CN113242200B - Method for dynamically calculating optimal decision threshold based on 4FSK signal soft demodulation - Google Patents

Abstract

The invention discloses a method for dynamically calculating an optimal decision threshold based on 4FSK signal soft demodulation, which comprises the following steps: calculating instantaneous frequency for the received I, Q data; passing the instantaneous frequency to a low pass filter; calculating an optimal sampling point and an optimal sampling value x based on the Gardner ring timing synchronization; and after the normalization processing is carried out on the optimal sampling value x, the probability distribution is solved, low _ gate and up _ gate are selected from 4 peak values of the sampling value and are used as decision thresholds together with 0, and the sampling value is decided to output a corresponding bit stream. The invention utilizes I, Q baseband data of 4FSK signals acquired by wireless monitoring equipment, adopts incoherent demodulation, and can minimize the bit error rate of the output bit stream by dynamically calculating the optimal decision threshold.

Description

Method for dynamically calculating optimal decision threshold based on 4FSK signal soft demodulation

Technical Field

The invention relates to the technical field of radio monitoring, in particular to a method for dynamically calculating an optimal decision threshold based on 4FSK signal soft demodulation.

Background

4FSK signal in base band transmission system, because the level of the received signal is stable, the decision threshold adopted in sampling decision is a fixed threshold method. In the field of radio monitoring, the level of a 4FSK signal received by a radio monitoring machine fluctuates, and if a decision threshold is directly fixed, a larger error code is caused. Therefore, in the field of radio monitoring, a method of dynamically adjusting a decision threshold is generally adopted to decide a 4FSK signal and output a corresponding bit stream. In the soft demodulation of a 4FSK signal, the common methods are: and sequencing the sampling values from small to large according to the normalized sampling values, and respectively calculating the mean value mean _ min of the smallest data and the mean value mean _ max of the largest data. The 4FSK signals have 3 decision gates, denoted low _ gate, up _ gate and 0, respectively. The difficulty is that the values of low _ gate and up _ gate are determined, different algorithms have different calculation methods, and the effect is different. Wherein:

delta＝mean_max-mean_min

low_gate＝mean_min+delta/4

up_gate＝mean_max-delta/4

the calculation method can obtain the optimal threshold when the channel is additive white Gaussian noise. However, in an actual wireless channel, there are various complicated situations such as multipath and fading, and the channel is not additive white gaussian noise, so that the bit error rate of the output bit stream is high, and the performance is lost.

Disclosure of Invention

The invention aims to provide a method for dynamically calculating an optimal decision threshold based on 4FSK signal soft demodulation, which is used for solving the problem that the bit error rate of a bit stream output by the traditional method for calculating the optimal decision threshold is higher under the condition that a channel is not additive white Gaussian noise.

The invention solves the problems through the following technical scheme:

the method for dynamically calculating the optimal decision threshold based on the soft demodulation of the 4FSK signal comprises the following steps:

step S1: calculating instantaneous frequency for the received I, Q data;

step S2: passing the instantaneous frequency to a low pass filter;

step S3: calculating an optimal sampling point and an optimal sampling value based on the Gardner ring timing synchronization;

step S4: carrying out normalization processing on the optimal sampling value to obtain a sampling value x, calculating the probability distribution of the sampling value, respectively recording 4 peak values of the probability distribution of the sampling value as peak _1, peak _2, peak _3 and peak _4, and respectively corresponding to 4 output levels of the 4FSK signal;

the 3 decision thresholds of the 4FSK signal are respectively denoted as low _ gate, up _ gate and 0, where:

low_gate＝min[peak_1:peak_2]

up_gate＝min[peak_3:peak_4]

outputting a corresponding bit stream according to the 3 decision thresholds and the sampling value x:

if x is less than or equal to low _ gate, outputting 0;

if x is less than or equal to 0 and less than low _ gate, outputting 1;

if x is more than or equal to 0 and less than up _ gate, outputting 2;

if x > up _ gate, output 3.

The step S1 specifically includes:

step S11: the expression for signal s (n) is as follows:

wherein A is₀Is the signal amplitude, g (n-m) is the amplitude1. Rectangular pulse gate function with width of reciprocal of symbol transmission rate, omega_cIs the carrier frequency, n is the signal number, m is the sampling time number, Δ ω is the carrier angular frequency interval, a_mIs an input symbol of_m＝0,1,2,3；

Step S12: performing quadrature decomposition on the signal s (n) to obtain an in-phase component X_I(n) and an orthogonal component X_Q(n)：

Step S13: calculating instantaneous frequency f (n):

where φ' (n) is the derivative of the phase φ (n).

The step S3 specifically includes:

based on a Gardner timing synchronization loop, an independent sampling clock source is adopted, and an optimal sampling point is obtained through a timing recovery algorithm of interpolation filtering; the timing recovery algorithm of interpolation filtering comprises an interpolation filter and an interpolation filtering control algorithm, wherein the interpolation filtering control algorithm comprises timing error detection, a loop filter and a numerical control oscillator and is used for providing interpolation phases and weights of all signals during interpolation output for the interpolation filter; and the interpolation filter is used for obtaining a sampling value signal of the optimal interpolation moment through an interpolation algorithm according to the input signal, and the interpolation moment is controlled and generated by the numerical control oscillator.

Compared with the prior art, the invention has the following advantages and beneficial effects:

(1) the invention utilizes I, Q baseband data of 4FSK signals acquired by wireless monitoring equipment, adopts incoherent demodulation, and can minimize the bit error rate of the output bit stream by dynamically calculating the optimal decision threshold.

(2) Compared with the traditional method, the method has better performance, and the bit error rate is better than 1e-3 when the signal-to-noise ratio is greater than 28 db.

(3) The instantaneous frequency signal obtained by calculation is subjected to low-pass filtering and then is subjected to timing synchronization extraction, so that the sampling rate is reduced, and the calculation burden of demodulation processing is reduced.

Drawings

FIG. 1 is a flow chart of the present invention.

Detailed Description

The present invention will be described in further detail with reference to examples, but the embodiments of the present invention are not limited thereto.

Example (b):

with reference to fig. 1, a method for dynamically calculating an optimal decision threshold based on soft demodulation of a 4FSK signal includes:

step S1: calculating instantaneous frequency for the received I, Q data; the method specifically comprises the following steps:

step S11: the expression for signal s (n) is as follows:

wherein A is₀For signal amplitude, g (n-m) is a rectangular pulse gate function with amplitude of 1 and width of reciprocal symbol transmission rate, ω_cIs the carrier frequency, n is the signal number, m is the sampling time number, Δ ω is the carrier angular frequency interval, a_mIs an input symbol of_m＝0,1,2,3；

Step S12: performing orthogonal decomposition on the signal s (n) to obtain an in-phase component X_I(n) and an orthogonal component X_Q(n)：

Step S13: calculating instantaneous frequency f (n):

where φ' (n) is the derivative of the phase φ (n).

Step S2: passing the instantaneous frequency to a low pass filter; the instantaneous frequency signal is subjected to low-pass filtering, the sampling rate is reduced, and the calculation burden of demodulation processing is reduced;

step S3: calculating an optimal sampling point and an optimal sampling value based on the Gardner ring timing synchronization;

based on a Gardner timing synchronization loop, an independent sampling clock source is adopted, and an optimal sampling point is obtained through a timing recovery algorithm of interpolation filtering; the timing recovery algorithm of interpolation filtering comprises an interpolation filter and an interpolation filtering control algorithm, the interpolation filtering control algorithm is used for providing interpolation phases and weights of all signals during interpolation output for the interpolation filter and comprises timing error detection, a loop filter and a numerical control oscillator, the timing error detector detects a phase difference between a local clock sampling moment and an optimal sampling moment, and the detected phase difference is sent to the numerical control oscillator to generate the next interpolation moment after being filtered by the loop filter; and the interpolation filter is used for obtaining a sampling value signal at the optimal interpolation moment through an interpolation algorithm according to the input signal. To achieve normal demodulation, the sample values are required to be located at the symbol "midpoint," i.e., the decision point and the symbol transition point. Therefore, as long as the timing phase error is known, the sampling value of the optimal decision point can be calculated, and the symbol synchronization is realized.

Step S4: normalizing the optimal sampling value (the size is between-0.5 and 0.5) to obtain a sampling value, calculating the probability distribution of the sampling value x,

assuming that the number of sampling values y _ sample is N, the interval from-0.5 to 0.5 is divided into M segments, and p (j) is the number of sampling values in 1 to M segments. low _ point ═ 0.5.

A probability distribution p (j) of the sample values is obtained.

4 peak values of probability distribution p (j) of sampling values of the FSK signal are respectively marked as peak _1, peak _2, peak _3 and peak _4 from-0.5 to 0.5, and respectively correspond to 4 output levels of the 4FSK signal;

the 3 decision thresholds of the 4FSK signal are respectively denoted as low _ gate, up _ gate and 0, where:

low_gate＝min[peak_1:peak_2]

up_gate＝min[peak_3:peak_4]

outputting a corresponding bit stream according to the 3 decision thresholds and the sampling value x:

if x is less than or equal to low _ gate, outputting 0;

if x is less than or equal to 0 and less than low _ gate, outputting 1;

if x is more than or equal to 0 and less than up _ gate, outputting 2;

if x > up _ gate, output 3.

The bit error rate performance of the output 4FSK bit stream is superior to the common 4FSK soft demodulation performance. As shown in the following table, the bit error rate is better than 1e-3 when the SNR is greater than 28 db.

Although the present invention has been described herein with reference to the illustrated embodiments thereof, which are intended to be preferred embodiments of the present invention, it is to be understood that the invention is not limited thereto, and that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the spirit and scope of the principles of this disclosure.

Claims (3)

1. The method for dynamically calculating the optimal decision threshold based on the soft demodulation of the 4FSK signal is characterized by being applied to a channel which is not additive white Gaussian noise, and comprises the following steps:

step S1: calculating instantaneous frequency for the received I, Q data;

step S2: passing the instantaneous frequency to a low pass filter;

step S3: calculating an optimal sampling point and an optimal sampling value based on the Gardner ring timing synchronization;

step S4: and (3) calculating an optimal threshold:

normalizing the optimal sampling value to obtain a sampling value x, calculating the probability distribution of the sampling value, respectively recording 4 peak values of the probability distribution of the sampling value as peak _1, peak _2, peak _3 and peak _4 from-0.5 to 0.5, and respectively corresponding to 4 output levels of the 4FSK signal;

the 3 decision thresholds of the 4FSK signal are respectively denoted as low _ gate, up _ gate and 0, where:

according to the 3 decision thresholds and the sampling value x, outputting the corresponding bit stream:

if x is less than or equal to low _ gate, outputting 0;

if x is less than or equal to 0 and less than low _ gate, outputting 1;

if x is more than or equal to 0 and less than up _ gate, outputting 2;

if x > up _ gate, output 3.

2. The method for dynamically calculating an optimal decision threshold based on the soft demodulation of a 4FSK signal according to claim 1, wherein the step S1 specifically comprises:

step S11: signal

The expression of (a) is as follows:

wherein the content of the first and second substances,

in order to be the amplitude of the signal,

is a rectangular pulse gate function with amplitude of 1 and width of the reciprocal of the symbol transmission rate,

is the carrier frequency and is,

is a serial number of the signal, and is,

is a serial number of the sampling time instant,

is a carrier angular frequency interval and is,

for the purpose of the input symbols, the symbols are,

=0,1,2,3；

step S12: to the signal

Performing orthogonal decomposition to obtain in-phase component

And the orthogonal component

：

Step S13: calculating instantaneous frequency

：

Wherein the content of the first and second substances,

to phase position

And (6) taking a derivative.

3. The method for dynamically calculating an optimal decision threshold based on the soft demodulation of a 4FSK signal according to claim 1, wherein the step S3 specifically comprises:

based on a Gardner timing synchronization loop, an independent sampling clock source is adopted, and an optimal sampling point is obtained through a timing recovery algorithm of interpolation filtering; the timing recovery algorithm of interpolation filtering comprises an interpolation filter and an interpolation filtering control algorithm, wherein the interpolation filtering control algorithm comprises timing error detection, a loop filter and a numerical control oscillator and is used for providing interpolation phases and weights of all signals during interpolation output for the interpolation filter; and the interpolation filter is used for obtaining a sampling value signal of the optimal interpolation moment through an interpolation algorithm according to the input signal, and the interpolation moment is controlled and generated by the numerical control oscillator.

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