EE 552/452 Wireless Communications (and Networks) 2007 Class Notes PDF

EE 552/452, Spring, 2007 Wireless Communications (and Networks) Zhu Han Department of Electrical and Computer Engineering Class 19 March 22nd, 2007  Outline  Review – Equalization...

EE 552/452, Spring, 2007 Wireless Communications (and Networks) Zhu Han Department of Electrical and Computer Engineering Class 19 March 22nd, 2007  Outline  Review – Equalization – Purpose? – Classification – Examples  Diversity EE 552/452 Spring 2007 Overcoming Channel Impairments Deep Fading Channel Coding EE 552/452 Spring 2007  Diversity Techniques  Requires no training overhead  Can provides significant link improvement with little added cost  Diversity decisions are made by the Rx, and are unknown to the Tx  Diversity concept – If one radio path undergoes a deep fade, another independent path may have a strong signal – By having more than one path to select from, both the instantaneous and average SNRs at the receiver may be improved, often by as much as 20 dB to 30 dB – Diversity order  How many independent copies  How many links to bring down the system EE 552/452 Spring 2007  Diversity Motivation  Aim: Reduce effects of fast fading – Concept:  Multiple branches, independent fading  Process branches to reduce fading probability – If probability of a deep fade on one channel is p, probability on N channel pN. – e.g. 10% chance of losing contact for one channel becomes 0.13=0.001=0.1% with 3 channels  Requirements for Diversity – Multiple branches – Low correlation between branches – Similar mean powers: – Efficient combiner EE 552/452 Spring 2007  Diversity Example EE 552/452 Spring 2007  Different Diversity  Spatial Diversity – Multiple input multiple out system (MIMO) – Beamforming, smart antenna – Space time coding – Horizontal and Vertical Combining  Frequency diversity – Frequency diversity transmits information on more than one carrier frequency – Frequencies separated by more than the coherence bandwidth of the channel will not experience the same fads  Time diversity – Time diversity repeatedly transmits information at time spacings that exceed the coherence time of the channel  Polarization diversity  Multi-user diversity EE 552/452 Spring 2007  Space Diversity  Large antenna spacing or large scatterer spacing produce large path length differences  Hence multipath will combine differently at each antenna EE 552/452 Spring 2007  Analysis of Space Diversity  Phase difference:  exp(  jkd sin  )  Signals from one scatterer: 1 r  2 re j ns ns  Signals from ns scatterer: 1   ri  2   ri e ji  Correlation: ns i 1 ns i 1      Evaluate expectation 2 12 E    i 1 exp(  ji ) E     i 1 exp( jkd sin  i )  12 (d )  p( ) exp( jkd sin  )d  0 Angle-of-arrival PDF EE 552/452 Spring 2007  Horizontal Space Diversity EE 552/452 Spring 2007  Vertical Space Diversity  Restricted vertical angle spread, so greater separation needed in vertical direction EE 552/452 Spring 2007  Polarisation Diversity  Scattering shifts and decorrelates polarisation  Advantage: Very compact  Disadvantage: Unequal branch powers - less diversity gain EE 552/452 Spring 2007  Polarization diversity  Theoretical model for polarization diversity – the signal arrive at the base station x r1 cos(t  1 ) y r2 cos(t  2 ) – the correlation coefficient can be written as 2  tan 2 ( ) cos2 (  )      2 2   tan ( ) cos (  )    R22   R12 R1  r12a2  r22b2  2r1r2ab cos(1  2 ) R1  r12a2  r22b2  2r1r2ab cos(1  2 ) EE 552/452 Spring 2007  Polarization diversity Theoretical Model for base station polarization diversity based on [Koz85] EE 552/452 Spring 2007  Time Diversity  Retransmit with Time Separation  Advantage: Need only one receiver  Disadvantage: Wastes bandwidth, adds delay EE 552/452 Spring 2007  Frequency Diversity  Wideband Channel  Simultaneous Transmission  Wastes power and bandwidth  Equalizers Channel Spectrum Frequency EE 552/452 Spring 2007  Combining Techniques  How to combine the multiple received copies – Selection diversity – Feedback diversity – Maximal ration combining – Equal gain diversity EE 552/452 Spring 2007  Selection diversity  The receiver branch having the highest instantaneous SNR is connected to the demodulator  The antenna signals themselves could be sampled and the best one sent to a single demodulation EE 552/452 Spring 2007  Selection Combining EE 552/452 Spring 2007  Derivation of Selection Diversity  Microscopic diversity and Macroscopic diversity – The former is used for small-scale fading while the latter for large-scale fading – Antenna diversity (or space diversity)  Performance for M branch selection diversity PrSNR  r  1  Pr1 ,.... , M r  1  (1  e  r/ )M d    PM (r)  Pr SNR r  (1  e  r/ )M  1 e  r/ dr Γ r M 1   k 1 k EE 552/452 Spring 2007  Performance  Example 7.4 Graph of probability distributions of SNR= threshold for M branch selection diversity. The term  represents the mean SNR on each branch EE 552/452 Spring 2007 Effect of Varying Branch Mean Powers EE 552/452 Spring 2007  Maximal Ratio Combining Diversity  The signals from all of the M branches are weighted according to their signal voltage to noise power ratios and then summed  Like stock investigation M M  Gii M N T  N  Gi 2 M2 rM  i 1 i 1 2 NT 2 1 N 2 2  N  N N N M  ( i ) 2 E   ni i  ( i ) PN  i  i * 2 2 2 2 i 1  i 1  i 1 i 1 i 1 r  r/ M ( r /  )k  1 Pr{rM r} p( rM )drM 1  e  0 k 1 ( k  1)! M  1  rM /  rM e P( rM )  M  ( M  1)! EE 552/452 Spring 2007  Varying Branch Correlations EE 552/452 Spring 2007 Effect of Non-zero correlation on MRC EE 552/452 Spring 2007  SNR for BPSK with MRC EE 552/452 Spring 2007  Feedback diversity  The signal, the best of M signals, is received until it falls below threshold and the scanning process is again initiated EE 552/452 Spring 2007  Switched Combining  Avoids multiple receivers  Switch and stay strategy  Must set appropriate threshold relative to mean level  Performance always worse than selection combining EE 552/452 Spring 2007  Equal Gain Combining  The branch weights are all set to unity but the signals from each are co-phased to provide equal gain combining diversity  Make use of energy in all branches EE 552/452 Spring 2007  Equal Gain Combining Performance x1 s1  n1  Received signals: x2 s 2  n2  Combiner output: y  x1e  j1  x2 e  j 2 ( sr1e j1  n1 )e  j1  ( sr2 e j 2  n2 )e  j 2 s (r1  r2 )  n1e  j1  n2 e  j 2  SNR: (r1  r2 ) 2 2 c   2   j1 E n1e  n2e  j 2 2    1  2  2 12 (r1  r2 ) 2 c   2 4 PN EE 552/452 Spring 2007 Comparison of Combining Techniques EE 552/452 Spring 2007  RAKE Receiver M Z m2 Z   m Zm m  M m 1  Z m2 m 1 An M-branch (M-finger) RAKE receiver implementation. Each correlator detects a time shifted version of the original CDMA transmission, and each finger of the RAKE correlates to a portion of the signal which is delayed by at least one chip in time from the other finger. EE 552/452 Spring 2007  Interleaving Block interleaver where source bits are read into columns and out as n-bit rows EE 552/452 Spring 2007  Questions? EE 552/452 Spring 2007