CENG 210 Chapter 2

Noisy Channel: Shannon Capacity Maximum transmission rate over a channel with bandwidth B, with Gaussian distributed noise, and with signal-to-noise ratio SNR=S/N, is

Cnoisy = Blog2(1+SNR) [bps]

'intersymbol interference'

Critical for composite-analog & digital signals - some of the signal components of one bit position will spill over into other bit

Major limiting factor in communications system performance

Noise (cannot be predicted - appears at random!)

Causes of impairment are

- Attenuation - Distortion - Noise

Why use composite signals?

A single-frequency sine wave is not useful in data communications; we need to send a composite signal, a signal made of many simple sine waves

Frequency

- in Hertz refers to the number of periods in one second (1/T) - it is the rate of change with respect to time

Signals

- quantity that can represent and convey information - passed between devices to send and receive information

Wavelength

- the distance a simple signal can travel in one period wavelength = lambda & propagation speed = c & frequency = f - lamda = c/f - the propagation speed of electromagnetic signals depend on the medium and on the frequency of the signal

Bit rate

- used to describe digital signals - the number of bits sent in one second, expressed in bits per second (bps)

The performance can be measured using the following:

-Bandwidth -Throughput -Latency (Delay) •Processing delay •Queuing delay •Transmission delay •Propagation delay

In networking, we use the term bandwidth in two contexts

1. The first, bandwidth in hertz, refers to the range of frequencies in a composite signal or the range of frequencies that a channel can pass 2. The second, bandwidth in bits per second, refers to the speed of bit transmission in a channel or link

Challenges in combating attenuation

1. received signal must have sufficient strength so that receiver can detect the signal 2. signal must maintain a level sufficiently higher than noise at all times, to be received without error

Data rate depends on three factors:

1.The bandwidth available 2.The level of the signals we use 3.The quality of the channel (the level of noise)

For a noiseless channel, the Nyquist bit rate formula defines the theoretical maximum bit rate

BitRate= 2 × bandwidth× log2 L -bandwidth is the bandwidth of the channel, -L is the number of signal levels used to represent data, and -BitRate is the bit rate in bits per second.

A digital signal has eight levels. How many bits are needed per level?

Number of bits per levels = log2 8 = 3 Each signal level is represented by 3 bits. 000-0 100-4 001-1 101-5 010-2 110-6 011-3 111-7

An application of a simple sine way in our daily life:

Power company sends a single sine wave with a frequency of 50/60 Hz to distribute electric energy to our houses

•Because SNR is the ratio of two powers, it is often described in decibel units, SNRdB, defined as

SNRdB = 10log10(SNR)

Signal-to-Noise Ratio (SNR)

The ratio of the signal power to the noise power. The signal-to-noise ratio is defined as SNR = average of received SIGNAL power/average of received NOISE power

decibel is negative if ______________

a signal is attenuated

Transmission Time

a time between the first bit leaving the sender and the last bit arriving at the receiver - The time required for transmission of a message depends on the size of the message and the bandwidth of the channel - Transmission Time = message size/bandwidth

Propagation Time

measures the time required for a signal (or a bit) to travel from one point of transmission medium to another p = d/c d = length of physical link [m] c = signal propagation speed in medium ∼ speed of light in vacuum is 2*10^8 [m/s]

Analog signals can have ______________________; digital signals can have __________________

an infinite number of values in a range only a limited number of values

Data can be _____________

analog or digital

Fourier analysis

any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases

We will discuss only the components related to _________________________________

characteristics of the channel, i.e. propagation time and transmission time

dB can be measured

dB = 10log10(P2/P1) P1 and P2 are the powers of a signal at points 1 and 2

Information can be represented by _____________________ or _______________________

digital signal analog signal

Signals often fall ____________, so loss is easily expressed in terms of decibel - linear function in ________

exponentially log-plot

latency is made of _______ components:

four propagation time, transmission time, queuing time and processing time Latency = Proptime + Txtime + Qtime + Proctime

Digital data refers to information that ________________

has discrete states

- Change in a short span of time means ______ frequency - Change over a long span of time means ______ frequency - If a signal does not change at all, its frequency is ________ - If a signal changes instantaneously, its frequency is _________

high low zero infinite

A very important consideration in data communications is _______________, over a channel

how fast we can send data, in bits per second

Latency (Delay)

how long it takes for an entire message to completely arrive at the destination from the time the first bit is sent out from the source

The term analog data refers to____________________

information that is continuous

A high SNR means the signal is ______ corrupted by noise A low SNR means the signal is _____ corrupted by noise

less more

Attenuation

loss of energy - Energy lost in overcoming the resistance of the medium - To compensate for this loss, amplifiers are used to amplify the signal

Throughput

measurement of how fast data can pass through an entity in the network (computer, router, channel, etc.) - If we consider this entity as a wall through which bits pass, throughput is the number of bits that can pass this wall in one second //throughput is the number of bits passing a wall in a second

No indication of levels (Shannon)

no matter how many levels we use, we cannot achieve a data rate higher than the capacity of the channel

Most digital signals are ____________, and thus period and frequency are _________________ characteristics

nonperiodic not appropriate

Signals travel through transmission media, which are ___________. The _____________ causes ___________

not perfect imperfection signal impairments

A complete sine wave in the time domain can be represented by _______________ in the frequency domain.

one single spike

One important issue in networking is the _______________________________

performance of the network—how good is it?

a 1 can be encoded as a ____________ and a 0 as ____________. A digital signal can have ___________________. In this case, _________________________

positive voltage zero voltage more than two levels (not just level bit 0 and level bit 1) we can send more than 1 bit for each level

Each signal component has its own ________________ through a medium, and therefore, its _________________________

propagation speed own delay in arriving at the final destination

Decibel (dB) measures

relative strength of two signals or one signal at two different points

the most fundamental form of a periodic analog signal

sine wave

The peak amplitude of a signal is ____________________________________________________

the absolute value of its highest intensity, proportional to the energy it carries.

Period

the amount of time, in seconds, a signal needs to complete one cycle (1/f)

Bandwidth of a composite signal

the difference between the highest and the lowest frequencies contained in that signal

Message

the information (data) to be communicated. Forms of information include text, numbers, pictures, audio, and video.

Phase

the position of the waveform relative to time 0 it's measured in degrees or radians 360˚ is 2pi && 1˚ is 2pi/360 && 1 rad is 360/2pi

Presence of noise limits __________________________

the reliability with which the receiver can correctly determine the information that was transmitted

Distortion means _________________

the signal changes its form or shape

Theoretical limit in relation to Shannon

there are numerous impairments in every real channel besides those taken into account in Shannon's Law (e.g. attenuation, delay distortion, or impulse noise)

A sine wave can be represented by ______ parameters: ___________________________

three the peak amplitude, the frequency, and the phase

A sine wave can be presented via ____________________ or ____________________

time domain plot frequency domain plot

To be transmitted, data must be ـــــــــــــــــــــــــــ

transformed to electromagnetic signals

Noise

unwanted signals that get inserted / generated somewhere between transmitter and receiver

The Shannon capacity gives us the ____________. The Nyquist formula tells us how ______________

upper limit many levels we need

In practice, _______________________________ to find what ____________________ are appropriate for each particular channel

we need to use both methods (Nyquist & Shannon) data rate and signal levels