EE 615 Lecture 7

1. October 12, 2006 EE 615 Lecture 7 Space (Antenna) Diversity

2. October 12, 2006 HW Due today: Implement OFDM with 9Mbits/sec and check performance with different rms delay spread values.

3. October 12, 2006 MC Modulation & Demodulation IFFT for Mod, addition of cyclic prefix at TX. Removal of cyclic prefix, FFT for Demod.

4. October 12, 2006 Antenna Diversity Increase link performance or throughput OMOD: OFDM Modulation ODEMOD: OFDM Demodulation

5. October 12, 2006 Definitions No. of transmit Antennas N No. of Receive Antennas M Noise at each receiver vi(t) iid Gaussian process, w/ power N0 Average SNR at each receiver g=P/ N0 Channel impulse response h(t)NxM H(f)=DFT{h(t)}

6. October 12, 2006 Capacity [Shannon] Maximum achievable throughput without distortion (asymptotically error free data) Multiple parallel channel capacity.  For parallel independent channels, let H=IN

7. October 12, 2006 Additive White Gaussian Noise Channel Capacity scales linearly with number of channels rather than logarithmically Benefit of parallel transmission!

8. October 12, 2006 The assumption: independent channels, in reality interference / correlation between channels What to do if channel is not AWGN?

9. October 12, 2006 Fading Channels Diversity at receiver (even if single tranmitter) increases capacity Linear combination of antenna outputs to maximize SNR. Selection Diversity (choose antenna with

10. October 12, 2006 Observations Rayleigh channel HMxN entries iid complex Gaussian RV Note: Sum of squares of k iid squared zero mean Gaussian RV is chi-squared RV with k degrees of freedom. Special Cases: M=N=1 No Diversity M=n,N=1, Receive Diversity M=1, N=n, Transmit Diversity

11. October 12, 2006 Tx Diversity Does not improve SNR by Since, the total power is constrained Combine Tx Diversity w/ Rx Diversity, N>=M If channel is known by both transmitter and receiver simultaneously

12. October 12, 2006 Cyclic Delay Diversity One transmitter of N transmit antennas is delayed to N-1 antennas and received by M antennas.

13. October 12, 2006 Channel Model MIMO N transmitter, M receiver antennas

14. October 12, 2006 Diversity Temporal when time selective Interleaving Spectral when frequency selective DSSS, FHSS, OFDM Spatial due to multiple antennas Transmit vs Receive Diversity

15. October 12, 2006 Selection Diversity Simple, 802.11b WLAN use it at AP/MT Choose, receive antenna with largest SNR, each antenna subject to independent & identically distributed Gaussian noise. Therefore, select receive antenna with largest instantaneous power.

16. October 12, 2006 Selection Diversity The probability that SNR (g) among the is less than z, is the cdf of the R.V.

17. October 12, 2006 Selection Diversity Simple All receive antennas share same RF receiver chain.

18. October 12, 2006 Maximal Ratio Combining Maximize instantaneous SNR

19. October 12, 2006 Maximal Ratio Combining MRC combining can be large even if individual SNRs are small. For two receivers: MRC provides nearly 10dB improvement at 1% BER, while selection diversity 2-3dB. MRC is optimum solution. Assumes perfect channel knowledge, which is subject to estimation errors which in turn depends on SNR�

20. October 12, 2006 Equal Gain Diversity Weights for MRC are all set to unity. Modify MRC module in the Website to perform task and plot selection diversity, equal gain diversity and MRC

21. October 12, 2006 Transmit Diversity Criteria, to minimize BER typically maximum likelihood Types: Delay Diversity Trellis Space Time Codes Layered Space Time Codes Block Space Time Codes

22. October 12, 2006 Transmit Diversity Receive diversity beneficial, but impractical for Mobile Terminals, the diversity branches should be separated several wavelengths, several feet �for 1 GHz, 30cm=1 foot wavelength Using multiple antennas at transmitter, spatial diversity can be exploited.

23. October 12, 2006 Transmit Diversity Criteria for Fading Channel N transmittter M receive antennas Design depends on channel Criteria: Minimize pairwise error probability (PEP)

24. October 12, 2006 Chernoff Upper Bound Solving for PEP difficult, Chernoff bound instead� For tightest bound optimize l:

25. October 12, 2006 Delay Diversity Repeat transmission on N antennas Received signal:

26. October 12, 2006 Decoding for Delay Diversity Assuming perfect knowledge of channel at the receiver, solve:

27. October 12, 2006 Space Time Codes Trellis Layered Space Time, Bell Labs Multiplexing bits in a hierarchical manner Block Space Codes Decoding complexity lower than Trellis No Loss in BW, orthogonal designs, no coding gain, simple implementation

28. October 12, 2006 Trellis Code Four State STC using QPSK

29. October 12, 2006 Trellis 8 state, 16 state diversity order 2

30. October 12, 2006 STTC QPSK, 2bps/Hz, Diversity order 4, 2 rx, 2tx antennas

31. October 12, 2006 Multicarrier and Space Time The space time coding can be concatenated to the modulation either before or as shown after the DFT

32. October 12, 2006 Comparison of STTC OFDM 24 Mbit/s 802.11a compare with SSTC 24Mbps, 2Tx, 1Rx, 16-ary sphere decoder, delay diversity, STC,

33. October 12, 2006 Space-Time Codes Assuming ideal channel state information, PEP derived from the Chernoff bound:

34. October 12, 2006 Criteria Distance/Rank Criterion: To achieve diversity of pm in a fading channel with codewords c and e, codewords must be different for at least p values Product/Determinant: To achieve most coding gain, the minimum squared product distance must be maximized

35. October 12, 2006 Decoding Trelllis Trellis, using state transition. For K memory element conv. Encoder, there are 2^K states.

36. October 12, 2006 Observations The determinant criteria can be maximized by equal eigen values

37. October 12, 2006 Layered Space Time Codes Multiplex multiple streams at transmitter with N antennas At receiver, suppress interfering N-1 antennas by spatial filtering iteratively. First assume, antenna 1 is desired, decode, then treat antenna 2 as desired, etc. Powerful coding techniques are needed, the rate and diversity are traded off.

38. October 12, 2006 Waterfilling Power allocation Bit Loading

39. October 12, 2006 HW due 10/19 Due next week: Exercise 5 on p150-151: Compare performances of 2x2 block STC w/QPSK to 2 receive w/ MRC in 5 tap Rayleigh fading channel. Exercise 1&2 Exercise 3, Comparison of MRC vs EGC Exercise 4 Delay diversity Exercise 5 Space Time Block Code