WC-UNIT NOTES.pdf

DEPARTMENT OF ECE
III YEAR/ VI SEMESTER
EC8652- WIRELESS COMMUNICATION
KNCET
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UNIT - I
WIRELESS CHANNELS
Large scale path loss – Path loss models: Free Space and Two-
Ray models - Link Budget design – Small scale fading-
Parameters of mobile multipath channels – Time dispersion
parameters-Coherence bandwidth – Doppler spread & Coherence
time, Fading due to Multipath time delay spread – flat fading –
frequency selective fading – Fading due to Doppler spread – fast
fading – slow fading.
KNCET 2
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MULTI-PATH PROPAGATION
KNCET 3
More version of the transmitted signal takes more
than one transmission path to reach the receiver
from the transmitter at a slightly different times.
MULTIPATH PROPAGATION
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EFFECTS OF FADING
– Rapid changes in signal strength over a
small travel distance or time interval
– Random frequency modulation due to
varying Doppler shifts on different multi-
path signals
– Time dispersion (echoes) caused by multi-
path propagation delays
KNCET 4
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Factors Influencing small scale Fading
1. Multipath Propagation
– Presence of reflecting objects and scatters in the channel
creates a constantly changing environment that dissipates
the signal energy in terms of amplitude, phase and time
– time delay of signal arrival
– Multiple version of transmitted signal arrive at the
receiving antenna
– Increases the time required for the actual information
portion of the signal to reach the receiver due to Inter
Symbol Interference
KNCET 5
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2. Speed of Mobile
– relative motion between base station & mobile
causes random frequency modulation due to
different Doppler shift (fd)
– Different multipath components may have
different frequency shifts.
– The shift in received signal frequency due to
motion-Doppler shift-movement of mobile
terminal towards or away from base station
transmitter
KNCET 6
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3. Speed of Surrounding Objects
– Objects in radio channel are in motion, induce time varying
Doppler shifts on multipath components.
– Doppler shift effect dominates small-scale fading if speed
of objects > mobile speed
4. Transmission bandwidth of the signal
– If the transmitted radio signal bandwidth is greater than the
bandwidth of the multipath channel, received signal will be
distorted.
– Small scale signal will not be significant
KNCET 7
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Parameters of mobile multipath channels
Time Dispersion Parameters
– “excess delay” : all values computed relative to
the time of first signal arrival τo
– __
Mean excess delay (τ)→Average delay measured
with respect to the first (arrival) moment of the
power delay profile
KNCET 8
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RMS delay spread
– Square root of the second central moment of the power
delay profile
– RMS delay spread and mean excess delay are
defined from a single power delay profile which
is temporal or spatial average of the consecutive
impulse response measurements and averaged
over a local area
KNCET 9
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Maximum excess delay ( X dB ):
• Measured with respect to certain power level
• Defined as the time delay during which multipath
energy falls to XdB below the maximum level
• Maximum excess delay = τX - τ0
• τ0 first arriving signal
• τX Maximum delay at which multipath components is
within XdB of the strongest arriving multipath signal
KNCET 10
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TYPES OF SMALL SCALE FADING
KNCET 11
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Fading due to Multipath Delay
A）Flat Fading → Bs << Bc or Ts >>
- Symbol period > Delay spread
- signal fits easily within the bandwidth of the
channel
- channel BW >> signal BW
• most commonly occurring type of fading
KNCET 12


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A）Flat Fading → Bs << Bc or Ts >>
•spectral properties of Tx signal are preserved
– signal is called a narrowband channel, since the
bandwidth of the signal is narrow with respect to the
channel bandwidth
– signal is not distorted
– Flat fading channels are known as amplitude varying
channels
KNCET 13


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Flat Fading
KNCET 14
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KNCET 15
B) Frequency Selective Fading → Bs > Bc or Ts <
– Symbol period < Delay spread
– Bs > Bc → certain frequency components of the
signal are attenuated much more than others


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Frequency Selective Fading
KNCET 16
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Fading due to Doppler Spread
KNCET 17
A) Fast Fading → Bs < BD or Ts > Tc
Channel impulse response changes rapidly within the symbol
duration
– Bs < BD
• Doppler shifts significantly alter spectral BW of TX
signal
• signal “spreading”
– Ts > Tc
• Coherence time of the channel is smaller than the
symbol period of the transmitted signal
• Signal distortion increases relative to the bandwidth of
the transmitted signal
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Fading due to Doppler Spread
KNCET 18
B) Slow Fading → Ts << Tc or Bs >> BD
– Channel impulse response changes at a rate much slower
than the transmitted baseband signal.
– slow amplitude fluctuations
• Bs almost always >> BD for most applications
• Velocity of the mobile and the baseband signaling determines
whether a signal undergoes fast fading or slow fading.
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UNIT - 2
CELLULAR ARCHITECTURE
Multiple Access techniques - FDMA, TDMA, CDMA –
Capacity calculations–Cellular concept- Frequency
reuse - channel assignment- hand off- interference &
system capacity- trunking & grade of service –
Coverage and capacity improvement
KNCET 1
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Cellular Concept
KNCET 2
• If a given set of frequencies or radio channels
can be reused without increasing the
interference, then the large geographical area
covered by a single high power transmitter can
be divided into a number of small areas, each
allocated a subset of frequencies
• Small geographical coverage, lower power
transmitters with lower antennas can be used
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Frequency Reuse
• Each cellular base station is allocated a group of radio
channels within a small geographic area called a cell.
• Neighboring cells are assigned different channel groups.
• By limiting the coverage area to within the boundary of
the cell, the channel groups may be reused to cover
different cells.
• Frequency reuse or frequency planning
• Hexagonal geometry has
– exactly six equidistance neighbors
– each of its neighbors are
separated by multiples of 60 degrees.
KNCET 3
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Frequency Reuse
• Consider a cellular system which has a total of S duplex channels.
• Each cell is allocated a group of k channels, .
• The S channels are divided among N cells.
• The total number of available radio channels
• The N cells which use the complete set of channels is called cluster.
• The cluster can be repeated M times within the system. The total number of
channels, C, is used as a measure of capacity
• The capacity is directly proportional to the number of replication M.
• The cluster size, N, is typically equal to 4, 7, or 12.
• Small N is desirable to maximize capacity.
• The frequency reuse factor is given by
KNCET 4
S
k 
kN
S 
MS
MkN
C 

N
/
1
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Rules for determining the nearest
co-channel neighbours
• Step 1: Move i cells along any chain of hexagons.
• Step 2: Turn 60 degrees counter clockwise and more j
cells
• Only certain cluster sizes and cell layout are possible.
• The number of cells per
cluster, N, can only have values which satisfy
• Co-channel neighbors of a
particular cell,
ex, i=3 and j=2.
KNCET 5
2
2
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ij
i
N 


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Channel Assignment Strategies
Two Channel assignment approach
– fixed channel assignment
– dynamic channel assignment
• Fixed channel assignment(FCA)
– each cell is allocated a predetermined set of voice channel
– any new call attempt can only be served by the unused
channels in that particular cell
– the call will be blocked if all channels in that cell are
occupied
– A cell is allowed to borrow channels from neighbouring
cell if all of its own channels are already occupied
KNCET 6
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Channel Assignment Strategies
• Dynamic channel assignment(DCA)
– allocate channels based on request.
– channels are not allocated to cells permanently
– reduce the likelihood of blocking, increase
capacity.
– Simple to implement
– If traffic in the network is uniform , number of
active users in each cell are same, results in
optimum channel allocation strategy
KNCET 7
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Handoff Strategies
When a mobile moves into a different cell while a conversation
is in progress, the MSC automatically transfers the call to a new
channel belonging to the new base station.
• Handoff operation
– identifying a new base station
– re-allocating the voice and control channels with the new
base station.
• Handoff margin
– If is too large, unnecessary handoffs burden the MSC
– If is too small, there may be insufficient time to complete
handoff before a call is lost.
KNCET 8
usable
minimum
,
, r
handoff
r P
P 


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Handoff Strategies
KNCET 9
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Handoff Methods
• Mobile controlled Handoff(MCHO)
Desirable method because it reduces the burden on the
network
• Network controlled Handoff(NCHO)
BS or Access point(AP) monitor the signal quality from
the mobile and report the measurements to the MSC. MSC is
responsible for choosing AP and initiating the handoff
• Mobile Assisted Handoff(MAHO)
Mobile measures the signal levels from various APs. The
mobile collects a set of power levels from different AP and
feeds it back to MSC for decision making
KNCET 10
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Co-channel Interference and System Capacity
• Interference between the signals from co-channel cells
• To reduce co-channel interference, co-channel cell must be
separated by a minimum distance.
• When the size of each cell is same
• Base station transmit same power
– co-channel interference is independent of the transmitted
power
– co-channel interference is a function of
• R: Radius of the cell
• D: distance to the center of the nearest co-channel cell
KNCET 11
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• Let be the number of co-channel interfering cells. The
signal-to-interference ratio (S/I) for a mobile receiver can be
expressed as
S: the desired signal power
: interference power caused by the ith interfering co-channel
cell base station
• The average received power at a distance d from the
transmitting antenna is
n is the path loss exponent.
P0 Power received at the reference point in far field region at a distance d0
KNCET 12


 0
1
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i
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I
S
I
S
0
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d
P
P


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






0
0
i
I
TX
0
d
0
P :
m easued pow er
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• When the transmission power of each base station is equal
path loss exponent is same, throughout the coverage area,
S/I is
• Di – distance between the i-th interferer and the mobile
• If all the interfering base stations are equidistant from the
desired station and distance is equal to distance D between the
cell centers,
KNCET 13
 




 0
1
i
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D
R
I
S
 
0
0
3
)
/
(
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N
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D
I
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

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• For hexagonal geometry with 7-cell cluster, with the mobile
being at the cell boundary, experiences worst case Co-channel
Interference , signal-to-interference ratio for the worst case
can be approximated as
The mobile is at a distance
D-R from the two nearest co-channel
Interfering cells and is exactly D+R/2,
D, D-R/2 and D+R from the
other interfering cells
KNCET 14
4
4
4
4
4
4
)
(
)
2
/
(
)
2
/
(
)
(
2 







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
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

D
R
D
R
D
R
D
R
D
R
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S
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Adjacent Channel Interference
• An interference resulting from the signals which are
adjacent in frequency to the desired signal.
– Imperfect receiver filters allow nearby frequencies to
leak into the passband
– Performance degrade seriously due to near-far effect.
KNCET 15
desi
red si
gnal
recei
vi
ng fi
l
t
er
response
desi
red si
gnal
i
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erference
i
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erference
si
gnalon adj
acentchannel
si
gnalon adj
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FILTER
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Power Control for Reducing Interference
• Power levels transmitted by every subscriber unit are
under constant control
• Each mobile transmits small power to maintain good
quality link
• Power control
– maintain prolong battery life
– reduces S/I in the system
– Solve near far problem
KNCET 16
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Trunking and Grade of Service
Erlangs: One Erlangs represents the amount of traffic
density carried by a channel that is completely
occupied
• Grade of Service (GOS): Measure of ability of a
user to access the trunking system during the busiest
hour
• Trunking allows a large number of users to share
relatively small number of channels in a cell by
providing access to each user on demand.
KNCET 17
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• Each user generates a traffic intensity of Erlangs given by
H: average duration of a call.
λ : average number of call requests per unit time
• For a system containing U users and an unspecified number of
channels, the total offered traffic intensity A, is given by
• For C channel trunking system, the traffic intensity per
channel, is given as
KNCET 18
u
A = λH
u
UA
A 
C
UA
A u
c /

c
A
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Trunking theory : is used to determine the number of
channels required to service a certain offered traffic at a
specific GOS.
Set-Up time: Time required to allocate a trunked radio
channel to a requesting user
Blocked Call: Call which cannot be completed at the time of
request due to congestion, also referred as lost call
Holding Time: Average duration of a typical call
Trunking efficiency(A) : Measure of number of users which
can be offered a particular GOS with a particular
configuration of fixed channels
KNCET 19
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KNCET 20
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KNCET 21
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KNCET 22
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Improving the coverage and Capacity
in Cellular Systems
• Methods for improving capacity in cellular
systems
– Cell Splitting: subdividing a congested cell
into smaller cells.
– Sectoring: directional antennas to control the
interference
– Coverage zone approach: Distributing the
coverage of a cell and extends the cell
boundary
KNCET 23
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Cell Splitting
• Split congested cell into smaller cells(reduction in
antenna height and transmitted power)
• Increases the capacity of cellular system(frequency
reuse)
• Radius is reduced half that of original
KNCET 24
microcell
Reduce R to R/2
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Cell Splitting
KNCET 25
• Cell splitting reduces the cell blocking probability and
increases the frequency
• Transmission power reduction from to
• Examining the receiving power at the new and old cell
boundary
• If we take n = 4 and set the received power equal to each other
• Problem: if only part of the cells are splitted
– Different cell sizes will exist simultaneously
1
t
P 2
t
P
n
t
r R
P
P 
 1
]
boundary
cell
old
at
[
n
t
r R
P
P 
 )
2
/
(
]
boundary
cell
new
at
[ 2
16
1
2
t
t
P
P 
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Sectoring(Directional Antennas)
KNCET 26
• Decrease the co-channel interference and keep the cell radius
R unchanged
– Replacing single omni-directional antenna by several
directional antennas
– Radiating within a specified sector
– Cell is partitioned into three 120 sectors or six 60 sectors
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KNCET 27
• Directional antennas increase the system capacity.
• Reduce signal-to-interference ratio(S/I) thus reduces cluster
size, thereby increasing the capacity
• Reduces Co-channel interference thus increases the system
performance
• Area covered by each directional antenna – section or sector
• Co-channel interference is reduced by the amount of sectoring
used.
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KNCET 28
• Interference Reduction
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Microcell Zone Concept
KNCET 29
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KNCET 30
• Antennas are placed at the outer edges of the cell(reduce the
number of BS)
• Lee’s Microcell zone technique exploits corner excited BS to
reduce the number of handoffs and thus eliminates partitioning
of channels between the sectors of a cell
• Any channel may be assigned to any zone by the base station
• Mobile is served by the zone with the strongest signal.
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KNCET 31
• Handoff within a cell
– No channel re-assignment
• Mobile travels from one zone to another within the cell, it
retains same channel
• Base station switches the channel to a different zone site
• Given channel is active only in the particular zone in which the
mobile is traveling
• Reduce interference
– Low power transmitters are employed
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UNIT - 3
DIGITAL SIGNALING FOR FADING CHANNEL
Structure of a wireless communication link, Principles
of Offset-QPSK, p/4-DQPSK, Minimum Shift Keying,
Gaussian Minimum Shift Keying, Error performance in
fading channels, OFDM principle – Cyclic prefix,
Windowing, PAPR.
KNCET 1
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Wireless communication link
2
Fig: Block diagram of a digital transmitter and channel
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KNCET 3
The information source provides an analog source signal and
feeds it into the source ADC and then converts the signal into a
stream of digital data
• The source coder uses a priori information on the properties of
the source data in order to reduce redundancy in the source
signal.
Eg:(GSM) speech coder reduces the source data rate from 64
kbit/s mentioned above to 13 kbit/s.
• The channel coder adds redundancy in order to protect data
against transmission errors.
• Signaling adds control information for the establishing and
ending of connections, for associating information with the
correct users, synchronization, etc.
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KNCET 4
• The TX Digital to Analog Converter (DAC) generates a pair of
analog, discrete amplitude voltages corresponding to the real and
imaginary part of the transmit symbols.
• The analog low-pass filter in the TX eliminates the (inevitable)
spectral components outside the desired transmission bandwidth.
• The TX Local Oscillator (LO) provides an unmodulated
sinusoidal signal, corresponding to one of the admissible center
frequencies.
• The upconverter converts the analog, filtered baseband signal to
a passband signal by mixing it with the LO signal.
• The RF TX filter eliminates out-of-band emissions in the RF
domain.
•The (analog) propagation channel attenuates the signal, and
leads to delay and frequency dispersion
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KNCET 5
Fig: Block diagram of a digital receiver
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The RX filter performs a rough selection of the received band.
• The low-noise amplifier amplifies the signal, so that the noise
added by later components of the RX chain has less effect on the
Signal-to-Noise Ratio (SNR).
• The RX LO provides sinusoidal signals corresponding to
possible signals at the TX LO.
• The RX down converter converts the received signal (in one or
several steps) into baseband.
• The RX low-pass filter provides a selection of desired
frequency bands for one specific user. It eliminates adjacent
channel interference as well as noise.
• The Automatic Gain Control (AGC) amplifies the signal such
that its level is well adjusted to the quantization at the subsequent
ADC.
KNCET 6
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KNCET 7
• The RX ADC converts the analog signal into values that are
discrete in time and amplitude.
• Carrier recovery determines the frequency and phase of the
carrier of the received signal, and uses it to adjust the RX LO.
• The baseband demodulator obtains soft-decision data from
digitized baseband data, and hands them over to the decoder.
• The decoder uses soft estimates from the demodulator to find
the original (digital) source data
• The demultiplexer separates the user data and signaling
information and reverses possible time compression of the TX
multiplexer.
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Quadrature Phase Shift Keying (QPSK)
• Quadrature Phase Shift Keying (QPSK) has twice the
bandwidth efficiency of BPSK, since 2 bits are transmitted in a
single modulation symbol.
• The phase of the carrier takes on 1 of 4 equally spaced values,
such as 0, π/2, π, 3π/2 [or] π/4, 3π/4, 5π/4,7π/4. where each
value of phase corresponds to a unique pair of message bits.
• The QPSK signal for this set of symbol states may be defined
as,
• where Ts - symbol duration and is equal to twice the bit period
KNCET 8
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Quadrature Phase Shift Keying (QPSK)
• Constellation Diagram
KNCET 9
The average probability of bit error in the AWGN
channel is obtained as
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Spectrum and Bandwidth of QPSK
KNCET 10
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QPSK Transmitter
KNCET 11
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QPSK Transmitter
KNCET 12
• The unipolar binary message stream has bit rate Rb and it is
first converted into a bipolar NRZ sequence.
• The bitstream m(t) is then split into two bit streams in mI(t)
and mQ (t) (in-phase and quadrature streams),each having a bit
rate of Rs = Rb/2.
• The bit stream mI(t) is called the "even" stream and mQ (t) is
called the "odd" stream.
• The two binary sequences are separately modulated by two
carriers ϕ1(t) and ϕ2(t), which are in quadrature.
• The filter at the output of the modulator confines the power
spectrum of the QPSK signal within the allocated band.
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QPSK Receiver
KNCET 13
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QPSK Receiver
KNCET 14
• The frontend bandpass filter removes the out-of-band noise
and adjacent channel interference.
• The filtered output is split into two parts, and each part is
coherently demodulated using the in-phase and
• quadrature carriers.
• The outputs of the demodulators are passed through decision
circuits which generate the in-phase and
• quadrature binary streams.
• The two components are then multiplexed to reproduce the
original binary sequence.
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Offset QPSK(OQPSK)
KNCET 15
• OQPSK signaling is similar to QPSK signaling, as
represented by equation
• In OQPSK, after splitting the even and odd bit streams,
mI(t) and mQ(t), one bit stream is made offset by one bit
period with each other.
• Phase transitions occur every Tb sec. maximum phase
shift = ±90°. Does not cause the signal envelope to go to
zero.
• Allows nonlinear amplification, so regeneration of side
lobes are eliminated.
• OQPSK signal is identical to that of a QPSK signal.
Hence, both signals occupy the same bandwidth.
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Minimum Shift Keying (MSK)
KNCET 16
• Minimum shift keying (MSK) is a special type of Continuous
Phase Frequency Shift Keying (CPFSK)
• wherein the peak frequency deviation is equal to 1/4 the bit
rate.
• In other words, MSK is continuous phase FSK with a
modulation index of 0.5.
• The modulation index is defined as,
Where,
ΔF - peak RF frequency deviation
Rb - bit rate.
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Minimum Shift Keying (MSK)
MSK signal can be defined as,
KNCET 17
where mI(t) and mQ(t) are the "odd" and "even" bits of the
bipolar data streams.
- MSK waveform can be seen as a special type of a continuous
phase FSK and the above equation is rewritten as,
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MSK Power Spectrum
KNCET 18
The normalized power spectral density for MSK is given by
• From above Figure, it is seen that the
MSK spectrum has lower side lobes
than QPSK and OQPSK.
• Main lobe of MSK is wider than that of
QPSK and OQPSK.
• MSK is less spectrally efficient than the
phase-shift keying techniques
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MSK-Transmitter
KNCET 19
• Multiplying a carrier signal with cos (πt/2T) produces two phase-coherent
signals at fc+ 1/4T and fc- I/4T.
• These two FSK signals are separated using two narrow bandpass filters and
appropriately combined to form the in-phase and quadrature carrier
components x(t) and y(t), respectively.
• These carriers are multiplied with the odd and even bit streams, mI(t) and
mQ(t), to produce the MSK modulated signal SMSK(t).
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MSK-Receiver
KNCET 20
• The received signal SMSK(t) is multiplied by the respective in-
phase and quadrature carriers x(t) and y(t).
• The output of the multipliers are integrated over two bit
periods. Then, it is given to a decision circuit which has a
threshold detector.
• Based on the level of the signal above or below the threshold,
the threshold detector decides whether the signal is 0 or 1.
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GMSK(Gaussian Minimum Shift
Keying)
– It is a simple binary modulation scheme
– It is a derivative of MSK
– The sidelobes level of the spectrum are further
reduced by passing the modulating waveform
through a pre-modulation Gaussian pulse shaping
filter
– Has excellent power and spectral efficiency due to
constant envelope
– GMSK premodulation filter has an impulse
response given by,
KNCET 21
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GMSK(Gaussian Minimum Shift
Keying)
– Transfer function is given by,
– The parameter α is related to B, the 3dB baseband
bandwidth of HG(f) is
– Power spectrum
KNCET 22
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GMSK - Bit Error rate
KNCET 23
– BER for GMSK was found for AWGN channels
– Bit error probability is a function of BT, since the
pulse shaping impacts ISI
– Bit Error probability of GMSK is
– Where γ is related to BT by
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GMSK Transmitter
KNCET 24
- The simplest way to generate a GMSK signal is to pass a
message bit stream through a Gaussian baseband filter
followed by an FM detector.
- Spectrum of LPF has Gaussian shape
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GMSK Receiver
– GMSK signals can be detected using orthogonal
coherent detectors or with simple noncoherent detectors
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GMSK Receiver
– Carrier recovery is performed by using a method
suggested by de Buda
– Sum of two discrete frequency components contained at
the output of a frequency doubler is divided by four
– This type of receiver can be implemented using digital
logic circuit
– Two D-Flip flops act as quadrature product demodulator
and XOR gates act as baseband multipliers
– Mutually orthogonal reference carriers are generated
using two D-Flip Flops
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Error Performance of Modulation
Techniques in Fading Channels
Error Probability in Flat-Fading Channels
– In fading channels, the received signal power (and thus
the SNR) is not constant but changes as the fading of the
channel changes
– To compute BER in such a channel, we have three steps:
1. Determine the BER for any arbitrary SNR
2. Determine the probability that a certain SNR occurs in
the channel – in other words, determine the pdf of the
power gain of the channel.
3. Average the BER over the distribution of SNRs
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• In AWGN channel, the BER decreases exponentially
as the SNR increases
• In contrast, a fading channel the BER decreases only
linearly with the (average) SNR
• Sometimes fading leads to high SNRs, sometimes it
leads to low SNRs, and it could be assumed that high
and low values would compensate for each other.
• The relationship between (instantaneous) BER and
(instantaneous) SNR is highly nonlinear
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•In AWGN channel, the BER decreases exponentially
as the SNR increases
•In contrast, a fading channel the BER decreases only
linearly with the (average) SNR
•Sometimes fading leads to high SNRs, sometimes it leads
to low SNRs, and it could be assumed that high and low
values would compensate for each other.
•The relationship between (instantaneous) BER and
(instantaneous) SNR is highly nonlinear
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OFDM(Orthogonal Frequency
Division Multiplexing)
• Orthogonal Frequency Division Multiplexing
(OFDM) is a modulation scheme that is especially
suited for high-data-rate transmission in delay
dispersive environments.
• It converts a high-rate data stream into a number
of low-rate streams that are transmitted over
parallel, narrowband channels that can be easily
equalized.
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Principle of OFDM
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Principle of OFDM
• The spectra of different modulated carriers
overlap, but each carrier is in the spectral nulls of
all other carriers.
• The data streams of any two subcarriers will not
interfere.
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Implementation of transceivers
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Implementation
• Let us first consider the analog interpretation. Let
the complex transmit symbol at time instant i on
the nth carrier be Cn,i . The transmit signal is then
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Implementation
• consider the signal for i = 0, sample it at
instances
• The input to IFFT is made up of N samples (the symbols
for the different subcarriers), and therefore the output
from the IFFT also consists of N values.
• These N values have to be transmitted, one after the
other, as temporal samples – this is the reason why we
have a P/S (Parallel to Serial) conversion directly after
the IFFT.
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Implementation
• At the receiver, we can reverse the process:
sample the received signal, write a block of N
samples into a vector – i.e., an S/P (Serial to
Parallel) conversion and perform an FFT on this
vector.
• The result is an estimate of the original data
Cn.
• OFDM can also be interpreted in the time–
frequency plane.
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Cyclic Prefix(CP)
• The OFDM transmitter and receiver work in an
Additive White Gaussian Noise (AWGN)
channel
• Which leads to delay dispersion also leads to a
loss of orthogonality between the subcarriers,
and thus to Inter Carrier Interference (ICI).
• Both these negative effects can be eliminated
by a special type of guard interval, called the
cyclic prefix (CP).
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Cyclic Prefix(CP)
• Base function for transmission
• W/N is the carrier spacing,
• Ts =
• For duration , normal OFDM symbol is
transmitted
• During time a copy of the last part of the
symbol is transmitted
• Total signal s(t) transmitted during time
is a copy of s(t) during the last part
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Cyclic Prefix(CP)
• Cyclic Prefix converts linear convolution into a cyclical
convolution
• is the number of samples in the cyclic
prefix
• During the time period, the received signal suffers from Inter
Symbol Interference (ISI), as echoes of the last part of the
preceding symbol interfere with the desired symbol.
• ISI is eliminated by discarding the received signal during this
time interval.
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Peak to Average Power
Ratio(PAPR)
• Drawback of OFDM
• When the signals of all the sub-carriers are
added, the peak power can be the number of
sub-carriers times the average power
• It is very high compared to the whole system
• The ratio of peak to average power value is
called PAPR
• Addition of N signals of same phase produces
a peak which is N times the average signal
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Peak to Average Power
Ratio(PAPR)
• OFDM signals have high PAPR.
• It is passed through High Power Amplifier at the
transmitter
• Large PAPR – ADC (large dynamic range)
• Increase in complexity
• Efficiency is reduced
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PAPR in OFDM systems
• OFDM signal consists of N data symbol
• Transmitted signal s(t),
• The PAPR of the transmit signal is defined as
ratio between instantaneous power to its average
power during the OFDM symbol period
( )
1
2
0
1
,0
N
j n ft
n
n
x t X e t T
N

−

=
=   

( )
( )
2
0
2
0
max
1/
t T
T
x t
PAPR
T x t dt
 
=

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PAPR in OFDM systems
• PAPR reduction is achieved by minimizing the
maximum instantaneous signal power
• Maximum PAPR can be expressed as
MAX PAPR[x(t)] = N
• PAPR increases with the number of sub-carriers
• Best way is to reduce the number of sub-carriers
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PAPR Reduction Techniques
• Coding for PAPR reduction – PAPR which is
lower than the given threshold is acceptable
• Phase Adjustments- Phase adjustments vector
are known to both transmitter and receiver
OFDM symbol x Phase vector = Transmitter signal
• Correction by multiplicative function- OFDM
signal is multiplied by a Gaussian function which
reduces PAPR
• Correction by Additive function – Out of band
inference is reduced, but BER is increased
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UNIT - 4
MULTIPATH MITIGATION TECHNIQUES
Equalisation – Adaptive equalization, Linear and Non-Linear
equalization, Zero forcing and LMS Algorithms. Diversity –
Micro and Macro diversity, Diversity combining techniques,
Error probability in fading channels with diversity reception,
Rake receiver
KNCET 1
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Introduction
KNCET 2
• Different techniques can improve link performance without
altering air interface
increasing transmit power or bandwidth
1. Equalization used to counter ISI (time dispersion)
2. Diversity used to reduce depth & duration of fades due to
motion
3. Channel Coding: coded bits improve small-scale link
performance
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Equalization
Inter symbol Interference (ISI) is caused by multipath time
delay spread
• results in signal distortion
• occurs in time dispersive, frequency selective fading
(bandlimited) channels
Equalization is a method of overcoming ISI
• adaptive equalizers can cancel interference
- mobile fading channel is random & time varying
- adaptive equalizers track time varying channel
characteristics
- Adapts to channel variations
KNCET 3
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Adaptive Equalizers
Two Operating Modes
(1) training
(2) tracking
(1) training adaptive equalizer
i. send training sequence of known fixed-length & bit pattern
• typically a pseudo random binary signal
• designed to permit acquisition of filter coefficients in
worst case
ii. receiver’s equalizer recovers training sequence
• adapts settings to minimize BER
iii. convergence: training obtains near optimal filter coefficients
KNCET 4
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Adaptive Equalizers
(1) tracking adaptive equalizer
Continually track and adjust filter coefficients as data is received
• adjustments compensate for time-varying channel
• data can be encoded (channel coded) for better
performance
At the receiver
• recursive algorithm evaluates channel & estimates filter
coefficients
• filter compensates for multipath in the channel
KNCET 5
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Adaptive Equalizer
KNCET 6
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Adaptive Equalizer
KNCET 7
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Adaptive Equalizer
KNCET 8
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Classification of Equalizers
linear equalizer: If the output d(t) is not used in
feedback path to adapt the equalizers
non-linear equalizer:
If the output d(t) is used in feedback path
KNCET 9
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Classification of Equalizers
KNCET 10
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Linear Transversal Equalizer
most common equalizer structure
• tapped delay lines spaced at symbol period, Ts
• delay element’s transfer function given by z-1 or exp(-jwTs)
• delay elements have unity gain
(i) Finite Impulse Response (FIR) filter is the simplest LTE
• only feed-forward taps
• transfer function = polynomial in z-1
• many zeros
• poles only at z = 0
KNCET 11
Basic FIR LTE Structure
y(t) + nb(t)
clock
Ts Ts Ts
taps
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Linear Transversal Equalizer
• FIR LTE Structure showing weights
KNCET 12
y(t) + nb(t)
clock
Ts Ts Ts

  
w0k w1k w2k

w3k
DSP
)
(
ˆ k
d
T
)
(
ˆ k
d =  






1
0
)
(
)
(
N
k
b
ik i
k
n
i
k
y
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Lattice Filter
Input signal y(k) is transformed into N intermediate signals
classified as
i. fn(k) = forward error signals
ii. bn(k) = backward error signals
intermediate signals are used:
• as input into tap multipliers
• to calculate & update coefficients
each stage characterized by recursive equations for fn(k), bn(k)
KNCET 13
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Lattice Filter
– Structure
KNCET 14
Σ
Σ
f1(k) f2(k)
K1


KN-1


Σ
fN(k)
T Σ

 
b2(k) bN(k)
c1 c2 cN
Σ
b1(k)
T
y(k)
)
(
ˆ k
d
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Lattice Filter
– Evaluation of lattice equalizer
KNCET 15
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Non-Linear Equalization
common in practical wireless systems
• used with severe channel distortion
• Used when ISI is severe
• linear equalizers don’t perform well in channels with deep
spectral nulls
- tries to compensate for distortion
- high gain enhances noise at spectral null
3 effective non-linear methods used
1. Decision Feedback Equalization (DFE)
2. Maximum Likelihood Symbol Detection (MLSD)
3. Maximum Likelihood Sequence Estimation (MLSE)
KNCET 16
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Decision Feedback Equalization (DFE)
basic idea:
i. detect information symbol and pass it through the decision
device
ii. after detection - estimate ISI induced
iii. subtract estimated ISI from detection of future symbols
Direct Transversal Form of DFE consists of FFF and FBF filter
• FFF = feed forward filter with N1+N2+1 taps
• FBF = feedback filter with N3 taps
- driven by detector’s output (decision threshold)
- filter coefficients adjusted based on past detected symbol
- goal is to cancel ISI on current symbol
KNCET 17
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• y(k - N2 + i) are past equalizer inputs used for FFF segment
• y(k + N1 – i) are delayed equalizer inputs for FFF segment
KNCET 18
y(k+N1-1) y(k) y(k-N2+1)
y(k+N1) y(k-N2)
d(k)
+ + + +
)
(
ˆ k
d
Ts Ts Ts
Ts
*
1
N
c
*
1
1
N
c
*
0
c *
1
2 
N
c
*
2
N
c
    
Ts
Ts
Ts
*
3
F *
2
F
*
1
F
+
+
  
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DFE output given by:
KNCET 19
y (k-n) = equalizer inputs, including past, current, and delayed
d(k-i) = previous decision outputs
Minimum MSE for Direct Transversal DFE given by DFE
DFE =
  






















dw
N
e
N
T
T
T
jwT
/
/ 0
2
0
ln
2
exp


 F
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Predictive DFE
KNCET 20
consists of FFF and FBF
FBF is driven by the input sequence given by
d(k) – FFF output
FBF is called noise & ISI predictor
- predicts noise & residual ISI contained in signal at FFF output
- subtracts this from d(k) after some feedback delay
Predictive DFE performs well as conventional DFE as number of
taps in FFF and FBF approach infinity
Predictive Equalizer can also be realized as lattice equalizer
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Predictive DFE
KNCET 21
y(k)
e(k)
e(k)
d(k)
d’(k)
i
+
FFF 
Decision
Device
FBF


- +
i
+
y(k) = kth received signal
sample
d(k) = output decision
e(k) = error signal
d’(k) = output prediction
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Maximum Likelihood Sequence
Estimation Equalizer (MLS)
• optimal in the sense that it minimizes probability of sequence
error
• requires knowledge of
i. channel characteristics to compute metrics for making
decision
ii. statistical distribution of noise corrupting the signal
KNCET 22
{si}
+ -
y(t)
Channel
Estimator

delay
Match
Filter MLSE
z(t) z(k)
{an}
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Algorithms for Adaptive Equalization
• A wide range of algorithms exist to compensate for unknown
& time-varying channel
• algorithms are used to
i. update equalizer coefficients
ii. track channel variations
• 3 basic algorithms for adaptive equalization
(i) zero-forcing (ZF)
(ii) least mean square (LMS)
(iii) recursive least squares (RLS)
KNCET 23
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Performance Measure of Algorithms
(1) Rate of Convergence (RoC)
(2) Misadjustment
(3) Computational Complexity
(4) Numerical Properties & Inaccuracies
(5) practical cost & power issues
(6) radio channel characteristics
(1) Rate of Convergence (RoC): iterations needed for converge to
optimal solution in response to stationary inputs
- fast RoC allows rapid adaptation to stationary environment of
unknown statistics
2) Misadjustment: quantitative measure of the amount by which the
final value of mean square error, averaged over adaptive filters
- Deviations from minimum mean square error
KNCET 24
obtained - minimum
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Performance Measure of Algorithms
(3) Computational Complexity: number of operations required to
complete iteration of the algorithm
(4) Numerical Properties: inaccuracies produced by round-off noise
• representation errors in digital format (floating point) in
computers
• errors can influence stability of the algorithm
5) Practical Issues in the choice of equalizer structure & algorithms
• equalizers must justify cost, including relative cost of
computing platform
• power budget-battery drain: radio propagation characteristics
KNCET 25
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Zero Forcing (ZF) Algorithm
• assume tapped delay line filter with N taps delayed by T &
weights cn‘s
• cn‘s selected to force samples of hch(t)heq(t) to 0
- N sample points each delayed by Ts (symbol duration)
let n increase without bound  obtain infinite length equalizer with
zero ISI at ouput
The equalizer coefficients are chosen to force the samples of the
combined channel and equalizer impulse response to zero
Nyquist Criterion must be satisfied by combined channel response
Hch(f)Heq(f) = 1, | f | < 1/2Ts
Heq(f) = frequency response of equalizer that is periodic with 1/Ts
Hch (f) = folded channel frequency response
KNCET 26
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Least Mean Square (LMS)
LMS seeks to compute minimum mean square error, min
• more robust than ZF algorithm for adaptive equalizers
• criterion = minimization of MSE between desired and actual
equalizer outputs
• e(k) = prediction error given by
x(k) = original transmitted baseband signal
d(k) = x(k)  known training sequence transmitted
KNCET 27
e(k) = d(k) - )
(
ˆ k
d
= x(k) - )
(
ˆ k
d
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KNCET 28
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KNCET 29
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KNCET 30
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KNCET 31
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.
KNCET 32
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.
KNCET 33
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DIVERSITY
– To Compensate fading channel impairments, implemented by
using two or more transmitting and receiving antennas
Principle:
– Receiver has multiple copies of the transmit signal
– Same signal is transmitted by more than one antenna
– Selects the best signal
– Average SNR at the receiver may be improved
KNCET 34
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DIVERSITY
KNCET 35
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CLASSIFICATION OF DIVERSITY
MACRO- DIVERSITY
– Provides a method to mitigate the effect of shadowing as in
case of Large scale fading
MICRO-DIVERSITY
– Provides a method to mitigate the effect of multi-path fading
as in case of small scale fading
KNCET 36
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MICRO DIVERSITY
KNCET 37
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CLASSIFICATION OF MICRO DIVERSITY
Five common methods are
(1) Spatial diversity : Several antenna elements separated in
space
(2) Temporal diversity : Repetition of the transmit signal at
different times
(3) Frequency diversity : Transmission of the signal on different
frequencies
(4) Angular diversity: Multiple antennas with different antennas
with different antenna patterns
(5) Polarization diversity: Multiple antennas receiving different
polarizations
KNCET 38
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Spatial Diversity
KNCET 39
• Space Diversity or Antenna diversity
• Use more than one antenna to receive the signal.
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Temporal Diversity
KNCET 40
• As the wireless propagation channels are time variant, signals
that are received at different times are uncorrelated
• Temporal Distance
Vmax Maximum Doppler frequency
• Temporal diversity can be realized in 3 different ways.
• Repetition coding- signal is repeated several times
• Automatic repeat request- Rx sends message to TX
• Combination of interleaving and coding – Forward Error
Correction codes. Transmitted code is reconstructed
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Frequency Diversity
KNCET 41
• Frequency diversity is implemented by transmitting same
signal at two or more different carrier frequencies.
• Our aim is to make these carrier frequencies uncorrelated to
each other, so that they will not experience the same fades.
• Frequency diversity is often employed in microwave line –of
sight links.
• These links uses Frequency division multiplexing mode(FDM)
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Angular or Pattern Diversity
• It enhances the decorrelation of signals at closely spaced
antennas by using Different antenna patterns
• Even identical antennas can have different patterns when they
are mounted close to each other.
• This effect is due to Mutual Coupling.
• Place 2 identical antennas close to
each other
• Here antenna B acts as a reflector for antenna A.
• Different patterns are used when located on different cases
KNCET 42
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Polarization Diversity
• Multiple versions of a signal are transmitted and received via
antennas with different polarization.
i.e. horizontal and vertical.
• A diversity combining technique is applied on the receiver
side.
• Signals are transmitted through two orthogonally polarized
propagation paths
• Improves link margin and capacity
KNCET 43
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Macro Diversity
KNCET 44
• Combat large-scale fading (fading created by
shadowing effects)
• Large distance between BS1 and BS2 gives rise to
macro diversity.
• Use on-frequency repeaters (receive the signal and
retransmit the amplified version).
• Simulcast (same signal transmitted simultaneously
from different BSs.)
• Simulcast is widely used for broadcast applications
like digital TV.
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Macro Diversity-Methods
KNCET 45
• Selection diversity - 'Best' signal copy is selected
and processed (demodulated and decoded) and all
other copies are discarded
• Combining Diversity - All signal copies are
combined and combined signal is decoded
• Note: Combining diversity leads to better
performance but Rx complexity higher than Selection
Diversity.
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Selection Diversity
KNCET 46
• The receiver selects the signal with largest power
• RSSI-Received Signal Strength Indication
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Selection Diversity
KNCET 47
• First transmit the training sequence
• Receiver demodulates the signal and compare it with the
transmit signal
• Based on smaller BER, suitable channel is selected
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Combining Diversity Types
KNCET 48
• Maximal Ratio Combining – Weights all signal copies
by their amplitude
• Equal Gain Combining – Signals are not weighted but
undergo phase correction
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Maximal Ratio Conbining
KNCET 49
• Signals from all the branches are weighted according to their
individual signal voltage to noise power ratios and then
summed
• Signals must be co-phased before being summed
• Requires an individual receiver and phasing circuit for each
antenna element
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Equal Gain Combining
KNCET 50
• Weighting circuits are omitted
• Branch weights are set to unity
• Signals from each branch are co-phased to provide equal gain
combining diversity
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RAKE Receiver
KNCET 51
– Used in CDMA cellular systems
– Combine multipath components which are time
delayed versions of original signal transmission
– Combinations improve SNR
– RAKE receiver collects the time shifted versions
of the original signal by providing separate
correlation receiver for each of multipath signals
– RAKE receiver uses multipath diversity principle
– It is like a rake that rakes the energy from the
multipath propagated signal components
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RAKE Receiver
KNCET 52
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RAKE Receiver
KNCET 53
• Consider M correlators are used in CDMA receiver to
capture M strongest multipath components
• weighting network provides a linear combination of
the correlator output for bit decision.
• Correlator 1 is synchronized to the strongest
multipath m1
• Multipath component m2, arrived t1 later than m1,
but has low correlation than m1
• Outputs of the M correlators are denoted as Z1, Z2…
ZM and weighted by α1, α2… αM
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UNIT - 5
MULTIPLE ANTENNA TECHNIQUES
MIMO systems – spatial multiplexing -System model -
Pre-coding - Beam forming - transmitter diversity,
receiver diversity- Channel state information-capacity in
fading and non-fading channels.
KNCET 1
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MIMO Systems
KNCET 2
- By using Multiple Output Multiple Input (MIMO)
systems
- Diversity gain mitigates the fading and increases
coverage and improves QoS
- Multiplexing gain increases capacity and spectral
efficiency with no additional power or bandwidth
expenditure
- Array gain results in an increase in average receive
SNR.
- Spatial Diversity and Spatial Multiplexing can be
conflicting goals
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MIMO Systems
KNCET 3
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Spatial Diversity and Spatial
Multiplexing
• Spatial Diversity
– Signal copies are transferred from multiple antennas or
received at more than one antenna
– redundancy is provided by employing an array of antennas,
with a minimum separation of λ/2 between neighbouring
antennas
• Spatial Multiplexing
– the system is able to carry more than one data stream over
one frequency, simultaneously
KNCET 4
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Spatial Multiplexing
• MIMO channels can be decomposed into a number of R
parallel independent channels → Multiplexing Gain
– Principle: Transmit independent data signals from different
antennas to increase the throughput, capacity
KNCET 5
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Pre-coding
- To decrease MUI(Multi-user interface) and increase data rate
in MIMO system
- Performs Transmit diversity
- Similar to equalization
- Main difference is we need to optimize the precoder with a
decoder
- Channel equalization minimize channel errors
KNCET 6
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Pre-coding
KNCET 7
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Implementation of MIMO-Vertical
Bell Labs layered space-time
Architecture
KNCET 8
-V-BLAST is a transmitter –receiver which is mainly
used to implement multiplexing MIMO
- Achieve diversity of the order of number of
received samples
- Each coded symbol is transmitted from one antenna
and received by number of received antennas.
- BLAST can average over the randomness of the
individual sub-channels and get better outage
performance.
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Implementation of MIMO-Vertical
Bell Labs layered space-time
Architecture
KNCET 9
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Linear Precoding
KNCET 10
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Non-Linear Precoding
KNCET 11
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Beam Forming
KNCET 12
• Used in any antenna system, particularly in MIMO
systems in order to create certain required antenna
directive pattern to give required performance.
• Combination of radio signals from a set of small non-
directional antennas to simulate a large directional
antenna
• Smart antenna are normally used because it can be
controlled automatically according to the required
performance
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SMART ANTENNA - TYPES
KNCET 13
Smart antennas are divided into two types
(i)Phased array systems(PAS)
- Have number of predefined patterns
- The required one being switched according to the
direction required
(ii)Adaptive array systems(AAS)
- Uses infinite number of patterns
- Adjusted based on the requirements in real time
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Transmit Diversity
• Multiple antenna elements are required at the
transmitter
• Only one antenna at the receiver end provides better
performance
KNCET 14
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Transmit Diversity-Types
Two Types
• (i)Transmitter diversity with the channel state
information(closed loop transmit diversity)
• (ii)Transmitter diversity without the channel state
information(open loop transmit diversity)
KNCET 15
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Closed loop Transmit Diversity
KNCET 16
• Transmitter knows perfectly about the channel
• This information is obtained by means of
feedback from the receiver
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Closed loop Transmit Diversity
KNCET 17
• If the selected antenna maximizes the signal to
Interference Noise ratio(SINR), then the
transmit encoder receives feedback channel
state information from the receiver
• This fine encoding matrix maximizes SNR at
the receiver
• Space Time Block Coder(STBC) is an efficient
means of achieving optimal transmitter
diversity gain.
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Open loop Transmit Diversity
KNCET 18
• Transmission of signals from different antenna
elements allows the receiver to distinguish
different transmitted signal components.
• One method is delay diversity
• We transmit data streams with the delay of one
symbol duration from each of the transmit
antennas
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Receiver Diversity
• One transmitting antenna and many receiving
antennas are used.
• Desired message is transmitted by using single
transmitting antenna and received by multiple
antennas
• Different antennas appropriately separated are
deployed at the receiver to combine the uncorrelated
fading signals called SPACE DIVERSITY
KNCET 19
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Receiver Diversity
KNCET 20
- Single transmitting antenna and multiple
receiver antenna
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Classification of Space Diversity
KNCET 21
1) Selection diversity
2) Feedback diversity
3) Maximal radio combining
4) Equal gain combining diversity
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Selection Diversity
• The receiver monitors the SNR value of each
diversity channel and chooses the one with the
maximum SNR value.
• The receiver with M demodulators are used to
provide M diversity branches, whose gains are
adjusted to provide the same average SNR for each
branch
• Receiver branch having the highest instantaneous
SNR is connected to the demodulator
KNCET 22
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Selection Diversity
KNCET 23
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Feedback/scanning Diversity
• Similar to selection diversity except that instead of always
using the best of ‘n’ signals, the ‘n’ signals are scanned in a
fixed sequence until one is found to be above a predetermined
threshold.
KNCET 24
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Maximal Ratio Combining
KNCET 25
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Maximal Ratio Combining
• The signals from all of the M branches are
weighted according to their individual signal
voltage to noise power ratios and then summed
up
• Individual signals must be co-phased before
being summed which generally requires an
individual receiver and the phasing circuit for
each antenna element
• MRC produces an output SNR which is equal
to the sum of the individual SNRs.
KNCET 26
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Equal Gain Diversity
- Similar to MRC except that there will be an
omission of the weighted circuits
- The branch weights are all set to unity but the
signals from each branch are co-phased to
provide an equal gain combining diversity
- Allows the receiver to exploit the signals that
are simultaneously received on each branch.
KNCET 27
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CHANNEL STATE INFORMATION(CSI)
• Represents the properties of a communication link
between the transmitter and receiver.
• CSI describes how a signal propagates from the
transmitter to the receiver
• Represents the combined effect of scattering, fading
and power decay with distance
• It is usually estimated at the receiving end and then
quantized and fed back to the transmitter side
KNCET 28
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CHANNEL STATE INFORMATION(CSI)-
TYPES
INSTANTANEOUS CSI
• Short term CSI
• Current conditions of the channel are known
which can be viewed as knowing the impulse
response of the digital filter.
• Optimize the received signal for spatial
multiplexing or to achieve low bit error rates
KNCET 29
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CHANNEL STATE INFORMATION(CSI)-
TYPES
STATISTICAL CSI
• Long term CSI
• Statistical characterization of the channel are
known .
• Include the type of fading distribution, the
average channel gain, line-of-sight component
and spatial correlation
KNCET 30
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MIMO-CSI Transmission
Algorithms used for MIMO transmission can be categorized based
on the amount of CSI
Full CSI at the transmitter and Full CSI at the receiver:
• Both TX and RX have full and perfect knowledge of the channel
• Results in highest possible capacity
Average CSI at the transmitter and Full CSI at the receiver:
• Rx has full information about the instantaneous channel state, but
Tx knows only the average CSI
KNCET 31
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No CSI at the transmitter and Full CSI at the receiver:
• Without any feedback this is achieved
• Transmitter does not use any CSI while Receiver learns
the instantaneous channel state from a training sequence
No CSI at the transmitter and No CSI at the receiver:
• The channel capacity is high when neither the TX nor
the RX have CSI
KNCET 32
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Noisy CSI:
• When we assume Full CSI at the receiver, implies
that receiver has learned the channel state perfectly.
• Any received training sequence will get affected by an
additive noise as well as quantization noise
• receiver processes the signal based on the observed
channel Hobs, while the signal pass through the actual
channel, Hact
• Hact = Hobs + Δ
• Δ - changes due to noise
KNCET 33
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MIMO capacity on fading channels
The capacity increase can be seen by comparing MIMO systems
with SISO, SIMO, and MISO systems
– SISO:capacity is given by Shannon’s classical formula:
Where B is the BW and h is the fading gain
– SIMO (with M transmitting antennas), the capacity is given by
– MISO (with M transmitting antennas), the capacity is given by
KNCET 34
)
2
1
(
2
log h
snr
B
C 


)
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2
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(
2
log 




m
n
n
h
snr
B
C
)
1
2
1
(
2
log 




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N
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N
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C
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• The capacity for MIMO systems can have the following forms
(Assuming Tx antennas = Rx antennas = N):
A) If the channel is not known at the transmitter:
– Where Es is the total power, σ2 is noise level of AWGN
– Hence the power is equally shared by each channel
– The capacity grows linearly with the number of antennas
B) If the channel is known at the transmitter
KNCET 35
)
2
2
1
(
2
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n
h
N
s
E
N
C 












 















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

N
n n
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n
E
C
1
)
2
2
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(
2
log

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• No CSI at transmitter and Full CSI at Receiver
Special Cases:
NT = NR = N
(i) All transfer functions are identical
- All antenna elements are very close together
Capacity, C = log2(1+Nγ)
(ii) All transfer functions are Different
- All antenna elements are spaced far apart
Capacity, C = N log2(1+γ)
Capacity increases linearly with the number of antenna elements
KNCET 36
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MIMO capacity on fading or Frequency
selective channels
• With the channel known at the transmitter and receiver, the total
power allocation the each channel will be based on water filling.
–Water filling: Strong Sub-channel, with low noise power level
will be assigned with a higher signal power.
Where σN
2 = σ2 / │hn
2│
KNCET 37
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MIMO capacity on fading or Frequency
selective channels
• Imagine a number of connected vessels
• Bottom of each vessel is a block of concrete with height
equal to noise power of corresponding sub channel
• Amount of water poured is proportional to the total
transmit power
• Water filling makes sure that energy is not wasted on
sub-channels that have poor SNR.
• Some part of the vessel will not be covered by water.
These parts correspond to sub channel with strong noise
KNCET 38
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Capacity in flat fading or non fading
Channels
Three cases:
• Fading statistics known
• No CSI at TX and perfect CSI at RX
• Perfect CSI at TX and RX
KNCET 39
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Channels
Two types
• Ergodic (Shannon) capacity
• Outage Capacity
Ergodic capacity
• Expected value of the capacity, taken over all
realizations of the channel.
Outage Capacity
• It is the minimum transmission rate that is achieved
over a certain fraction of time
KNCET 40
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Channels
No CSI at TX and perfect CSI at the RX
Capacity, C = ∫ Blog2(1+γ) p(γ)dγ
Full CSI at TX and RX
For fixed transmit power, same capacity will be available
only when the receiver knows fading.
- Fading reduces capacity
- Transmit power and transmission rate can be adapted
Channel capacity
C = S ∫ Blog2(1+(p(γ) γ/s)) p(γ)dγ
KNCET 41
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WC-UNIT NOTES.pdf

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WC-UNIT NOTES.pdf