Fundamentals of Short Range Wireless: Outline

1. Fundamentals of Short Range Wireless: Outline • Digital transmission and detection on the AWGN channel • digital transmission systems • equivalentbasebandmodel • digital modulationand ML-detection • Fading channels • fading channels • diversity • MIMO wireless • Modulation schemes for frequency selective channels • multicarrier modulation • Orthogonal Frequency Division Multiplexing (OFDM) Communication Technology Laboratory Wireless Communication Group

2. Frequency-Flat Fading Channel • block fading: fading variable instead of fading process • note multiplication with magnitude of fading variable due to • channel matched "filter" • normalization of decision vector channel matched "filter" fading channel Symbol discrete system model with block fading Communication Technology Laboratory Wireless Communication Group

3. In frequency-flat block fading the error performance of QPSK is determined by the instantaneous value of the fading variable We can define various figures of merit. Frequently used are outage probability: probability, that the instantaneous bit error probability is above a target value fading averaged bit error probability Clearly these figures of merit depend on the probability density function (pdf) of the fading amplitude here is a chi2 random variable with 2 degrees of freedom Error Performance of QPSK in Frequency-Flat Block Fading fading averaged bit error probability Communication Technology Laboratory Wireless Communication Group

4. Special case L=1 the fading variable z is complex normally distributed; is the sum of two statistically independent squared real-valued normal random variable If , is Rayleigh distributed; Rayleigh fading if , is Rician distributed. K-factor: General case L=N: N-fold diversity For , is the sum of 2L squared real-valued Gaussian random variables chi2-distribution with 2L degrees of freedom e.g. achievable with L receive antennas Approximation: BER (c/SNR)L Diversity fading averaged bit error probability Communication Technology Laboratory Wireless Communication Group

5. Vector/Matrix Channels • Single Input/Single Output (SISO) • channel coefficient • Single Input/Multiple Output (SIMO) • channel vector • Multiple Input/Multiple Output (MIMO) • channelmatrix 5

6. Multipath Propagation, Narrowband Fading location dependant: cf. spatial diversity • Multipath propagation: • constructive and destructive interference • random fluctuations of receive power – (small-scale) Fading • strong influence on quality of the transmission • no direct path:Rayleigh Fading mean Diversity, MIMO

7. Diversity Techniques Wireless channel varies in time, frequency and space Time, frequency and space diversity available Examples: Time diversity: repeat same codeword after channel varied (Repetition Code) Frequency diversity: transmit same symbol over two or more OFDM sub-carriers (if fading of the sub-carriers is uncorrelated) Space diversity: use more than one antenna at RX or TX or on both sides (But usually pure repetition is not an efficient way to code: repetition of the same information in time or frequency sacrifices bandwidth => space diversity seems promising) 7 Diversity, MIMO

8. Spatial (or Antenna) Diversity RX TX • Receive diversity: using NRX receive antennas • (spatial dimension) • Transmit diversity: in addition a temporal coding needed • => Space-Time Codes • High diversity factors available for high carrier frequencies and large bandwidths 8 Diversity, MIMO

9. System Model with RX Diversityand Maximum Ratio Combining (MRC) • note multiplication with magnitude of fading vector due to • channel matched "filter" • normalization of decision vector channel matched "filter" block fading vector channel Scalar symbol discrete system model Communication Technology Laboratory Wireless Communication Group

10. Probability of Error RX TX • Receive diversity:hi: channel gain between the TX antenna and the RX antenna i new argument of Q-Function: 10 Diversity, MIMO

11. Array Gain and Diversity Gain Array (Power) gain Diversity gain • 3 dB gain per • doubling of the • number of RX antennas • Expression converges to constant for increasing NRX • i.e. fading is eliminated in the limit 11

12. Diversity / Beamforming Techniques and Channel Knowledge • Channel State Information at the Rx (CSIR): • Our usual assumption: CSIR is available at the Rx, e.g. a training sequence (pilots) in the burst of Tx is used to estimate CSIR at Rx • MRC needs CSIR • Channel State Information at the Tx (CSIT) • With CSIT beamforming at the Tx is possible (smart antennas) • coherent combining (Tx array gain) • Without CSIT: Transmit diversity schemes (e.g. Space-Time Codes, Delay Diversity) Diversity, MIMO

13. Multiple Input/ Multiple Output • Single Input/Single Output (SISO) • channel coefficient • Single Input/Multiple Output (SIMO) • channel vector • Multiple Input/Multiple Output (MIMO) • channel matrix 13

14. MIMO Channel - Notation MIMO channel matrix (flat fading model): NTX: number of TX antennas, NRX: number of RX antennas NRX Received signal: Or often normalized: NTX Diversity, MIMO

15. Free Space vs. Multipath Propagation scattering fading 15

16. Multiple Antennas and Spatial Multiplexing Channel Matrix Singular Value Decomposition unitary • full rank • 3 spatial subchannels • spatial multiplexing rank 1 16

17. MIMO Wireless Capacity (1) RX TX • MIMO channel capacity grows nearly linearly with N = min(NTX, NRX)[Foschini, Gans, 1998][Telatar, 1999] K-factor of Rician fading • Higher data rate without need of higher bandwidth=> spectral efficiency • N decoupled spatialsub-channels available (Spatial Multiplexing) 17 Diversity, MIMO

18. MIMO Wireless Capacity (2) RX TX K-factor of Rician fading Telatar, Foschini: NTX: number of TX antennas, NRX: number of RX antennas. 18 Diversity, MIMO

19. MIMO Wireless Capacity (3) Rank, Eigenvalues of a MIMO channel λi(M): Eigenvalues of matrix M i(M): Singularvalues of matrix M N: Channel rank With CSIT: the power the TX spends per Eigenvalue can be optimized (Water-filling algorithm) Diversity, MIMO 19

20. MIMO Wireless Capacity (4) • λi: Eigenvalues of the matrix HHH • N: Rank of channel matrix H w1 s1 r1 ... ... ... wN sN rN + + • With CSIT: TX power per Eigenvalue to be optimized (Water-filling algorithm): SNR -> SNRi Diversity, MIMO

21. Spatial Multiplexing Gain N • MIMO channel capacity grows nearly linearly with N = min(NTX, NRX) Diversity, MIMO

22. MIMO Systems: Spatial Subchannels Subchannels A priori Tx channel state information (CSIT) necessary ! TX Diversity: Take only the “best“ Subchannel, or repeat over all ! Spatial Multiplexing: Take all (no repetition) ! SVD of MIMO channel matrix: 22 Diversity, MIMO

23. MIMO Systems without CSIT: Spatial Subchannels Receiver has to compensate ISI due to V (cf. BLAST); if no a priori CSIT: TX Combining not possible;Spatial multiplexing leads to ISI 23 Diversity, MIMO

24. BLAST Architecture [Gesbert, et al.: From Theory to Practice: An Overview of MIMO Space–Time Coded Wireless Systems] 24 Diversity, MIMO

25. Fundamentals of Short Range Wireless: Outline • Digital transmission and detection on the AWGN channel • digital transmission systems • equivalent baseband model • digital modulation and ML-detection • Fading channels • fading channels • diversity • MIMO wireless • Modulation schemes for frequency selective channels • multicarrier modulation • Orthogonal Frequency Division Multiplexing (OFDM) Communication Technology Laboratory Wireless Communication Group