CN111698057B

CN111698057B - Method for analyzing probability of unary coded modulation symbols for wireless data simultaneous transmission

Info

Publication number: CN111698057B
Application number: CN202010386768.2A
Authority: CN
Inventors: 杨鲲; 赵毅哲
Original assignee: Hebei Baiya Information Technology Co ltd
Current assignee: Hebei Baiya Information Technology Co ltd
Priority date: 2020-05-09
Filing date: 2020-05-09
Publication date: 2022-11-04
Anticipated expiration: 2040-05-09
Also published as: CN111698057A

Abstract

The invention discloses a unitary coding modulation symbol probability analysis method for wireless data simultaneous transmission aiming at the problem of mutual coupling of an encoder and a modulator in wireless data simultaneous transmission (SWIPT); the invention uses the coder and modulator controlled by unitary coding to transmit information under Rayleigh channel; constructing a Markov state machine for the unary coding, and analyzing the state transition process of the unary coding; analyzing a symbol probability expression under any certain modulation mode (M-QAM); the theoretical analysis was verified using monte carlo simulations.

Description

Method for analyzing probability of unary coded modulation symbols for wireless data simultaneous transmission

Technical Field

The invention belongs to the technical field of wireless data energy simultaneous transmission coding modulation, and particularly relates to a method for analyzing probability of unary coding modulation symbols for wireless data energy simultaneous transmission.

Background

In recent years, wireless communication has been rapidly developed, and studies on wireless communication have been advanced. In the upcoming era of the internet of things, a novel communication mode of wireless digital simultaneous transfer (SWIPT) is to provide energy for low-power devices powered by batteries or super capacitors on the basis of traditional wireless communication.

At present, there are many coding designs for SWIPT. For example, some coding designs are discussed in "Nonlinear code design for joint energy and information transfer", "Constrained code for joint energy and information transfer" and "Constrained-code for real-time simultaneous energy and information transfer", which respectively design Nonlinear low-density parity-check (LDPC) codes, run-length Constrained (RLL) codes and sub-block constraint codes. In "Unary coding controlled simultaneous wireless information and power transfer", hu et al have studied the SWIPT system controlled by Unary coding, and have proved the feasibility of Unary coding in wireless data simultaneous transmission by virtue of its low complexity decoding mode.

However, the coding and modulation design of SWIPT is still largely explored. For conventional data communication, researchers usually only focus on the channel capacity between the source and the sink, but there is not much research on the received power at the receiving end. For simultaneous data energy transmission, the power of the receiving end directly affects the efficiency of wireless energy transmission. Therefore, in the wireless digital simultaneous transmission network, the transmission probability analysis needs to be performed on the modulation symbols of the physical layer, and then the average acceptable energy of the receiving end can be deduced. However, some of the existing paper works are limited to studying coding and modulation designs separately. For example, in "unknown coded controlled sinusoidal wireless information and power transfer", the univariate coded controlled SWIPT analysis is only applicable to modulators using on-off keying (OOK), where only the binary symbol "1" is represented by the presence of an RF signal. In a communication system, a source is encoded into a sequence of bits, which are then mapped to different symbols by a modulator. The mapping results of different modulators for unary coding are also different, resulting in the difference in the probability of the transmitted symbol and thus the energy collection amount at the receiving end. Therefore, it is important to analyze the probability of the modulation symbol based on unary coding for the generalized modulator.

Disclosure of Invention

Unary coding is widely used in wireless data simulcast research due to its low coding and decoding complexity. The present invention aims to obtain the corresponding symbol probabilities by considering both the encoder and the modulator controlled by unary coding.

The invention realizes the purpose through the following technical scheme:

the method for analyzing the probability of the unary coding modulation symbol facing the simultaneous transmission of wireless data comprises the following steps:

s1, establishing a transceiver structure, selecting to transmit unary codes under a Rayleigh channel, and transmitting data information by adopting an unary coding mode;

s2, constructing a Markov state machine for the unary coding, and analyzing the state transition process of the unary coding;

s3, analyzing a symbol probability expression according to different conditions under different modulation modes;

and S4, verifying theoretical analysis by adopting Monte Carlo simulation.

The invention has the beneficial effects that: the joint coding modulation technology is adopted, so that the two are not independent links any more, and the method is more suitable for the actual situation; and simulation verification is performed in a Monte Carlo mode, so that the verification sample is more random.

Drawings

FIG. 1 is a flow chart of a method for analyzing probability of unary coded modulation symbols for simultaneous transmission of wireless data according to the present invention;

FIG. 2 is a diagram of a transceiver structure of the method for analyzing probability of unary coded modulation symbols for simultaneous wireless data transmission according to the present invention;

FIG. 3 is a state transition Markov chain encoded for a unary of order K in the present invention;

fig. 4 is gray mapping for 16-QAM of the present invention;

FIG. 5 is a validation of Markov analysis symbol probabilities in accordance with the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.

Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.

In the description of the present invention, it is to be understood that the terms "upper", "lower", "inside", "outside", "left", "right", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, or the orientations or positional relationships that the products of the present invention are conventionally placed in use, or the orientations or positional relationships that are conventionally understood by those skilled in the art, and are used for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.

Furthermore, the terms "first," "second," and the like are used merely to distinguish one description from another, and are not to be construed as indicating or implying relative importance.

In the description of the present invention, it should be further noted that, unless otherwise explicitly stated or limited, the terms "disposed" and "connected" and the like are to be broadly construed, for example, "connected" may be a fixed connection, a detachable connection, or an integral connection; can be mechanically or electrically connected; the connection may be direct or indirect through an intermediate medium, and the connection may be internal to the two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.

FIG. 1 is a schematic flow diagram of the present invention. As shown in fig. 1, the specific implementation process of the present invention is as follows:

s1, the transceiver structure of the system is shown in figure 2. A joint coding and modulation system comprises a transmitter and a receiver, the transmitter having N _t The receiver has only one antenna, thus forming a MIMO system. First, a source X enters the encoder, the output of which is a coded binary sequence

. Next, a classical digital modulator is responsible for converting a bit sequence into a modulated symbol sequence S. After passing through the baseband-to-RF converter, the wireless signal is transmitted into a rayleigh fading channel and then acquired by the receiver. At the receiving end, the RF signal is converted into a baseband signal, which becomes a bit sequence

Is demodulated. After passing through the decoder, the original message Y is recovered using a symbol level trellis.

As for the encoding module, the present invention selects unary coding as the encoding method, which is widely used for source coding in wireless communication systems because of its low encoding and decoding complexity.

S2, analyzing the state transition process of the unary code to obtain information association of the unary code, wherein the specific analysis process is as follows:

s21, assuming that the source X randomly generates K different information, which is expressed as X ₁ ,…,X _K Then the K-ary unary coding is responsible for mapping these input information to the coded source

In the information source

With K code words

The kth code word

With k-1 symbols "1" followed by a symbol "0". Will input information X ₁ ,…,X _K Is expressed as Pr _ X = { p (X) ₁ ),…,p(X _K ) Then the final codeword

Has a probability of

S22, as shown in figure 3, a Markov chain for K order unary coded state transitions is created. The resulting encoded source

Generating a bit sequence X of length L _L ＝{X ₁ ,…,X _L }. Introducing bit state C _L ＝{C ₁ ,…,C _L In which C is _l Is shown at X _L The 1 run after the transmission of the ith bit in (1). Since the run-length of "1" is K-1 when using unary coding of K th order, we have C _l E {0, …, K, …, K-1} (L =1, …, L). Transitions between different states follow a markov property. p is a radical of _k ＝Pr{C _l+1 ＝k+1|C _l = K } (K =0, …, K-2) is slave state C _l K to state C _l+1 Transition probability of = k +1, expressed as:

s23, if the current state meets C _l = K (K =0, …, K-2), the transmitter may transmit at p _k Sends bit "1" with probability, and then transitions to new state C _l+1 K +1. Or 1-p _k Then the next state is C _l+1 =0. Specifically, if the current status is C _l K-1, the transmitter must send a bit of "0" because the run of "1" is at most K-1 long. Then the transition probability Pr _ C (k' | k) = Pr { C _l+1 ＝k'|C _l = k } is summarized below:

s24, adding C _l Is expressed as Pr _ c with a size of K × K, the element on the K 'th column of the K-th row thereof represents the probability of Pr _ c (K' | K), and the steady-state probability pi _c This can be obtained by solving the following system of equations:

wherein pi _c The kth element of (1) _c,k Is represented by C _l = steady state probability of k.

And S3, carrying out theoretical analysis on the symbol probability according to the situation under the condition of adopting an M-QAM modulation mode. The specific analysis process is as follows:

assuming that conventional M-QAM modulation is used at the transmitter, the bit sequence from the unary coder then enters the modulator and is mapped to different symbols according to the gray mapping rule S31. Given the mth symbol s in an M-QAM constellation _m (M =1, …, M), its corresponding bit sequence is denoted as ζ _m ＝{ζ _m，1 ，…，ζ _m,n ,…,ζ _m,N } (N =1, …, N), where N = log ₂ (M)。

S32, mixing

Is defined as s _m Is a backward continuation number from ζ _m,N A backward run of "1" is started. For symbols s satisfying 1. Ltoreq. M < M _m Is provided with

Because at their corresponding bit sequence ζ _m At least one "0". For symbols s _M If K-1 is not less than N, then

May be N, N +1, …, K-1, depending on the previously transmitted bits.

S33, mixing

Is defined as s _m Is a forward continuous number from ζ _m,1 A positive run of "1" is started. The symbols in 16-QAM modulation and their corresponding bit sequences ζ are illustrated in Table 1 _m Backward direction continuous number

And forward continuous number

The mapping relationship of (2).

TABLE 1 mapping between bit sequences and symbols of QAM and its characterization

S34, analyzing the probability of the transmitted symbols, wherein the probability is divided into two different conditions that K-1 is more than N and K-1 is more than or equal to N:

s341, K-1 < N: in this case, δ _m,n Is defined as being at the transmission bit ζ _m,n Following the inverted "1" run. Delta _m,n Expressed as:

wherein ζ _m' Is at ζ _m A previously transmitted bit sequence.

Furthermore, by applying each symbol s _m (M =1, …, M) as a Markov state b _t A Markov chain can be generated having M transition states, where s _m Is at the completion of X _L After the mapping of bits to symbols, the tth symbol is sent. According to Markov analysis of unary codes, b _t And b _t+1 Transition probability Pr _ s (m | m') = Pr { b) between two states _t+1 ＝s _m |b _t ＝s _m' Is also the symbol s _m At s _m' The probability of the subsequent transmission is calculated as follows:

the transition probability matrix of the markov chain is represented by Pr _ s of size M × M, whose elements on the M ' th row and M ' th column represent the transition probability Pr _ s (M | M '). Then, all possibilities are obtained according to the following equationStationary probability vector of states pi _s ：

Finally, the symbol s _m Steady state transmission probability τ of _m Is denoted by τ _s,m In which τ is _s,m Denotes pi _s The m-th element in (b).

S342 and K-1 are more than or equal to N: when K-1 ≧ N, it is ineffective to use the same Markov chain as K-1 < N. The currently transmitted symbol may be related not only to the last symbol but also to some of the previously transmitted symbols. Therefore, more states need to be added in order to keep only the markov properties between two adjacent states.

Will be with s _m Each state of the correlation is represented as

Therefore, if M < M, since the backward continuation number

Is a definite value, so there is only one state and bit sequence ζ _m And (4) correlating. However, if M = M, there may be ζ from the bit sequence _m Related K-N different states, i.e.

Thus, the probability of state transition

The derivation of (c) is as follows:

m is less than M: since the backward continuation number is determined for each state, we can be based on

The transition probability is calculated. In this case, the probability

Is expressed with P obtained in the formula (9) _s (m | m') are the same.

M = M: in this case, the bit sequence ζ is obtained _m There is no bit "0" in it, so the backward continuous number

Must be transmitted by the last transmitted symbol s _m' To determine, expressed as

Thus, at s _m' After which the symbol s is transmitted _m Probability of (2)

Expressed as:

similarly, in the case of K-1 < N, the transition probability matrix of the Markov chain is represented as Pr _ s, which is (M + K-N-1) × (M + K-N-1) in size. M (M < M) th state and state

Related, and the M (M ≧ M) th state and state

And (4) correlating. Thus, by solving the same set of equations for the steady state probabilities as before, the steady state probabilities π for all M + K-N-1 states can be obtained _s . Finally, the symbol s _m Steady state probability of (1) _m Expressed as:

and S4, verifying the effectiveness of theoretical analysis by using Monte Carlo simulation. The system uses gray mapping between bits and symbols, fig. 4 is an example of gray mapping for 16-QAM.

A 16-QAM modulator is used in the system. Fig. 5 compares the theoretical symbol probability and the simulated symbol probability given an arbitrary input distribution Pr _ x, where unary coding of

order

4 and 6 is envisaged, respectively. By generating 10 ⁶ Each codeword to implement the monte carlo method. As can be seen from fig. 5, the simulation results and the theoretical results are the same, which demonstrates the effectiveness of the markov analysis.

It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. The method for analyzing the probability of the unary coding modulation symbol facing the wireless data simultaneous transmission is characterized in that a transceiver structure is established, and data information is transmitted by adopting an unary coding mode; constructing a Markov state machine for the K-order unary coding, and analyzing the state transition process of the unary coding; under different modulation modes, analyzing a symbol probability expression according to different conditions; verifying theoretical analysis by adopting Monte Carlo simulation;

using M-QAM modulation at a transmitter, a sequence of bits generated by a unitary encoder enters a modulator and is mapped to different symbols s according to a gray mapping rule _m Its corresponding bit sequence is denoted as ζ _m ＝{ζ _m，1 ，…，ζ _m,n ,…,ζ _m,N } (N =1, …, N), where N = log ₂ (M); introducing a transmission symbol s _m Forward continuous number of

And reverse continuous number

To be from ζ _m,N The run of "1" in the backward direction is started,

to be from ζ _m,1 Starting a forward run of '1's, analysing the probability of transmitting symbols, K-1 < log ₂ At M, the symbol s is found by Markov state transition _m Steady state transmission probability τ of _m Is denoted by τ _s,m In which τ is _s,m Represents pi _s The m-th element in (1), the stationary probability vector of all possible states, pi _s Obtained according to the following equation:

where Pr _ s is the transition probability matrix of the Markov chain, where the element in row m ' represents the transition probability Pr _ s (m | m '), pr _ s (m | m ') being the symbol s _m At s _m' The probability of subsequent transmission is specifically:

wherein, delta _m,n Is defined as being at the transmission bit ζ _m,n Follows an inverted "1" run; pr _ C (k' | k) represents the slave state C _l K to state C _l+1 Transition probability of = k'; c _l Is shown at X _L The run of "1" after the transmission of the ith bit in (1),

being a source of binary sequences, X _L As a source of information

Generating a bit sequence with length L;

when K-1 is more than or equal to N, the symbol s is obtained by analyzing according to two conditions that M is less than M and M = M _m Steady state probability of (1) _m Expressed as:

2. the method of claim 1, wherein the transceiver structure comprises an encoder, a modulator, a transmitter and a receiver, the transmitter has N _t The receiver has an antenna, the wireless signal is encoded by a unary encoder, modulated by a modulator, then sent to a Rayleigh fading channel, and then acquired by the receiver.

3. The method of claim 2, wherein the probability of the input symbol is given, a Markov chain for K order unary coding state transition is created, the state transition probability is analyzed to obtain a steady state probability, and the state C is derived from the state _l K to state C _l+1 Transition probability of = k +1, expressed as:

wherein

Is the transmission probability of the kth codeword,

will C _l The state transition probability of (a) is represented by Pr _ c with a size of K × K, and the transition probability Pr _ c (K '| K) represented by the element on the K-th row and K' column is specifically:

probability of steady state pi _c Expressed as:

wherein pi _c The kth element of (1) < pi > _c,k Is represented by C _l Steady state probability of k.

4. The method for analyzing probability of unary coded modulation symbols for wireless simultaneous data transmission according to claim 3, wherein Monte Carlo simulation is used to verify effectiveness of theoretical analysis.