KR101380134B1 - Method and Apparatus for Finding BER Performance of QPSK Transmitted Signal for Power-line Channel with Nakagami Background Noise - Google Patents

Abstract

The present invention relates to a method and apparatus for obtaining a bit error rate (BER) performance in a power line channel of a quadrature phase shift keying (QPSK) transmission system having a Nakagami noise.

Description

Method and Apparatus for Finding BER Performance of QPSK Transmitted Signal for Power-line Channel with Nakagami Background Noise}

The present invention relates to a power line channel, and more particularly, to a method and an apparatus for obtaining a bit error rate (BER) performance in a power line channel of a quadrature phase shift keying (QPSK) transmission system having Nakagami noise.

In order to complete the smart grid, a reliable and secure communication method is required. The communication method supports two-way data transmission, and can be a wired, wireless or combined communication method. Power Line Communication (PLC), one of the wired communication methods, was applied to Automatic Meter Reading (AMR) to prove its effectiveness. PLC is emerging as a key element technology of smart grid as well as AMI (Advanced Metering Infrastructure).

In order to apply PLC stably, performance analysis should be done like other communication methods. However, no formal model exists for powerline channels. Recently, a research result was proposed that the background noise, which is one of several parameters constituting the channel model, can be modeled using the Nakagami probability distribution. In this paper, the characteristics of the background noise in the power line channel are expressed using the closed-form probability distribution function (see Korean Patent No. 10-0864213) and performance analysis of the Binary Phase Shift Keying (BPSK) method. (See Korean Patent Application No. 10-2010-0117720). With the recent spread of smart grids, data that needs to be transmitted through powerline channels has also become larger. To this end, a symbol error rate (SER) was analyzed by considering a Quadrature Phase Shift Keying (QPSK) method, which is faster than a BPSK method (see Korean Patent Application No. 10-2011-0123039).

However, modeling or analysis of the bit error rate (BER) in a power line communication system such as a QPSK scheme is not known yet.

Accordingly, an object of the present invention is to solve the above-described problem, and an object of the present invention is to express a BER performance of a power line communication system of a QPSK transmission system with Nakagami background noise by a mathematical expression and calculate the performance value, thereby easily predicting the performance figure. The present invention provides a method for obtaining BER performance in a powerline channel of a QPSK transmission scheme.

First, to summarize the features of the present invention, in accordance with an aspect of the present invention for achieving the object of the present invention, the real part and the imaginary part of the transmitter and the imaginary part transmitted by the QPSK method in the power line channel is composed of ± 1 ± j In the BER calculation method when a complex symbol is received at a receiver, a probability distribution function f (α) of background noise α expressed by the Nakagami-m distribution is determined by using a predetermined calculation means. Equation that is the SER of the received signal to follow,

To calculate 1/2 of the SER as BER,

로서 α²의 기대값,

인 것을 특징으로 한다., Where Γ () is the gamma function,

As expected value of α ² ,

.

BER is

으로 근사화되어 계산될 수 있다.. ≪ / RTI >

Can be approximated and calculated.

According to a method and apparatus for obtaining BER performance in a power line channel of a Nakagami noise-based QPSK transmission system, a background noise present in a signal transmitted and received in a power line communication system of a QPSK transmission system having a Nakagami background noise By using the closed-form PDF (Probability Density Function), the average BER performance of the transmitted / received signals can be obtained to easily predict and analyze the performance related to the bit error probability of the QPSK transmission / reception system, resulting in easy hardware design of the receiver. It becomes

In addition, the BER obtained by using the present invention facilitates performance analysis with other communication schemes, and also enables the application of various channel parameters to observe changes in the BER. As a result, performance analysis / prediction of the power line communication system is easy and the design of the transmission / reception system is predictable. In addition, the present invention may be modified and applied in various forms within the scope of the technical idea, and thus the scope of the present invention may be extended to a theoretical background of BER performance derivation, implementation to a recording medium such as a computer, and a communication system composed of actual hardware. Through this, it is possible to lead the related research technology and link with industry, thus contributing to the enhancement of competitiveness.

1 is a view for explaining a power line communication system of the QPSK transmission method.
FIG. 2 is a diagram for explaining signal constellation of the QPSK transmission method.
3 is a graph of analysis results for explaining theoretical SER performance and simulated BER performance at m = 0.6 of the Nakagami-m distribution.
4 is a graph of analysis results for explaining theoretical SER performance and simulated BER performance at m = 0.9 of the Nakagami-m distribution.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout.

In the power line communication system of the QPSK transmission system in the present invention, the closed-form PDF (Probability density) of the background noise of the SER (Symbol Error Rate) performance in the power line channel of the QPSK transmission system in which the background noise is expressed by Nakagami-m distribution We propose a method and apparatus for deriving from a function). Each of the equations as described below can be calculated by running on a computer using software or calculated in various devices necessary for analysis or application of the equations, such as a processor of the receiver.

1 is a view for explaining a power line communication system of the QPSK transmission method. As shown in FIG. 1, assuming that the transmitter transmits data modulated through gray encoding in a QPSK scheme, for example, binary data (eg, ± 1 ± j), the receiver may have I (in-phase). For the data received in the C) and Q (quadrature) channels, the data of each channel is demodulated through gray decoding for each.

The transmitted data may include background noise (y, jz) of the Nakagami-m distribution, similar to those used to model fading channels in wireless communications, and each gray decoding means uses a threshold of 0 and the received digital data. Using a simple comparator to compare, the received data can be determined as one of (± 1 ± j).

,

이고, 여기서,

는 β의 기대값을 나타낸다. [수학식 1]에서, 약 25MHz 정도의 고주파에서는 white Gaussian(m≒1)을 나타내며, 약 5MHz 정도의 저주파에서는 one-sided Gaussian(m<1)을 나타낸다. The closed-form PDF (Probability density function) of the Nakagami-m distribution background noise can be expressed as Equation 1 below. In Equation 1, the random variable α is the magnitude of the background noise, Γ () is the gamma function,

,

Lt; / RTI &gt;

Represents the expected value of β. In Equation 1, white Gaussian (m ≒ 1) is shown at a high frequency of about 25 MHz, and one-sided Gaussian (m <1) is shown at a low frequency of about 5 MHz.

 [Equation 1]

Such a noise magnitude is divided into a real part y and an imaginary part z as shown in [Equation 2] and [Equation 3], and each random variable uniformly distributed from -π to π of phase θ may be derived. .

&Quot; (2) &quot;

&Quot; (3) &quot;

At this time, the closed-form PDF (Probability density function) of the Nakagami-m distribution background noise for the real part y and the imaginary part z is derived as shown in [Equation 4], where a first kind confluent hypergeometric (second) Geometry) ₁ F ₁ function is defined as in Equation 5 below.

&Quot; (4) &quot;

&Quot; (5) &quot;

FIG. 2 is a diagram for explaining signal constellation of the QPSK transmission method.

The transmitter transmits a complex symbol composed of QPSK modulated data such as a real part and an imaginary part such as (± 1 ± j), and transmits a symbol set {s ₀ , s ₁ , s ₂ , s ₃ }. Assuming that the transmission is to be achieved, for each symbol set {s ₀ , s ₁ , s ₂ , s ₃ } received in each real part and imaginary part as shown in the signal constellation as shown in FIG. The received signal r may be expressed as Equation 6 below. Here, each of the four signals in the symbol set is stochastically equal, and it may be assumed that the optimum thresholds in the decision metric are the I and Q axes. For example, if the signal transmitted from the transmitter and distorted by noise is in the third quadrant, it is determined by the symbol s ₂ . Hereinafter, the symbol s ₂ will be described, but the symbols s ₀ , s ₁ , and s ₃ can be similarly described.

In this case, the symbol s ₂ is transmitted from the transmitter, and the probability p (C | s ₂ ) to be accurately determined as the symbol s ₂ may be represented by Equation 7 below. This means that noise-distorted symbols correspond to three quadrants. Accordingly, using Equation 8, Equation 9 (using Equation 4 for f (y), and Equation 10), Pe, which is a SER (Symbol Error Rate), is expressed as [Equation 8]. 11] can be calculated as follows. P (z <0 | s ₂ ) is equal to P (y <0 | s ₂ ). When SNR (proportional to 1 / Ω) is large, P ₁ of [Equation 11] appears to be very small, so ignoring P ₁ ² in [Equation 11] can be simplified to [Equation 12]. Can be. In other words, Pe is approximately twice the BER of BPSK. Equation 11 is calculated using Equation 13 and Equation 13 includes a confluent hypergeometric ₂ F ₂ function. On the other hand, BER is 1/2 of the SER Pe obtained as described above, Pb BER can be approximated to P ₁ according to [Equation 13].

&Quot; (6) &quot;

r = ± 1 ± j + y + jz

&Quot; (7) &quot;

&Quot; (8) &quot;

&Quot; (9) &quot;

&Quot; (10) &quot;

&Quot; (11) &quot;

&Quot; (12) &quot;

&Quot; (13) &quot;

3 is a graph of analysis results for explaining theoretical SER performance and simulated BER performance at m = 0.6 of the Nakagami-m distribution. 4 is a graph of analysis results for explaining theoretical SER performance and simulated BER performance at m = 0.9 of the Nakagami-m distribution. The analysis results assume that 10 ⁶ symbols are randomly generated at the transmitter, and Monte Carlo simulation software running on a computer is used. 3 and 4, it was confirmed that the theoretical / simulated SER according to [Equation 11] and the SER approximated according to [Equation 12] are almost identical, and the simulation for Pb, which is the BER approximated by P _1, was performed. The results also showed reliable results for the SNR (Signal to Noise Ratio) of all sections.

The method disclosed herein can be embodied as computer readable code on a computer readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored. Examples of computer-readable recording media include ROM, RAM, CD-ROM, USB, magnetic tape, floppy disks, optical data storage, mass storage, and the like, as well as carrier wave (for example, transmission over the Internet). It also includes implementations in form. In addition, the computer-readable recording medium may be distributed over a network-connected computer system so that computer-readable code can be stored and executed in a distributed manner.

The method and apparatus for obtaining closed-form BER performance in a power line channel according to the present invention can be modified and applied in various forms within the scope of the technical idea of the present invention and are not limited to the above embodiments. In addition, the embodiments and drawings are merely for the purpose of describing the contents of the invention in detail, not intended to limit the scope of the technical idea of the invention, the present invention described above is common knowledge in the technical field to which the present invention belongs As those skilled in the art can have various substitutions, modifications, and changes without departing from the technical spirit of the present invention, it is not limited to the above embodiments and the accompanying drawings, of course, and not only the claims to be described below but also claims Judgment should be made including scope and equivalence.

Probability density function (PDF)
Symbol Error Rate (SER)
Bit Error Rate (BER)

Claims (6)

In the BER calculation method when a receiver receives a complex symbol consisting of a real part and an imaginary part of ± 1 ± j transmitted by a transmitter in a QPSK scheme on a power line channel,
Equation that is the SER of the received signal according to the probability distribution function f (α) of the background noise (α) expressed by the Nakagami-m distribution,

To calculate 1/2 of the SER as BER,

, Where Γ () is the gamma function,

As expected value of α ² ,

BER calculation method characterized by the above-mentioned. The method of claim 1,
The BER is,

BER calculation method, characterized in that calculated on the basis of. 3. The method of claim 2,

BER calculation method characterized in that the approximation is calculated. In the BER calculation apparatus when a receiver receives a complex symbol consisting of a real part and an imaginary part of ± 1 ± j transmitted by a transmitter in a QPSK scheme on a power line channel,
Equation that is the SER of the received signal according to the probability distribution function f (α) of the background noise (α) expressed by the Nakagami-m distribution,

Calculating means for calculating 1/2 of the SER as BER,
Wherein said calculation means comprises:

, Where Γ () is the gamma function,

As expected value of α ² ,

BER calculation device, characterized in that. 5. The method of claim 4,
Wherein said calculation means comprises:

A BER calculation device, characterized in that for calculating a BER. 6. The method of claim 5,

BER calculation device characterized in that the approximation is calculated.

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