Eye diagram of digital baseband received signals

PROCEDURE

We designed the given model using the simulink library and tested for different SNR

values and different M values in the M-ary PAM modulator. Later we changed the PAM

modulator QAM block and tested. The observations are as follow.

Introduction

The eye diagram is a useful tool for the qualitative analysis of signal used in digital transmission.

It provides at-a-glance evaluation of system performance and can offer insight into the nature

of channel imperfections. Careful analysis of this visual display can give the user a first-order

approximation of signal-to-noise, clock timing jitter and skew.

Significance to the communication systems

The eye diagram is an oscilloscope display of a digital signal, repetitively sampled to get a good

representation of its behavior. In a radio system, the point of measurement may be prior to the

modulator in a transmitter, or following the demodulator in a receiver, depending on which

portion of the system requires examination. The eye diagram can also be used to examine

signal integrity in a purely digital system—such as fiber optic transmission, network cables or on

a circuit board.

The amount of energy in the harmonics, relative to the fundamental, is related to rise and fall

time and pulse duration. Fast rise and fall times (“square” transitions) and narrow pulse

durations create the most harmonic energy. This is unlike a purely digital system, where these

“clean” transitions are highly desirable

In order to reduce interference, radio transmission channels are not permitted to have

unlimited bandwidth. Otherwise, the harmonic energy in the data signal would create

corresponding modulation sidebands that extend well beyond the intended bandwidth of the

allocated communications channel.

To reduce these unwanted sidebands, the data signal must be band-limited (filtered) in a

manner that reduces the harmonic energy while maintaining the integrity of the transmitted

data. The eye diagram can be used to look at the signal before transmission, to assure that the

filter is behaving properly. A more obvious use of the eye diagram is to evaluate the received

signal quality. Impairments to the signal can occur in many places, from the pre-filtering in the

transmitter, through the frequency conversion and amplifier chain, propagation path, receiver

front-end, IF circuits and baseband signal processing. Information from the eye diagram can

help greatly with troubleshooting. Noise problems will most often be external to the equipment

and timing issues can be isolated to the receiver or transmitter with tests on each. It is also

important to record the eye diagram so it is available for comparison if new problems arise in

the future.

Figure1: Basic information contained in the eye diagram.

M=2

SNR 5 SNR 10

SNR 15 SNR 20

SNR 25 SNR 30

M=4

SNR = 5 SNR =10

SNR = 15 SNR = 20

20

25

SNR =25 SNR= 30

M = 8

snr=5

M=8

SNR=5 SNR=10

SNR=15 SNR=20

SNR=25 SNR=30

snr=25

QAM M=8

SNR=5 SNR=10

snr=15

SNR=15 SNR=20

snr=20

snr = 25

SNR=25 SNR=30

Results Interpretation

Based on the observations I can summarize following conclusions.

When we increase the SNR of the signal the eye becomes more and more opened or in other

words when we are transmitting at a high power the effects of noise becomes less and less

significant and hence the detector can guess rebuild the signal more correctly. If the signal can

be guessed more correctly that means the sample signal points the eye diagram overlap each

other and results in a more opened eye. The above fact can be verified for every M value in the

M-ary modulator and the results obtained also match with the theory.

When we increase the M value in the M-ary modulator the eye becomes more closed. That is

because when the M value increases there will be more signal positions and each contributes to

the eye diagram. Hence the eye will be more blocked.

Factors that can cause reduction of the eye diagram

Jitter

Jitter is a major phenomenon which causes the eye diagram to be distorted. Jitter can be

defined as “the deviation of the significant instances of a signal from their ideal location in

time.” To put it more simply, jitter is how early or late a signal transition is with reference to

when it should transition. In a digital signal the significant instances are the transition

(crossover) points. So sources of jitter can be identified as factors affecting the ideality of an eye

diagram.

Figure2: Idealized digital signal eye diagram (with finite rise and fall times).

Figure3: Timing error: (a) Misalignment of rise and fall times (jitter). (b) With a higher data rate, this diagram has much less open eye area than (a) despite a smaller absolute time error.

The sources of Jitter

1. System phenomena

These are effects on a signal that result from the characteristics of its being a digital system in an analog environment. Examples of these system- related sources include:

• Crosstalk from radiated or conducted signals• Dispersion effects• Impedance mismatch

2. Data-dependent phenomena

These are patterns or other characteristics of the data being transferred that affect the net jitter arriving in the receiver. Data-dependent jitter sources include:

• Intersymbol interference• Duty-cycle distortion• Pseudorandom, bit-sequence periodicity

3. Random noise phenomena

These are phenomena that randomly introduce noise in a system.These sources include:

• Thermal noise—kTB noise, which is associated with electron flow in conductors and increases with bandwidth, temperature, and noise resistance• Shot noise—electron and hole noise in semiconductors in which the magnitude is governed by bias current and measurement bandwidth• “Pink” noise—noise that is spectrally related to 1/f

Filtering

As mentioned in the significance section the filters are added to limit the bandwidth in order to reduce unwanted sidebands. This filtering process also causes the eye to be reduced.

Figure 4: At the top is the eye diagram of a raised cosine filtered signal (α = 0.6) as it might be applied to a modulator. The two lower waveforms represent the square-wave bit stream before and after filtering (these are not aligned with the eye diagram display).

The filter’s α parameter determines the opening of the eye.

Figure 5: Effects of filter coefficient over eye diagram

From the above figures, it can be observed that the horizontal eye opening with =0.5 is

smaller than with =1.

Reason: The tails of the raised cosine filter with =1 dies away faster than the case where

=0.5. Hence error in timing cause a bigger performance degradation for =0.5 than for =1

scenario. However, the flip side of using =1 is the increased bandwidth required for

transmission.

Inter symbol interference (ISI)

Inter symbol interference (ISI) is a form of distortion of a signal in which one symbol interferes

with subsequent symbols. The effects of ISI are shown in the second image which is an eye

pattern of the same system when operating over a multipath channel. The effects of receiving

delayed and distorted versions of the signal can be seen in the loss of definition of the signal

transitions. It also reduces both the noise margin and the window in which the signal can be

sampled, which shows that the performance of the system will be worse

Figure 6: Effects of ISI over eye diagram

ISI is usually caused by multipath propagation or the inherent non-linear frequency response of

a channel. So they can be treated as another factors that affecting the reduction in the eye.