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