P31Q DIGITAL COMMUNICATIONS

LECTURE 10

BPSK III

Before we continue with BPSK, we need to consider two important factors: Information throughput and Noise. In particular, additive white gaussian noise (AWGN). Thereafter, we will complete the topic of BPSK.

INFORMATION THROUGHPUT

If error-control coding is incorporated into the DCS, then the binary digit which is transferred across the channel is a code digit, and NOT an information digit.

Digital Communication System (DCS)

A* : binary digits/sec

C: binary digits/sec

Referring to the above diagram, it is essential that the rate binary digits/sec at point A* = rate at which the binary digits enter the binary sink. i.e. no reduction in information throughput.
Recall . To ensure no reduction in information throughput, a code digit duration
Energy per code digit , which simplifies to
If the energy per code digit is reduced below , then more errors will occur within the DMC. Hence, the error-control code must overcome the errors in the channel, and provide a better than if simply BPSK was used without an error-control code.

BPSK WITH ERROR CONTROL CODING

If error-control coding is used, then the binary digits which are sent through the channel are code digits. In this case, the probability of an error in a binary digit at the output of the demodulator is given by

Performance of a BPSK DCS in an AWGN Channel

Recall that the above expression is also the BSC crossover probability. Notice that with the use of error-control coding, the penalty incurred is an effective increase in the noise within the channel. This is because the energy per symbol within the channel has been reduced as shown above. Another disadvantage is a greater requirement of the channel bandwidth. We will discuss this in more detail later.
Of course for uncoded BPSK, the code rate = 1

[Student Excercise] Show that eq5.gif (1413 bytes)

NOISE SIGNAL n(t): ADDITIVE WHITE GAUSSIAN NOISE (AWGN)

An important question remains ... what is

? Recall is was introduced as the standard deviation of the probability distribution of

. To understand its origin, lets take a more fundamental look at noise in this section.

There are many potential sources of noise in a communication system. External sources of noise such as atmospheric noise, man-made noise, etc., do NOT place a fundamental limit on the performance of a DCS. It is the noise from electrical circuits (spontaneous fluctuations of current or voltage) which force a fundamental limit on the performance.
The two most common types of electrical noise are shot noise and thermal noise, of which thermal noise cannot be eliminated. The electrons which are responsible for electrical conduction are also responsible for thermal noise !

The noise analysis of communication system is customarily based on an idealized form of noise called white noise. To appreciate white noise, consider the sketch below of a noise signal n(t). You may have seen such a signal on an oscilloscope when the probes are not connected to any voltage source.

Look for this type of signal the next time you are in a Electronics Lab.

The probability distribution of n (along the y-axis) is given by

Normal or Gaussian distribution

From Fourier analysis, all frequencies are necessary to create signal n(t). The power spectral density spectrum of such a noise signal is shown below.

is the single-sided noise power spectral density (Watts / Hertz). More information.

N = Noise Power over the bandwidth B.

The term "white" is used because the spectrum is similar to white light which contains equal amounts of all frequencies within the visible electromagnetic waves spectrum.
can be measured using a spectrum analyzer.

BPSK' CONTINUED

Recall the BPSK receiver (shown below) in which .

fig4.gif (3105 bytes)

Using a noise signal n(t) of the type discussed in the previous section, it can be shown that the standard deviation of the probability distribution of the coordinate on the signal space diagram (refer to the diagram below) is Remember this. We will not prove this. Refer to a text book for more information. .

Probability distribution of the x1 co-ordinate

Thus, we can express the performance of a BPSK based DCS in the standard and convenient form as shown below.
The ratio is very special. It is referred to as the signal-to-noise ratio. A quantity we can measure for a given communication channel. Note that its the ratio of the signal to noise which is important and not the actual values of Eb or No.
Unfortunately, this ratio is number which is difficult to comprehend unless its mapped onto a decibel scale using the following definition.

eq11.gif (2044 bytes)

When is expressed in decibels, its convenient to simply refer to this as SNR.
Refer to the performance curves shown below. For a given signal-to-noise ratio SNR, the actual value of

Performance Curves

For more information about a curve, click on the corresponding legend below.

For example, for 9.6 dB is a very common point of reference

Hence the BSC crossover probability, or the uncoded BPSK probability of an error in a binary digit .
Using the approximation , we find Q(4.27) = . This means that for every 1 million bits processed through the DCS, we can expect approx. 10 errors.

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BPSK III

Send mail to janak with questions or comments.copy , yearLast modified: Wednesday November 22, 2000

APLICACIÓN DE UN TÉCNICA DE MUESTREO ENFATIZADO COMPUESTO A LA SIMULACIÓN DE UN SISTEMA DE COMUNICACIONES W-CDMA

: Gracía Martínez, Adolfo : Ingeniería Telecomunicación

Send mail to janak with questions or comments.
copy , year
Last modified: Wednesday November 22, 2000

: Gracía Martínez, Adolfo
: Ingeniería Telecomunicación