Space Time Coding and Channel Estimation By Orhan GAZI 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Outline Spatial Multiplexing Space Time Coding MIMO Channel Capacity MIMO channel estimation Our aim 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Spatial Multiplexing 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Data is divided into data streams Each stream is sent with an antenna Multiplexing gain is maximum The received symbols are decoded using different techniques Maximum Likelihood (ML) receiver Minimum Mean Square Error receiver ZF receiver 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Spatial Multiplexing Maximum multiplexing gain Maximum data transmission What about the system performance? - What about BER vs SNR graph - Is it the best one? 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi NO !! 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

For a better system performance Increase diversity Increase coding gain 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Diversity Spatial Diversity - Transmit diversity - Receive diversity Path Diversity - Time diversity - Frequency Diversity - Polarization Diversity 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Spatial Diversity More than one transmit antenna at the transmit side - Transmit diversity More than one receive antenna at the receiver side Receive diversity 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Correlation occurs if antennas are spaced at a distance d which is smaller than the half transmit wavelength. 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Path Diversity Frequency diversity Different frequencies are used to send the same symbol 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Delay Diversity Symbol and its delayed version are transmitted 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Polarization Diversity Antenna polarization is employed for diversity 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

How is the effect of diversity gain on the performance Diversity increases the slope 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Space Time Block Code Alamouti discovered space time block codes -He used 2 transmit antennas instead of one single antenna. -1 receive antenna is employed at the receiver side 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Alamouti transmit system 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Comparison with the classical one transmit two receive antenna case Slopes are the same 3dB loss in performance due to the power division between two transmit antennas 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Following Studies after Alamouti Tarokh worked on Space Time Codes Alamouti code only gives diversity gain Tarokh generalized Alamouti’s work for any number of transmit and receive antennas. Designed space time codes for real and complex signals. 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Tarokh discoveries on STBC For real signals full rate space time codes exist for only 2,4 and 8 transmit antennas. If transmission rate is not full, then is possible to construct space-time block codes for any number transmit antennas 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi for complex signals Full rate space time code exists for only two transmitter antenna case Rate ¾ complex orthogonal codes exists for 3 or 4 transmit antennas. Rate ½ complex orthogonal codes exists for any number of transmit antennas If Tx >4 then it is not possible to find a code with rate >1/2 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Examples ¾ complex orthogonal codes 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Trellis Codes Tarokh also designed space time trellis codes Space time trellis codes provides Diversity gain Coding gain Slope increases ( Diversity Gain), curve shifts to left (Coding Gain) 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Any Space Code Design Although Tarokh worked on STBC and STTC, his ideas can be generalized for any space time code design. While designing space time code we should try to maximize the diversity and coding gain 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Code Design Criteria The transmitted code matrix is C The received code matrix is C’ Error matrix E=(C-C’)(C-C’)T M is the number of receive antennas r is the rank of E is the eigenvalues of E 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Is called diversity gain Is called coding gain 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Rank Criterion To achieve maximum diversity the error matrix E must have full rank for any pair of distinct code words C and C’ Determinant Criterion - For the maximization of the coding gain the determinant of the error matrix must be maximized for a given target diversity order 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Multi Input Multi Output Communication System 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi N the number of transmit antennas M the number of receive antennas H the channel matrix between transmitter and receiver. S is the transmitted symbol data matrix Y is the received symbol data matrix Y=HS+N N is AWGN 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Ex N=3 M=4 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi MIMO Channel Capacity When channel knowledge is available at the receiver r is the rank of the channel and is are the positive eigenvalues of the HHT 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi When N=M, the channel capacity is given as TheMIMO channel capacity is N times SISO channel capacity 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

When channel knowledge is available at the transmitter side r is the rank of the channel matrix H 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi This idea is called water pouring Allocate power according to channel eigenvalues Give more power to larger eigenvalues Capacity is greater than the NO CSI at the transmitter but only at the receiver case. 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi The mentioned formulas are for static flat fading channels. 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi What about random channels 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi For random channels Ergodic Capacity Outage probability Outage Capacity 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Ergodic capacity is the expected value of the capacity over the distribution of the channel elements Outage probability is the probability that given a transmission rate R and transmit power constraint the channel capacity cannot support reliable communication Given an outage probability, the maximum information rate that can be supported by the communication channel is called the outage capacity of the channel P{C<Cout}=Pout 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

MIMO Channel Estimation Methods *Blind * *Training Based* 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Practical systems use training based channel estimation Ex: GSM frame structure Figure taken from* Tapio Mikael, Channel Estimation, Ms Thesis,Goteborg Sweden 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Complete System 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Channel Matrix Estimation Using the received signal matrix and knowing the transmitted training signal matrix, the MIMO channel matrix can be found with maximum likelihood method or minimum mean square error method Y is the received signal matrix, S is the sent training matrix 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Another approach to estimate the channel is to transform the received data linearly so as to minimize the estimation error and it is given as Y is the received signal matrix, S is the transmitted training signal matrix, is the average signal to noise ratio, I is the identity matrix 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Pilot Insertion methods Figure taken from Tapio Mikael, Channel Estimatio, Ms Thesis, Goteborg Sweden 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi

Space Time Coding and Channel Estimation by Orhan Gazi Our Initial Goal Using superimposed channel estimation technique and space time code design principles, a better MIMO communication system is to be designed 11/7/2018 Space Time Coding and Channel Estimation by Orhan Gazi