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EC8092 - Advanced
Wireless Communication
by
Mr. V. Prakash.,M.Tech.
Asst.Prof / ECE
Bharathidasan Engineering College
Natrampalli - 635854
Crowded Spectrum
 All about SPECTRUM
 Marconi pioneered wireless industry 100 years ago.
 Today life is not possible without wireless
 Wireless used widely in Fixed Role and Mobile Role
 Fixed Role – Desktop computers and Laptop
 Mobile Role – provides fast mobility in vehicles – voice and data
 Wireless Design Engineers finding uphill task – limited availability of radio freq
spectrum.
 Time varying problems i.e fading,multipath propagation, demand of high data rates
Fading Multipath
High data
rates
QOS-Quality
of Service
DSL(Modem)
& Cable
Interfering signals with crowded spectrum
Need for Data Rates
• Gradual Evolution of Mobile Communication – Quest for High Data Rates
• Data Rate – bps
• Spectral Efficiency – bps/Hz
• First Mobile Communication – Analog Comm – 1st Generation.
• Beginning of 1990’s – First Digital Systems emerged – 2nd Gen.
• Europe introduced 2G – GSM – 900MHZ or 1800MHZ
• Bit Rate – 22.8 kbps
Bandwidth
900 MHz or 1800
MHZ
Bit Rate
22.8 kbps
Europe
Introduced
Digital Systems -
2G -
GSM
GSM ARCHITECTURE
To satisfy higher data rates two methods were found during those days
1. HSCSD – High Speed Circuit Switched Data – 38.4 kbps
2. GPRS – General Packet Radio Service – 172.2 kbps
The Demand for higher data rates forced the development of 3G
 384 kbps – Mobile
 1mbps for indoor
UMTS – (Universal Mobile Telephone Systems)
 Leading Technology for 3G
 Also known as WCDMA – Wideband Code Division Multiple Access
 Popular Technology found by ITU – International Telecommunication Union
 UMTS widely used by GSM Operators – 850 million end users – 195 Countries –
70 % of today’s digital market
 Japan Launched its first commercial WCDMA in 2001 then
Austria,Italy,Sweden,UK….
 An alternative to 3G is EDGE - Enhanced Data rates for Gsm Evolution
 Like GSM two methods were adopted
1. ECSD – Enhanced Circuit Switched Data
2. EGPRS – Enhanced General Packet Data Service
 Data rates have been enhanced - 473.6 kbps
 EDGE was introduced in US
 With 200 operators world wide – high speed data – 2.5G – GPRS technology
 The new IEEE802.11 and HIPERLAN(High Performance LAN)–bit rate of 54
mbps – 24mpbs mostly used in several applications
 Such high data rates pushing and carrier freq to UHF imposing the large BW
 HIPERLAN occupy freq of 5GHz to 17 GHz
 MBS - Multimedia Broadcasting Systems – 40 – 60 GHz
 4G was first introduced in Japan in 2006
 Ease in video streaming,multitmedia systems – 20 to 40 mbps
Comparison of several systems based on Mobility and Data Rates
Possible candidates for 4G systems
• BWIF: Broadband wireless internet Forum – creating and
developing next gen. fixed wirless standards.
• Specifications based on VOFDM(Vector OFDM)
 BWIF formed to address needs of quickly emerging wireless broadband market
 Product road maps, lower the product costs.
TD-SCDMA
 Time Division Synchronous CDMA – Chinese contribution to ITU
 Integrates with existing GSM
 Designed to manage symmetric ckt switches (Speed &Video) and Asymmetric
Swithches (Mobile Internet)
 HSDPA
 High Speed Downlink Packet Access
 Packet based data service 8-10mbps (20 mbps in MIMO) over 5MHz BW channel
 Includes AMC- Adaptive Modulation and Coding , Hybrid Automatic Req(HARQ),
MIMO, Higspeed search of Cell.
MIMO - Multiple Input Multiple Output
Systems
 Based on theoretical work developed bt Teletar and Foschini
 Core of this idea – use multiple antenna for Transmission and Reception.
 Increases the capacity of the WL channel
 Capacity is expressed as the Max achievable data rate for low prob of error
MIMO system pioneered by AT&T Labs-Research in Middletown, New
Jersey
 AT & T conducted field tests to characterize the mobile MIMO radio channel
 measured the capacity of a system with four antennas on a laptop computer and
four antennas on a rooftop base station
 tests showed that fourfold increase in capacity over a single antenna system
 ( can be supported in a 30-KHz channel with dual polarized spatially separated
base station and mobile terminal antennas)
 dual-polarized antennas separated by 11.3 feet
Image of Dual Polarized Antenna
 Four antennas at the transmitter and receiver has the potential to provide four
times the data rate of a single antenna
 system without an increase in transmit power or bandwidth
 high capacities are theoretically possible
The MIMO Wireless Channel
Multiantenna Systems
 Single-Input Single-Output (SISO)
 Single-Input Multiple-Output (SIMO) - a single transmitting
antenna and multiple (MR) receive antennas
 Multiple-Input Single-Output (MISO) - multiple (MT)
transmitting antennas and one receive antenna
 MIMO has Multiple (MT) transmitting antennas and Multiple (MR)
receive antennas and
 MIMO-Multi User (MIMO-MU) - a base station with multiple
transmit/receive antennas interacting with multiple users, each
with one or more antennas
Array Gain
Array gain is the average increase in the signal-to-noise ratio (SNR) at the
receiver
that arises from the coherent combining effect of multiple antennas at the receiver
or transmitter or both
I.e increase in SNR due to multiple antenna at Tx and Rx MISO case
Transmitter Array Gain : If the channel is known to the multiple antenna transmitter,
the transmitter will weight the transmission with weights coefficients, depending on the
channel coefficients, so that there is coherent combining at the single antenna receiver
 SIMO case
Receiver Array Gain: only one antenna at the transmitter and no knowledge of the
channel and a multiple antenna receiver, which has perfect knowledge of the channel,
then the receiver can suitably weight the incoming signals so that they coherently add
up at the output (combining), thereby enhancing the signal
DIVERSITY GAIN
In a fading channel, signals experience fades (i.e., they fluctuate in their strength).
This gives rise to high bit error rates (BER).
Diversity used to combat fading.
This involves providing replicas of the transmitted signal over time, frequency, or space
 Spatial diversity
Antenna elements separated by space
 Temporal diversity
Transmission of signals at different time
 Frequency diversity
Transmission of signals at different frequencies
 Angular diversity
Multiple antennas with different antenna patterns
 Polarization diversity
Multiple antenna with different polarizations
 Transmit diversity :
It is the radio communication using signals that originate from two or
more independent sources that have been modulated with identical information-bearing
signals and that may vary in their transmission characteristics at any given instant.
 Receiver diversity:
It is the independent fading paths associated with multiple receive
antennas are combined to obtain a resultant signal that is then passed through a standard
demodulator.
 Polarization diversity:
In this type of diversity, horizontal and vertical polarization signals are
transmitted by two different polarized antennas and received correspondingly by two
different polarized antennas at the receiver.
 Angle diversity:
 This applies at carrier frequencies in excess of 10 GHz.
 At such frequencies, the transmitted signals are highly scattered in space.
 In such an event the receiver can have two highly directional antennas facing in
totally different directions.
 This enables the receiver to collect two samples of the same signal, which are
totally independent of each other.
Data Pipes
 The term data pipe is derived from fluid mechanics.
 Pipes are used to transfer water to a tank/reservoir.
 The more the number of pipes, the greater the quantum of flow of water into a
tank/reservoir.
 consider a case of two data pipes between the transmitter and receiver.
 either the data in the data pipes are identical to each other or they are
independent samples, completely different from each other
 Case 1: The data through both pipes are identical. 2nd is the replica of 1st one.
Full correlation. Throughput is less (Capacity).Same Data is transmitted.
 Case 2: The data through both pipes are not identical. Independent.No
correlation.
High Throughput. No Diversity. More the pipes , more throughput.
Spatial multiplexing
Spatial multiplexing or space-division multiplexing (often
abbreviated SM, SDM or SMX) is a multiplexing technique in MIMO wireless
communication, fibre-optic communication and other communications
technologies used to transmit independent channels separated in space
• Spatial multiplexing offers a linear increase in the transmission rate
• Same bandwidth and with no additional power expenditure
• The bit stream is split into two half-rate bit streams, modulated and
transmitted simultaneously from both the antennas.
• The receiver, having complete knowledge of the channel, recovers these
individual bit streams and combines them so as to recover the original bit
stream
Automatic request for repeat (ARQ).
 This is an error control mechanism in which received packets that cannot be
corrected are retransmitted. This is a type of temporal diversity.
Forward Error Correction (FEC).
 This is a technique that inserts redundant bits during transmission to help
detect and correct bit errors during reception.
Coding gain.
 The improvement in SNR at the receiver because of FEC is called coding gain.
MIMO System Model
 Consider a MIMO system with a transmit array of MT antennas and a receive
array of MR antennas
 The transmitted matrix is a MT  1 column matrix s where si is the ith component,
transmitted from antenna i.
 We consider the channel to be a Gaussian channel such that the elements of s are
considered to be independent identically distributed (i.i.d.) Gaussian variables.
 If the channel is unknown at the transmitter, we assume that the signals transmitted
from each antenna have equal powers of Es /MT .
 The covariance matrix for this transmitted signal is given by
 where Es is the power across the transmitterMT and IMT is an MT  MT identity
matrix.
 The channel matrix H is a MR MT complex matrix
 The component hi , j of the matrix is the fading coefficient from the jth transmit
antenna to the i th receive antenna.
 We assume that the received power for each of the receive antennas is equal
to the total transmitted power Es
 we ignore signal attenuation, antenna gains, and so on
 Thus we obtain the normalization constraint for the elements of H, for a
deterministic channel as
 We assume that the channel matrix is known at the receiver but unknown at the
transmitter.
 If we require the transmitter to know this channel, then we need to communicate
this information to the transmitter via a feedback channel.
 The noise at the receiver is another column matrix of size MR  1, denoted by n.
The components of n are Zero Mean Circularly Symmetrical Complex Gaussian
(ZMCSCG) variables.
 The covariance matrix of the receiver noise is
If there is no correlation between components of n, the covariance matrix is
obtained as
Each of the MR receive branches has identical noise power of N0 .
 we assumed that the total received power per antenna is equal to the total
transmitted power,
 The SNR can be written as
 Therefore, the received vector can be expressed as
 The received signal covariance matrix defined as E{rrH}, is given by
 while the total signal power can be expressed as tr (Rrr ).
MIMO SYSTEM CAPACITY
 The system capacity is defined as the maximum possible transmission rate such
that the probability of error is arbitrarily small.
 We assume that the channel knowledge is unavailable at the transmitter and
known only at the receiver.
 The capacity of MIMO channel is defined as
 where f (s) is the probability distribution of the vector s and I (s; y) is the
mutual information between vectors s and y.
 where H(y) is the differential entropy of the vector y, while H(y | s) is the
conditional
 differential entropy of the vector y
 Since the vectors s and n are independent,
H(y | s) = H(n)
 If we maximize the mutual information I (s; y)
 The covariance matrix of y,
Channel Unknown to the Transmitter
 If the channel is unknown to the transmitter, then the vector s is statistically
independent
i.e., Rss = IMT
 This implies that the signals are independent and the power is equally divided
among the transmit antennas.
 The capacity in such a case is
 This is not Shannon capacity.
 Det – Deterministic Channel – not a random value – fixed or determined value.
Channel Known to the Transmitter
 To learn the channel state information (CSI) at the transmitter.
 In such an event the capacity can be increased by resorting to the so-called
‘‘water filling principle’’
 assigning various levels of transmitted power to various transmitting antennas.
 This power is assigned on the basis that the better the channel gets, the more
power it gets and vice versa.
 This is an optimal energy allocation algorithm
Random Channels
 We have until now discussed MIMO capacity when the channel is a deterministic
channel.
 We now consider the case when H is chosen randomly according to a
 Rayleigh distribution in a quasi-static channel.
 For example, in wireless LANs with high data rates and low fade rates.
 We assume that the receiver has perfect knowledge of the channel and the
transmitter has no knowledge of the channel.
 Since the channel is random, the information rate associated with it is also
random.
 The cumulative distribution function (CDF) of the information rate of a flat
fading MIMO channel is shown in Figure 2.6 for a 2x2 system.
 The SNR is 10 dB and the channel is unknown to the transmitter
 The ergodic capacity of a MIMO channel is the ensemble average of the
information rate over the distribution of the elements of the channel matrix H
 It is the capacity of the channel when every channel matrix H is an independent
realization i.e., it has no relationship to the previous matrix but is typically
representative of it class (ergodic)].
 This implies that it is a result of infinitely long measurements.
 Since the process model is ergodic, this implies that the coding is performed over
an infinitely long interval.
 Hence, it is the Shannon capacity of the channel.
 The ergodic capacity is expressed as
Ergodic Capacity
 where r = Es /N0 .
 The expectation operator applies in this case because the channel is random.
 Since H is random, the information rate associated with it is also random
 In reality, the block lengths are finite. The common example is speech
transmission.
 In such cases, we speak of outage capacity. Outage capacity is the capacity
that is
 guaranteed with a certain level of reliability
Outage Capacity
Advanced Wireless Communication-EC8092

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Advanced Wireless Communication-EC8092

  • 1. EC8092 - Advanced Wireless Communication by Mr. V. Prakash.,M.Tech. Asst.Prof / ECE Bharathidasan Engineering College Natrampalli - 635854
  • 2. Crowded Spectrum  All about SPECTRUM  Marconi pioneered wireless industry 100 years ago.  Today life is not possible without wireless  Wireless used widely in Fixed Role and Mobile Role  Fixed Role – Desktop computers and Laptop  Mobile Role – provides fast mobility in vehicles – voice and data  Wireless Design Engineers finding uphill task – limited availability of radio freq spectrum.  Time varying problems i.e fading,multipath propagation, demand of high data rates
  • 4. Interfering signals with crowded spectrum
  • 5. Need for Data Rates • Gradual Evolution of Mobile Communication – Quest for High Data Rates • Data Rate – bps • Spectral Efficiency – bps/Hz • First Mobile Communication – Analog Comm – 1st Generation. • Beginning of 1990’s – First Digital Systems emerged – 2nd Gen. • Europe introduced 2G – GSM – 900MHZ or 1800MHZ • Bit Rate – 22.8 kbps
  • 6. Bandwidth 900 MHz or 1800 MHZ Bit Rate 22.8 kbps Europe Introduced Digital Systems - 2G - GSM
  • 8.
  • 9. To satisfy higher data rates two methods were found during those days 1. HSCSD – High Speed Circuit Switched Data – 38.4 kbps 2. GPRS – General Packet Radio Service – 172.2 kbps The Demand for higher data rates forced the development of 3G  384 kbps – Mobile  1mbps for indoor
  • 10. UMTS – (Universal Mobile Telephone Systems)  Leading Technology for 3G  Also known as WCDMA – Wideband Code Division Multiple Access  Popular Technology found by ITU – International Telecommunication Union  UMTS widely used by GSM Operators – 850 million end users – 195 Countries – 70 % of today’s digital market  Japan Launched its first commercial WCDMA in 2001 then Austria,Italy,Sweden,UK….
  • 11.  An alternative to 3G is EDGE - Enhanced Data rates for Gsm Evolution  Like GSM two methods were adopted 1. ECSD – Enhanced Circuit Switched Data 2. EGPRS – Enhanced General Packet Data Service  Data rates have been enhanced - 473.6 kbps  EDGE was introduced in US
  • 12.  With 200 operators world wide – high speed data – 2.5G – GPRS technology  The new IEEE802.11 and HIPERLAN(High Performance LAN)–bit rate of 54 mbps – 24mpbs mostly used in several applications  Such high data rates pushing and carrier freq to UHF imposing the large BW  HIPERLAN occupy freq of 5GHz to 17 GHz  MBS - Multimedia Broadcasting Systems – 40 – 60 GHz  4G was first introduced in Japan in 2006  Ease in video streaming,multitmedia systems – 20 to 40 mbps
  • 13. Comparison of several systems based on Mobility and Data Rates
  • 14. Possible candidates for 4G systems • BWIF: Broadband wireless internet Forum – creating and developing next gen. fixed wirless standards. • Specifications based on VOFDM(Vector OFDM)
  • 15.  BWIF formed to address needs of quickly emerging wireless broadband market  Product road maps, lower the product costs. TD-SCDMA  Time Division Synchronous CDMA – Chinese contribution to ITU  Integrates with existing GSM  Designed to manage symmetric ckt switches (Speed &Video) and Asymmetric Swithches (Mobile Internet)
  • 16.  HSDPA  High Speed Downlink Packet Access  Packet based data service 8-10mbps (20 mbps in MIMO) over 5MHz BW channel  Includes AMC- Adaptive Modulation and Coding , Hybrid Automatic Req(HARQ), MIMO, Higspeed search of Cell.
  • 17. MIMO - Multiple Input Multiple Output Systems  Based on theoretical work developed bt Teletar and Foschini  Core of this idea – use multiple antenna for Transmission and Reception.  Increases the capacity of the WL channel  Capacity is expressed as the Max achievable data rate for low prob of error
  • 18. MIMO system pioneered by AT&T Labs-Research in Middletown, New Jersey
  • 19.  AT & T conducted field tests to characterize the mobile MIMO radio channel  measured the capacity of a system with four antennas on a laptop computer and four antennas on a rooftop base station  tests showed that fourfold increase in capacity over a single antenna system  ( can be supported in a 30-KHz channel with dual polarized spatially separated base station and mobile terminal antennas)  dual-polarized antennas separated by 11.3 feet
  • 20. Image of Dual Polarized Antenna
  • 21.  Four antennas at the transmitter and receiver has the potential to provide four times the data rate of a single antenna  system without an increase in transmit power or bandwidth  high capacities are theoretically possible
  • 22. The MIMO Wireless Channel Multiantenna Systems  Single-Input Single-Output (SISO)  Single-Input Multiple-Output (SIMO) - a single transmitting antenna and multiple (MR) receive antennas  Multiple-Input Single-Output (MISO) - multiple (MT) transmitting antennas and one receive antenna  MIMO has Multiple (MT) transmitting antennas and Multiple (MR) receive antennas and  MIMO-Multi User (MIMO-MU) - a base station with multiple transmit/receive antennas interacting with multiple users, each with one or more antennas
  • 23. Array Gain Array gain is the average increase in the signal-to-noise ratio (SNR) at the receiver that arises from the coherent combining effect of multiple antennas at the receiver or transmitter or both I.e increase in SNR due to multiple antenna at Tx and Rx MISO case Transmitter Array Gain : If the channel is known to the multiple antenna transmitter, the transmitter will weight the transmission with weights coefficients, depending on the channel coefficients, so that there is coherent combining at the single antenna receiver  SIMO case Receiver Array Gain: only one antenna at the transmitter and no knowledge of the channel and a multiple antenna receiver, which has perfect knowledge of the channel, then the receiver can suitably weight the incoming signals so that they coherently add up at the output (combining), thereby enhancing the signal
  • 24.
  • 25. DIVERSITY GAIN In a fading channel, signals experience fades (i.e., they fluctuate in their strength). This gives rise to high bit error rates (BER). Diversity used to combat fading. This involves providing replicas of the transmitted signal over time, frequency, or space  Spatial diversity Antenna elements separated by space  Temporal diversity Transmission of signals at different time  Frequency diversity Transmission of signals at different frequencies  Angular diversity Multiple antennas with different antenna patterns  Polarization diversity Multiple antenna with different polarizations
  • 26.  Transmit diversity : It is the radio communication using signals that originate from two or more independent sources that have been modulated with identical information-bearing signals and that may vary in their transmission characteristics at any given instant.  Receiver diversity: It is the independent fading paths associated with multiple receive antennas are combined to obtain a resultant signal that is then passed through a standard demodulator.
  • 27.  Polarization diversity: In this type of diversity, horizontal and vertical polarization signals are transmitted by two different polarized antennas and received correspondingly by two different polarized antennas at the receiver.
  • 28.  Angle diversity:  This applies at carrier frequencies in excess of 10 GHz.  At such frequencies, the transmitted signals are highly scattered in space.  In such an event the receiver can have two highly directional antennas facing in totally different directions.  This enables the receiver to collect two samples of the same signal, which are totally independent of each other.
  • 29. Data Pipes  The term data pipe is derived from fluid mechanics.  Pipes are used to transfer water to a tank/reservoir.  The more the number of pipes, the greater the quantum of flow of water into a tank/reservoir.  consider a case of two data pipes between the transmitter and receiver.  either the data in the data pipes are identical to each other or they are independent samples, completely different from each other  Case 1: The data through both pipes are identical. 2nd is the replica of 1st one. Full correlation. Throughput is less (Capacity).Same Data is transmitted.  Case 2: The data through both pipes are not identical. Independent.No correlation. High Throughput. No Diversity. More the pipes , more throughput.
  • 30.
  • 31. Spatial multiplexing Spatial multiplexing or space-division multiplexing (often abbreviated SM, SDM or SMX) is a multiplexing technique in MIMO wireless communication, fibre-optic communication and other communications technologies used to transmit independent channels separated in space • Spatial multiplexing offers a linear increase in the transmission rate • Same bandwidth and with no additional power expenditure • The bit stream is split into two half-rate bit streams, modulated and transmitted simultaneously from both the antennas. • The receiver, having complete knowledge of the channel, recovers these individual bit streams and combines them so as to recover the original bit stream
  • 32.
  • 33. Automatic request for repeat (ARQ).  This is an error control mechanism in which received packets that cannot be corrected are retransmitted. This is a type of temporal diversity. Forward Error Correction (FEC).  This is a technique that inserts redundant bits during transmission to help detect and correct bit errors during reception. Coding gain.  The improvement in SNR at the receiver because of FEC is called coding gain.
  • 34. MIMO System Model  Consider a MIMO system with a transmit array of MT antennas and a receive array of MR antennas
  • 35.  The transmitted matrix is a MT  1 column matrix s where si is the ith component, transmitted from antenna i.  We consider the channel to be a Gaussian channel such that the elements of s are considered to be independent identically distributed (i.i.d.) Gaussian variables.  If the channel is unknown at the transmitter, we assume that the signals transmitted from each antenna have equal powers of Es /MT .  The covariance matrix for this transmitted signal is given by
  • 36.  where Es is the power across the transmitterMT and IMT is an MT  MT identity matrix.  The channel matrix H is a MR MT complex matrix  The component hi , j of the matrix is the fading coefficient from the jth transmit antenna to the i th receive antenna.  We assume that the received power for each of the receive antennas is equal to the total transmitted power Es  we ignore signal attenuation, antenna gains, and so on  Thus we obtain the normalization constraint for the elements of H, for a deterministic channel as
  • 37.  We assume that the channel matrix is known at the receiver but unknown at the transmitter.  If we require the transmitter to know this channel, then we need to communicate this information to the transmitter via a feedback channel.  The noise at the receiver is another column matrix of size MR  1, denoted by n. The components of n are Zero Mean Circularly Symmetrical Complex Gaussian (ZMCSCG) variables.  The covariance matrix of the receiver noise is If there is no correlation between components of n, the covariance matrix is obtained as Each of the MR receive branches has identical noise power of N0 .
  • 38.  we assumed that the total received power per antenna is equal to the total transmitted power,  The SNR can be written as  Therefore, the received vector can be expressed as  The received signal covariance matrix defined as E{rrH}, is given by  while the total signal power can be expressed as tr (Rrr ).
  • 39. MIMO SYSTEM CAPACITY  The system capacity is defined as the maximum possible transmission rate such that the probability of error is arbitrarily small.  We assume that the channel knowledge is unavailable at the transmitter and known only at the receiver.  The capacity of MIMO channel is defined as  where f (s) is the probability distribution of the vector s and I (s; y) is the mutual information between vectors s and y.  where H(y) is the differential entropy of the vector y, while H(y | s) is the conditional  differential entropy of the vector y
  • 40.  Since the vectors s and n are independent, H(y | s) = H(n)  If we maximize the mutual information I (s; y)  The covariance matrix of y,
  • 41. Channel Unknown to the Transmitter  If the channel is unknown to the transmitter, then the vector s is statistically independent i.e., Rss = IMT  This implies that the signals are independent and the power is equally divided among the transmit antennas.  The capacity in such a case is  This is not Shannon capacity.  Det – Deterministic Channel – not a random value – fixed or determined value.
  • 42. Channel Known to the Transmitter  To learn the channel state information (CSI) at the transmitter.  In such an event the capacity can be increased by resorting to the so-called ‘‘water filling principle’’  assigning various levels of transmitted power to various transmitting antennas.  This power is assigned on the basis that the better the channel gets, the more power it gets and vice versa.  This is an optimal energy allocation algorithm
  • 43.
  • 44.
  • 45.
  • 46.
  • 47. Random Channels  We have until now discussed MIMO capacity when the channel is a deterministic channel.  We now consider the case when H is chosen randomly according to a  Rayleigh distribution in a quasi-static channel.  For example, in wireless LANs with high data rates and low fade rates.  We assume that the receiver has perfect knowledge of the channel and the transmitter has no knowledge of the channel.  Since the channel is random, the information rate associated with it is also random.
  • 48.  The cumulative distribution function (CDF) of the information rate of a flat fading MIMO channel is shown in Figure 2.6 for a 2x2 system.  The SNR is 10 dB and the channel is unknown to the transmitter
  • 49.  The ergodic capacity of a MIMO channel is the ensemble average of the information rate over the distribution of the elements of the channel matrix H  It is the capacity of the channel when every channel matrix H is an independent realization i.e., it has no relationship to the previous matrix but is typically representative of it class (ergodic)].  This implies that it is a result of infinitely long measurements.  Since the process model is ergodic, this implies that the coding is performed over an infinitely long interval.  Hence, it is the Shannon capacity of the channel.  The ergodic capacity is expressed as Ergodic Capacity
  • 50.  where r = Es /N0 .  The expectation operator applies in this case because the channel is random.  Since H is random, the information rate associated with it is also random
  • 51.  In reality, the block lengths are finite. The common example is speech transmission.  In such cases, we speak of outage capacity. Outage capacity is the capacity that is  guaranteed with a certain level of reliability Outage Capacity