本发明而不用于限制本发明的范围，在阅读了本发明之后，本领域技术人员对本发明的各种等价形式的修改均落于本申请所附权利要求所限定的范围。Below in conjunction with accompanying drawing and specific embodiment, further illustrate the present invention, should be understood that these embodiments are only for illustrating the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various aspects of the present invention Modifications in equivalent forms all fall within the scope defined by the appended claims of this application.

本发明的一种基于信道估计的有限块长隐蔽通信实现方法包括：先得出看守者的最优错误概率，令它大于某个接近于1的数，作为隐蔽条件，然后最大化有效速率以优化导频数和功率分配因子。A finite block length covert communication implementation method based on channel estimation of the present invention includes: first obtain the optimal error probability of the watchman, make it greater than a certain number close to 1, as a covert condition, and then maximize the effective rate to Optimize the number of pilots and power allocation factors.

作为一种实施例，所述方法包括：存在信道估计误差的情况下，先求得接收端的有效速率。再分别在高斯和瑞利信道中求得看守者的虚警和漏检概率。在满足隐蔽约束的条件下，针对目标函数优化最优发送导频数和功率分配因子。As an embodiment, the method includes: if there is a channel estimation error, first obtain the effective rate of the receiving end. Then the false alarm and missed detection probabilities of the watchman are obtained in the Gaussian and Rayleigh channels respectively. Under the condition of satisfying the concealment constraints, the optimal transmission pilot number and power allocation factor are optimized for the objective function.

第一步：假设Alice在一个时隙中同时发送n个符号，其中包括np个导频(平均符号发送功率为ρp)和nd个数据(平均符号发送功率为ρd)。假设使用MMSE估计方法，则Alice-Bob之间的信道可以表示为估计信道和估计误差之和

Figure BDA0002065613000000041
由此推出Bob的有效信噪比为
Figure BDA0002065613000000042
其中，E[|hab|2]＝λab，
Figure BDA0002065613000000043
为Bob端的噪声功率。Step 1: Assume that Alice transmits n symbols simultaneously in a time slot, including n p pilots (average symbol transmission power is ρ p ) and n d data (average symbol transmission power is ρ d ). Assuming the MMSE estimation method is used, the channel between Alice-Bob can be expressed as the sum of the estimated channel and the estimated error
Figure BDA0002065613000000041
It follows that Bob's effective signal-to-noise ratio is
Figure BDA0002065613000000042
Among them, E[|h ab | 2 ]=λ ab ,
Figure BDA0002065613000000043
is the noise power at Bob's end.

第二步：由于存在四个优化参数，导频数np和功率ρp，导频数nd和功率ρd，为了简化分析，引入功率分配因子η，即ρdnd＝ηρn，ρpnp＝(1-η)ρn，0<η<1，其中ρ表示平均符号功率。于是Bob的有效信噪比可以简化为

Figure BDA0002065613000000044
有效速率为
Figure BDA0002065613000000045
Step 2: Since there are four optimization parameters, the number of pilots n p and power ρ p , the number of pilots n d and power ρ d , in order to simplify the analysis, a power allocation factor η is introduced, namely ρ d n d = ηρn, ρ p n p = (1-η)ρn, 0<η<1, where ρ represents the average symbol power. Then Bob's effective SNR can be simplified as
Figure BDA0002065613000000044
The effective rate is
Figure BDA0002065613000000045

第三步：在Alice-Bob之间的信道为衰落信道，Alice-Willie之间的信道为高斯信道的情况下，求得当ρp＝ρd＝ρ时Willie的虚警和漏检概率，并求得最优检测门限为

Figure BDA0002065613000000046
得到对应的最优错误概率ξ*，其中
Figure BDA0002065613000000047
为Willie的噪声功率。类似地，当ρp≠ρd时，求得Willie的最优检测门限为
Figure BDA0002065613000000051
其中Γ()表示Gamma函数， W(k,x)表示Lambert W函数的第k个分支，即给出了关于x＝tet的解t。Step 3: When the channel between Alice-Bob is a fading channel and the channel between Alice-Willie is a Gaussian channel, obtain the false alarm and missed detection probability of Willie when ρ p = ρ d = ρ, and The optimal detection threshold is obtained as
Figure BDA0002065613000000046
Get the corresponding optimal error probability ξ * , where
Figure BDA0002065613000000047
is Willie's noise power. Similarly, when ρ p ≠ ρ d , the optimal detection threshold of Willie is obtained as
Figure BDA0002065613000000051
Among them, Γ() represents the Gamma function, and W(k,x) represents the kth branch of the Lambert W function, that is, the solution t about x=te t is given.

第四步：在Alice-Bob和Alice-Willie之间的信道都为衰落信道的情况下，求得当ρp＝ρd＝ρ时，Willie的最优检测门限和高斯信道中等功率分配的情况相同。当ρp≠ρd时，根据马尔科夫不等式，求得漏检的近似表达式为

Figure BDA0002065613000000052
于是得到最优检测门限为
Figure BDA0002065613000000053
同时得到相应的ξ*。Step 4: In the case that the channel between Alice-Bob and Alice-Willie is a fading channel, when ρ p = ρ d = ρ, the optimal detection threshold of Willie is the same as that of the Gaussian channel medium power allocation . When ρ p ≠ ρ d , according to the Markov inequality, the approximate expression of missing detection is obtained as
Figure BDA0002065613000000052
Then the optimal detection threshold is obtained as
Figure BDA0002065613000000053
At the same time get the corresponding ξ * .

第五步：针对以上各种情况，在隐蔽约束ξ*≥1-∈下，分别优化导频数和功率分配因子η。算法主要步骤为，对于每个η，求解ξ*＝1-∈，得到固定η下最优的np，记为

Figure BDA0002065613000000054
取距
Figure BDA0002065613000000055
最近的两个整数，记为
Figure BDA0002065613000000056
和
Figure BDA0002065613000000057
分别代入ξ*的表达式得到
Figure BDA0002065613000000058
和
Figure BDA0002065613000000059
若
Figure BDA00020656130000000510
令
Figure BDA00020656130000000511
否则令
Figure BDA00020656130000000512
把
Figure BDA00020656130000000513
代入有效速率表达式得到
Figure BDA00020656130000000514
比较所有的
Figure BDA00020656130000000515
搜索最大值，得到全局最优的
Figure BDA00020656130000000516
和C*。Step 5: For the above situations, under the concealment constraint ξ * ≥ 1-∈, respectively optimize the number of pilots and the power allocation factor η. The main steps of the algorithm are, for each η, solve ξ * = 1-∈ to obtain the optimal n p under fixed η, denoted as
Figure BDA0002065613000000054
take distance
Figure BDA0002065613000000055
The nearest two integers, denoted as
Figure BDA0002065613000000056
and
Figure BDA0002065613000000057
Substituting into the expressions of ξ * respectively, we get
Figure BDA0002065613000000058
and
Figure BDA0002065613000000059
like
Figure BDA00020656130000000510
make
Figure BDA00020656130000000511
Otherwise order
Figure BDA00020656130000000512
Bundle
Figure BDA00020656130000000513
Substituting into the effective rate expression we get
Figure BDA00020656130000000514
compare all
Figure BDA00020656130000000515
Search for the maximum value to get the global optimal
Figure BDA00020656130000000516
and C * .

从图2展示出的一维搜索算法和二维算法仿真结果，可以看出该算法具有很高的精确度，而且大大降低了算法的复杂度。图3描绘了本发明方法得到的最优有效速率和现有的信道反转功率控制(CIPC)方法的比较，以看出在有限块长下，随着块长n的增加，所提方法性能明显优于CIPC。From the simulation results of the one-dimensional search algorithm and the two-dimensional algorithm shown in Figure 2, it can be seen that the algorithm has high accuracy and greatly reduces the complexity of the algorithm. Fig. 3 depicts the comparison between the optimal effective rate obtained by the method of the present invention and the existing channel inversion power control (CIPC) method, to find out that under the finite block length, with the increase of the block length n, the performance of the proposed method Significantly better than CIPC.

本发明提出的基于信道估计的有限块长隐蔽通信实现方法，性能优于现有的信道反转功率控制方法，且提出的一维搜索算法明显降低了复杂度，实现了性能与复杂度的良好权衡，提高了隐蔽通信的可靠性。The implementation method of finite block length covert communication based on channel estimation proposed by the present invention has better performance than the existing channel inversion power control method, and the proposed one-dimensional search algorithm significantly reduces complexity and achieves a good performance and complexity Trade-off, improved covert communication reliability.

Claims (1)

1. A method for implementing finite block length blind communication based on channel estimation is characterized by comprising the following steps:
since the channel gain is obtained by estimation and includes estimation error, an expression of effective rate needs to be obtained according to the estimated channel;
considering the first case that a Rayleigh fading channel is arranged between a sending end and a receiver and a Gaussian channel is arranged between the sending end and a watcher, considering the worst case from the sending end and considering the second case that fading channels are arranged between the sending end and the receiving end and between the sending end and the watcher; respectively calculating the false alarm and the missed detection probability of the watcher under two conditions;
according to the characteristics of optimization problem, a one-dimensional search method highly matched with two-dimensional search is provided so as to obtain optimal power distribution factor eta and pilot frequency number n p ；
Consider finding an effective rate expression from channel estimates, comprising:
step 11), firstly assuming that an MMSE estimator is utilized, a channel between a sending end Alice and a receiving end Bob is represented as
Figure FDA0003970663080000011
Wherein
Figure FDA0003970663080000012
In order to estimate the channel, the channel estimation method,
Figure FDA0003970663080000013
to estimate the error, E [ | h ab | 2 ]＝λ ab ，n p And ρ p Respectively representing the number of pilots and the average pilot symbol power,
Figure FDA0003970663080000014
is the noise power at the end of Bob,
Figure FDA0003970663080000015
and
Figure FDA0003970663080000016
respectively is recorded as
Figure FDA0003970663080000017
And
Figure FDA0003970663080000018
step 12), bob receives data representation as decoding stage
Figure FDA0003970663080000019
Wherein x is d Representing data symbols, p d Representing the average data symbol power, n b For additive Gaussian noise of Bob, the estimation error and the noise are simultaneously considered as interference n b' Then Bob has an effective SNR of
Figure FDA00039706630800000110
Step 13), introducing power distribution factors eta, rho for simplifying analysis d n d ＝ηρn，ρ p n p ＝(1-η)ρn，0<η<1 where ρ represents the average symbol power, n represents the total number of symbols, n p +n d ＝n，n d For the number of data symbols, bob's effective SNR is then reduced to
Figure FDA00039706630800000111
Effective rate of
Figure FDA00039706630800000112
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