04-03-2011, 10:10 AM
[attachment=9502]
Spectrum and bandwidth
• Electromagnetic signals are made up of many frequencies
• Shown in the next example
• Spectrum and bandwidth
• The 2nd frequency is an integer multiple of the first frequency
– When all of the frequency components of a signal are integer multiples of one frequency, the latter frequency is called fundamental frequency (f)
– period of the resultant signal is equal to the period of the fundamental frequency
• Period of s(t) is T=1/f
Fourier Analysis
• Any signal is made up of components at various frequencies, in which each component is a sinusoid.
– Adding enough sinusoidal signals with appropriate amplitude, frequency and phase, any electromagnetic signal can be constructed
• Spectrum and bandwidth
• It is the range of frequencies that a signal contains (among its components)
– In the example, spectrum is from f to 3f
– absolute bandwidth is the width of the spectrum
• 3f-f = 2f
• Data Rate and bandwidth
• There is a direct relationship between data rate (or signal carrying capacity) and bandwidth
• Suppose we let a positive pulse represent 1 and negative pulse represent 0
– Then the waveform (next slide) represents 1010..
– Duration of each pulse is tbit = (1/2) (1/f)
– Thus data rate is 1/ tbit = 2f bits/sec
• As we add more and more frequencies the wave looks more like a square wave
• Example
• Looking at FIG 2(a) the bandwidth = 5f-f = 4f
– If f=1MHz = 106 cycles/sec, then bandwidth = 4MHz
– The period of the fundamental frequency = T = 1/f = 1 μs
– So each bit takes up 0.5 μs i.e. data rate is 1/0.5 Mbps = 2 Mbps
• Example
• Looking at FIG 1© the bandwidth = 3f-f = 2f
– If f=2MHz = 2x106 cycles/sec, then bandwidth = 4MHz
– The period of the fundamental frequency = T = 1/f = 0.5 μs
– So each bit takes up 0.25 μs i.e. data rate is 1/0.25 Mbps = 4 Mbps
• Example
• Thus a given bandwidth can support different data rate, depending on the ability of the receiver to discern the difference between 0 and 1 in the presence of noise and interference
• Gain and Loss
• Ratio between power levels of two signals is referred to as Gain
– gain (dB) = 10 log10 (Pout/Pin)
– loss (dB) = -10 log10 (Pout/Pin) = 10 log10 (Pin/Pout)
– Pout is output power level and Pin is input power level
• Signal of power 10mw transmitted over wireless channel, and receiver receives the signal with 2mw power:
– gain (db) = 10 log10 (2/10) = -10 (0.698) = -6.98 dB
– loss (db) = 6.98 dB
• dBW power
• dB-Watt
– power in dB transmitted with respect to a base power of 1 Watt
• dBW = 10 log10 P
– P is power transmitted in Watt
– if power transmitted is 1 Watt
• dBW = 10 log10 1 = 0 dBW
– 1000 watt transmission is 30 dBW
• dBm power
• dB-milliwatt
– better metric in wireless network
– power in dB transmitted with respect to a base power of 1 milliwatt
• dBm = 10 log10 P
– P is power transmitted in milliwatt
– if power transmitted is 1 milliwatt
• dBm = 10 log10 1 = 0 dBm
– 10 milliwatt transmission is 10 dBm
– 802.11b can transmit at a maximum power of 100mw = 20 dBm
• Channel Capacity
Four concepts :
• Data Rate : rate (in bps) at which data can be communicated
• Bandwidth: bandwidth of the transmitted signal as constrained by the transmitter and the medium, expressed in Hz
• Noise : interfering electromagnetic signal that tend to reduce the integrity of data signal
• Error rate : rate at which receiver receives bits in error i.e. it receives a 0 when actually a 1 was sent and vice-versa
• Nyquist Bandwidth
• Given a bandwidth of B, the highest signal rate that can be carried is 2B (when signal transmitted is binary (two voltage levels))
– When M voltage levels are used, then each signal level can represent log2M bits. Hence the Nyquist bandwidth (capacity) is given by
C = 2 B log2M
• Shannon’s Capacity Formula
• When there is noise in the medium, capacity is given by
– C <= B log2 (1 + SNR)
• SNR = signal power/noise power
– SNRdB = 10 log10 SNR
• Bandwidth Allocation
• Necessary to avoid interference between different radio devices
– Microwave woven should not interfere with TV transmission
– Generally a radio transmitter is limited to a certain bandwidth
• 802.11channel has 30MHz bandwidth
– Power and placement of transmitter are regulated by authority
• Consumer devices are generally limited to less than 1W power
• ISM and UNII Band
• Industrial, Scientific and Medical (ISM) band
– 902-928 MHz in the USA
– 433 and 868 MHz in Europe
– 2400 MHz – 2483.5 MHz (license-free almost everywhere)
– Peak power 1W (30dBm)
• but most devices operate at 100mW or less
– 802.11 uses the ISM band of 2.4GHz
• Unlicensed National Information Infrastructure (UNII) bands
– 5.725 – 5.875 GHz
Antenna
• An electrical conductor or system of conductors used for radiating electromagnetic energy into space or for collecting electromagnetic energy from the space
– An integral part of a wireless system
• Radiation Patterns
• Antenna radiates power in all directions
– but typically does not radiate equally in all directions
• Ideal antenna is one that radiates equal power in all direction
– called an isotropic antenna
– all points with equal power are located on a sphere with the antenna as its center
• Omnidirectional Antenna
• Produces omnidirectional radiation pattern of equal strength in alldirections
• Vector A and B are of equal length
• Directional Antenna
• Radiates most power in oneaxis (direction)
– radiates less in other direction
– vector B is longer than
- vector A : more power radiated along B than A
– directional along X
• Dipole Antenna
• Half-wave dipole or Hertz antenna consists of two straight collinear conductor of equal length
• Length of the antenna is half the wavelength of the signal.
• Quarter-wave antenna
• Quarter-wave or marconi antenna has a veritcal conductor of length quarter of the avelength
of the signal
• Sectorized Antenna
• Several directional antenna
combined on a single pole
to provide sectorized antenna
• each sector serves receivers
listening it its direction
• Antenna Gain
• A measure of the directionality of an antenna
• Defined as the power output, in a particular direction, compared to that produced in any direction by a perfect isotropic antenna
– Example: if an antenna has a gain of 3dB, the antenna is better (in that direction) than isotropic antenna by a factor of 2
• Antenna Gain
• Antenna gain is dependent on effective area of an antenna.
– effective area is related to the physical size of the antenna and its shape
– Antenna Gain is given by
where
G = antenna gain
Ae = effective area
f = carrier frequency
c = speed of light
λ = carrier wavelength
• Signal Propagation
• Transmission range:
receiver receives signal with an error rate low enough to be able to communicate
• Detection range: transmitted power is high enough to detect the transmitter, but high error rate forbids communication
• Interference range: sender interferes with other transmissions by adding to the noise
• Signal Propagation
• Radio waves exhibit three fundamental propagation behavior
– Ground wave (< 2 MHz) : waves with low frequency follow earth’s surface
• can propagate long distances
• Used for submarine communication or AM radio
– Sky wave (2-30 MHz) : waves reflect at the ionosphere and bounce back and forth between ionosphere and earth , travelling around the world
• Used by international broadcast and amateur radio
• Signal Propagation
– Line of Sight (> 30 MHz) : emitted waves follow a straight line of sight
• allows straight communication with satellites or microwave links on the ground
• used by mobile phone system, satellite systems
• Free Space loss
• Transmitted signal attenuates over distance because it is spread over larger and larger area
– This is known as free space loss and for isotropic antennas
Pt = power at the transmitting antenna
Pr = power at the receiving antenna
λ = carrier wavelength
d = propagation distance between the antennas
c = speed of light
• Free Space loss
• For other antennas
Gt = Gain of transmitting antenna
Gr = Gain of receiving antenna
At = effective area of transmitting antenna
Ar = effective area of receiving antenna
Thermal Noise
• Thermal noise is introduced due to thermal agitation of electrons
• Present in all transmission media and all electronic devices
• a function of temperature
• uniformly distributed across the frequency spectrum and hence is often referred to as white noise
• amount of noise found in a bandwidth of 1 Hz is
N0 = k T
N0 = noise power density in watts per 1 Hz of bandwidth
k = Boltzman’s constant = 1.3803 x 10-23 J/K
T = temperature, in Kelvins
N = thermal noise in watts present in a bandwidth of B
= kTB where
Data rate and error rate
• A parameter related to SNR that is more convenient for determining digital data rates and error rates
– ratio of signal energy per bit to noise power density per Hertz, Eb/N0
– R = bit rate of transmission, S= power of the signal,
Tb = time required to send 1 bit. Then R = 1/Tb
Eb = S Tb
so
Data rate and error rate
• Bit error rate is a decreasing function of Eb/N0
– If bit rate R is to increase, then to keep bit error rate (or Eb/N0) same, the transmitted signal power must increase, relative to noise
• Eb/N0 is related to SNR as follows
B = signal bandwidth
(since N = N0 B)
Doppler’s Shift
• When a client is mobile, the frequency of received signal could be less or more than that of the transmitted signal due to Doppler’s effect
• If the mobile is moving towards the direction of arrival of the wave, the Doppler’s shift is positive
• If the mobile is moving away from the direction of arrival of the wave, the Doppler’s shift is negative
Doppler’s Shift
where
fd =change in frequency
due to Doppler’s shift
v = constant velocity of the
mobile receiver
λ = wavelength of the transmission
Doppler’s shift
f = fc + fd
where
f = the received carrier frequency
fc = carrier frequency being transmitted
fd = Doppler’s shift as per the formula in the prev slide
Multipath Propagation
• Wireless signal can arrive at the receiver through different pahs
– LOS
– Reflections from objects
– Diffraction
• Occurs at the edge of an impenetrable body that is large compared to the wavelength of the signal
Effect of Multipath Propagation
• Multiple copies of the signal may arrive with different phases. If the phases add destructively, the signal level reduces relative to noise.
• Inter Symbol Interference (ISI)
Multiplexing
• A fundamental mechanism in communication system and networks
• Enables multiple users to share a medium
• For wireless communication, multiplexing can be carried out in four dimensions: space, time, frequency and code
Space division multiplexing
• Channels are assigned on the basis of “space” (but operate on same frequency)
• The assignment makes sure that the transmission do not interfere with each (with a guard band in between)
Space division multiplexing
Frequency Division Multiplexing
• Frequency domain is subdivided into several non-overlapping frequency bands
• Each channel is assigned its own frequency band (with guard spaces in between)
Spectrum and bandwidth
• Electromagnetic signals are made up of many frequencies
• Shown in the next example
• Spectrum and bandwidth
• The 2nd frequency is an integer multiple of the first frequency
– When all of the frequency components of a signal are integer multiples of one frequency, the latter frequency is called fundamental frequency (f)
– period of the resultant signal is equal to the period of the fundamental frequency
• Period of s(t) is T=1/f
Fourier Analysis
• Any signal is made up of components at various frequencies, in which each component is a sinusoid.
– Adding enough sinusoidal signals with appropriate amplitude, frequency and phase, any electromagnetic signal can be constructed
• Spectrum and bandwidth
• It is the range of frequencies that a signal contains (among its components)
– In the example, spectrum is from f to 3f
– absolute bandwidth is the width of the spectrum
• 3f-f = 2f
• Data Rate and bandwidth
• There is a direct relationship between data rate (or signal carrying capacity) and bandwidth
• Suppose we let a positive pulse represent 1 and negative pulse represent 0
– Then the waveform (next slide) represents 1010..
– Duration of each pulse is tbit = (1/2) (1/f)
– Thus data rate is 1/ tbit = 2f bits/sec
• As we add more and more frequencies the wave looks more like a square wave
• Example
• Looking at FIG 2(a) the bandwidth = 5f-f = 4f
– If f=1MHz = 106 cycles/sec, then bandwidth = 4MHz
– The period of the fundamental frequency = T = 1/f = 1 μs
– So each bit takes up 0.5 μs i.e. data rate is 1/0.5 Mbps = 2 Mbps
• Example
• Looking at FIG 1© the bandwidth = 3f-f = 2f
– If f=2MHz = 2x106 cycles/sec, then bandwidth = 4MHz
– The period of the fundamental frequency = T = 1/f = 0.5 μs
– So each bit takes up 0.25 μs i.e. data rate is 1/0.25 Mbps = 4 Mbps
• Example
• Thus a given bandwidth can support different data rate, depending on the ability of the receiver to discern the difference between 0 and 1 in the presence of noise and interference
• Gain and Loss
• Ratio between power levels of two signals is referred to as Gain
– gain (dB) = 10 log10 (Pout/Pin)
– loss (dB) = -10 log10 (Pout/Pin) = 10 log10 (Pin/Pout)
– Pout is output power level and Pin is input power level
• Signal of power 10mw transmitted over wireless channel, and receiver receives the signal with 2mw power:
– gain (db) = 10 log10 (2/10) = -10 (0.698) = -6.98 dB
– loss (db) = 6.98 dB
• dBW power
• dB-Watt
– power in dB transmitted with respect to a base power of 1 Watt
• dBW = 10 log10 P
– P is power transmitted in Watt
– if power transmitted is 1 Watt
• dBW = 10 log10 1 = 0 dBW
– 1000 watt transmission is 30 dBW
• dBm power
• dB-milliwatt
– better metric in wireless network
– power in dB transmitted with respect to a base power of 1 milliwatt
• dBm = 10 log10 P
– P is power transmitted in milliwatt
– if power transmitted is 1 milliwatt
• dBm = 10 log10 1 = 0 dBm
– 10 milliwatt transmission is 10 dBm
– 802.11b can transmit at a maximum power of 100mw = 20 dBm
• Channel Capacity
Four concepts :
• Data Rate : rate (in bps) at which data can be communicated
• Bandwidth: bandwidth of the transmitted signal as constrained by the transmitter and the medium, expressed in Hz
• Noise : interfering electromagnetic signal that tend to reduce the integrity of data signal
• Error rate : rate at which receiver receives bits in error i.e. it receives a 0 when actually a 1 was sent and vice-versa
• Nyquist Bandwidth
• Given a bandwidth of B, the highest signal rate that can be carried is 2B (when signal transmitted is binary (two voltage levels))
– When M voltage levels are used, then each signal level can represent log2M bits. Hence the Nyquist bandwidth (capacity) is given by
C = 2 B log2M
• Shannon’s Capacity Formula
• When there is noise in the medium, capacity is given by
– C <= B log2 (1 + SNR)
• SNR = signal power/noise power
– SNRdB = 10 log10 SNR
• Bandwidth Allocation
• Necessary to avoid interference between different radio devices
– Microwave woven should not interfere with TV transmission
– Generally a radio transmitter is limited to a certain bandwidth
• 802.11channel has 30MHz bandwidth
– Power and placement of transmitter are regulated by authority
• Consumer devices are generally limited to less than 1W power
• ISM and UNII Band
• Industrial, Scientific and Medical (ISM) band
– 902-928 MHz in the USA
– 433 and 868 MHz in Europe
– 2400 MHz – 2483.5 MHz (license-free almost everywhere)
– Peak power 1W (30dBm)
• but most devices operate at 100mW or less
– 802.11 uses the ISM band of 2.4GHz
• Unlicensed National Information Infrastructure (UNII) bands
– 5.725 – 5.875 GHz
Antenna
• An electrical conductor or system of conductors used for radiating electromagnetic energy into space or for collecting electromagnetic energy from the space
– An integral part of a wireless system
• Radiation Patterns
• Antenna radiates power in all directions
– but typically does not radiate equally in all directions
• Ideal antenna is one that radiates equal power in all direction
– called an isotropic antenna
– all points with equal power are located on a sphere with the antenna as its center
• Omnidirectional Antenna
• Produces omnidirectional radiation pattern of equal strength in alldirections
• Vector A and B are of equal length
• Directional Antenna
• Radiates most power in oneaxis (direction)
– radiates less in other direction
– vector B is longer than
- vector A : more power radiated along B than A
– directional along X
• Dipole Antenna
• Half-wave dipole or Hertz antenna consists of two straight collinear conductor of equal length
• Length of the antenna is half the wavelength of the signal.
• Quarter-wave antenna
• Quarter-wave or marconi antenna has a veritcal conductor of length quarter of the avelength
of the signal
• Sectorized Antenna
• Several directional antenna
combined on a single pole
to provide sectorized antenna
• each sector serves receivers
listening it its direction
• Antenna Gain
• A measure of the directionality of an antenna
• Defined as the power output, in a particular direction, compared to that produced in any direction by a perfect isotropic antenna
– Example: if an antenna has a gain of 3dB, the antenna is better (in that direction) than isotropic antenna by a factor of 2
• Antenna Gain
• Antenna gain is dependent on effective area of an antenna.
– effective area is related to the physical size of the antenna and its shape
– Antenna Gain is given by
where
G = antenna gain
Ae = effective area
f = carrier frequency
c = speed of light
λ = carrier wavelength
• Signal Propagation
• Transmission range:
receiver receives signal with an error rate low enough to be able to communicate
• Detection range: transmitted power is high enough to detect the transmitter, but high error rate forbids communication
• Interference range: sender interferes with other transmissions by adding to the noise
• Signal Propagation
• Radio waves exhibit three fundamental propagation behavior
– Ground wave (< 2 MHz) : waves with low frequency follow earth’s surface
• can propagate long distances
• Used for submarine communication or AM radio
– Sky wave (2-30 MHz) : waves reflect at the ionosphere and bounce back and forth between ionosphere and earth , travelling around the world
• Used by international broadcast and amateur radio
• Signal Propagation
– Line of Sight (> 30 MHz) : emitted waves follow a straight line of sight
• allows straight communication with satellites or microwave links on the ground
• used by mobile phone system, satellite systems
• Free Space loss
• Transmitted signal attenuates over distance because it is spread over larger and larger area
– This is known as free space loss and for isotropic antennas
Pt = power at the transmitting antenna
Pr = power at the receiving antenna
λ = carrier wavelength
d = propagation distance between the antennas
c = speed of light
• Free Space loss
• For other antennas
Gt = Gain of transmitting antenna
Gr = Gain of receiving antenna
At = effective area of transmitting antenna
Ar = effective area of receiving antenna
Thermal Noise
• Thermal noise is introduced due to thermal agitation of electrons
• Present in all transmission media and all electronic devices
• a function of temperature
• uniformly distributed across the frequency spectrum and hence is often referred to as white noise
• amount of noise found in a bandwidth of 1 Hz is
N0 = k T
N0 = noise power density in watts per 1 Hz of bandwidth
k = Boltzman’s constant = 1.3803 x 10-23 J/K
T = temperature, in Kelvins
N = thermal noise in watts present in a bandwidth of B
= kTB where
Data rate and error rate
• A parameter related to SNR that is more convenient for determining digital data rates and error rates
– ratio of signal energy per bit to noise power density per Hertz, Eb/N0
– R = bit rate of transmission, S= power of the signal,
Tb = time required to send 1 bit. Then R = 1/Tb
Eb = S Tb
so
Data rate and error rate
• Bit error rate is a decreasing function of Eb/N0
– If bit rate R is to increase, then to keep bit error rate (or Eb/N0) same, the transmitted signal power must increase, relative to noise
• Eb/N0 is related to SNR as follows
B = signal bandwidth
(since N = N0 B)
Doppler’s Shift
• When a client is mobile, the frequency of received signal could be less or more than that of the transmitted signal due to Doppler’s effect
• If the mobile is moving towards the direction of arrival of the wave, the Doppler’s shift is positive
• If the mobile is moving away from the direction of arrival of the wave, the Doppler’s shift is negative
Doppler’s Shift
where
fd =change in frequency
due to Doppler’s shift
v = constant velocity of the
mobile receiver
λ = wavelength of the transmission
Doppler’s shift
f = fc + fd
where
f = the received carrier frequency
fc = carrier frequency being transmitted
fd = Doppler’s shift as per the formula in the prev slide
Multipath Propagation
• Wireless signal can arrive at the receiver through different pahs
– LOS
– Reflections from objects
– Diffraction
• Occurs at the edge of an impenetrable body that is large compared to the wavelength of the signal
Effect of Multipath Propagation
• Multiple copies of the signal may arrive with different phases. If the phases add destructively, the signal level reduces relative to noise.
• Inter Symbol Interference (ISI)
Multiplexing
• A fundamental mechanism in communication system and networks
• Enables multiple users to share a medium
• For wireless communication, multiplexing can be carried out in four dimensions: space, time, frequency and code
Space division multiplexing
• Channels are assigned on the basis of “space” (but operate on same frequency)
• The assignment makes sure that the transmission do not interfere with each (with a guard band in between)
Space division multiplexing
Frequency Division Multiplexing
• Frequency domain is subdivided into several non-overlapping frequency bands
• Each channel is assigned its own frequency band (with guard spaces in between)