PhD Qualifying Exam University of Utah Dept. of ECE David Landon

1. PhD Qualifying ExamUniversity of UtahDept. of ECEDavid Landon

2. My Area of Focus • Background • DSP, communications, Modem design at L-3 • Coursework • Inversion, Adv. Commumications, Numerical E&M • Research Plan • Antenna optimization for MIMO systems • Relevance of these papers • Good survey of MIMO and multi-user communication issues

3. Presentation of Literature • Wallace, J.W.; Jensen, M.A.; Swindlehurst, A.L.; Jeffs, B.D.; “Experimental Characterization of the MIMO Wireless Channel: Data Acquisition and Analysis,” IEEE Trans. Wireless Communications, vol 2, no 2, pp. 335-343, Mar 2003. • Jensen, M.A.; Wallace, J.W.; “A Review of Antennas and Propagation for MIMO Wireless Communications,” IEEE Trans. Antennas and Propagation, vol 52, no 11, pp. 2810-2824, Nov 2004. • Onggosanusi, E. N., Sayeed, A. M., Van Veen, B. D., “Multi-Access Interference Suppression in Canonical Space-Time Coordinates: A Decentralized Approach,” IEEE Trans. on Communications, vol 50, no 5, pp. 833-844, May 2002.

4. Introduction • Multi-antenna communications systems • Single vs. multi-user • Capacity • Multiple access interference suppression

5. Paper #1Measuring a NLOS channel &diminished returns for array size

6. Experimental Characterization of the MIMO Wireless Channel:Data Acquisition and Analysis • Data acquisition • Channel estimation • Statistics of channel matrices • Polarization • Diminishing returns

7. Platform for Channel Estimation • 2.45 GHz, 25 kHz BW • 2, 4 or 10 antennas • Channel: all indoor, NLOS • Estimate Channel Matrix, H, where y = Hp (p for PN) p H y

8. Estimating Channel Matrix from Data • PN code alignment (Ω, pn[k]) • FFT peak (Ω) • Test each alignment of each code (pn[k]) • Carrier Recovery (φk) • H obtained via least-squares (matrix inversion)

9. Preview of Results • Statistical Characterization for modeling • Hmn Rayleigh • High temporal correlation (night vs. day) • Spatial correlation problematic • Capacity Measurements • Waterfilling capacity • Dual vs. Single polarized antennas • Diminishing returns

10. Capacity: channel quality • Capacity is the maximum data rate for error-free communication • Single channel C = log2( 1+ SNR ) • MIMO Capacity • MIMO gains: • log2(1+20) = 4.4 • 2*log2(1+20/2) = 6.9 • Antenna strategies impact capacity

11. 1/λ3 Q22 Q11 1/λ2 1/λ1 Waterfilling capacity • Optimal power allocation • Fill best eigenchannels first

12. Per Channel Capacities CCDF • MIMO Capacity scales with min(NT, NR, L) • For large L, per channel capacity is constant • Monte-Carlo simulations give CCDF of capacity • Step function means delta function in PDF

13. Wallace’s Simulated vs.Measured Results • Wallace’s simulations match mine • Wallace concludes that there is a law of diminishing returns • Wallace fails to conclude that L is too small

14. Suppose we do not water-fill With Without Waterfilling • Identical realizations of H • Only slightly lower capacities without water-filling • H is i.i.d., justified by statistical characterization

15. Conclusions:Significance of results • Indoor channel model with Rayleigh distribution is good. • When antennas are closely spaced, consider orthogonal polarizations. • Capacity for a channel is bounded leading to diminishing returns on element count.

16. Conclusions:Significance of the work • Not a groundbreaker • Solid, elegant results • Well-cited • Relevant • Good how-to for confirming my results • Cautious affirmation of Rayleigh model • Warning about using Jake’s model • Warning about large antenna element counts

17. Conclusions:Extending Wallace’s research • Widen BW: is fading flat? • Put transmitter outside (i.e. cell B.S.): is the Rayleigh model still useful? • Put the receiver on a vehicle: what are the Doppler effects and the delay spread? • Re-simulate sSP with mutual coupling: does that adequately predict model behavior? • Vary antenna spacing: why does Jakes’ model only poorly predict element coupling?

18. Paper #2Blind detectionwith MAI suppression

19. Multi-Access Interference Suppression in Canonical Space-Time Coordinates: A Decentralized Approach • Canonical Space-Time Coordinates (CSTC) • Estimate data of desired user: efficiently exploit time & spatial dimensions • MAI suppression: an example with near-far • Faster channel estimation, more robust

20. Canonical Space-Time Coordinates:a new basis • Represent signal content in new basis • Use orthogonal array steering vectors • Non-orthogonal delayed copies of PN code CSTC

21. Representing a signal using CSTC • K, k: simultaneous users of the channel • b: transmitted bit • r(t): received signal • A: spatial basis • Q: temporal basis • H: time-, space-dependent channel matrix

22. A simpler formulation • Stack r(t), Hk, n(t) into tall column vectors • Use vec(AHQT) = Q A vec(H)=Bh

23. Estimate data of desired user:(1) without MAI • Suppose we had just r = bBh • Remove B via its pseudo-inverse: y = B†r = bh • Obtain b via maximal ratio combining (MRC)

24. Estimate data of desired user:(2) with MAI • Form y as before, y = B†r • B = [ BABI ] • Here spatially limited, not temporally

25. Estimate data of desired user:LCMV detector Combine y = bh + MAI into estimate of b Base combiner on correlation statistics For known H, this is easier than a decentralized computation based on Rnn=Ryy-Rss

26. An example • Delay spread less than symbol period • 8 user CDMA via length-31 Gold codes • Try to recover b1

27. MAI suppression for various BA, BI • SINR decays rapidly for MRC, active only • Various selections of B = [ BA BI ] improve MAI significantly • Good in near-far situations SINR

28. My results • Good agreement

29. Dependence on H • As H becomes degenerate, signal recovery degrades

30. Robust to channel estimation errors σε2=0 σε2=0.01 • CDF beats CSTC when estimation perfect • C-MRC best for poor estimation • MRC without MAI suppression • serial cancellation structure: gA=estimate of h1

31. Conclusions: Significance of results • Effective detection in the presence of MAI • Results are somewhat channel dependent • More robust than CDF to channel estimation errors • Efficient • Lower dimensionality means fewer samples needed to estimate the channel • Accommodates shorter coherence times

32. Conclusions:Significance of the work • Brilliant • Novel approach • New, unproven • Relevance • Muli-user not single user MIMO • Interference suppression useful • May not apply until later in my research • Mind-stretching

33. Conclusions:Extensions on Onggosunasi’s work • How dependent are results on the channel matrix? • How well would measurements match predictions? • What level of hardware simplification is likely?

34. Paper #3Losses due to array density & an upper limit on capacity

35. A Review of Antennas and Propagation for MIMO Wireless Communications • Measuring and modeling channels • Key MIMO results from the perspective of antennas and propagation • Antenna array properties lead to points of diminishing returns for channel capacity

36. Measuring and modeling channels • Parallel measurement: costly▼ • Switched or simulated (moved) arrays: temporal, coupling weaknesses▼ • Double-directional (DOA, DOD, path gain--Hmn,TOA): decouples apparatus and channel▲ • i.i.d. CN(0,σ2) • Separable Kronecker product: J0 Bessel▼ • Deterministic ray tracing + diffraction theory • Statistical placement of discrete scatterers • Cluster models with exp. decay: more accurate▲ underestimate▼ Measurements Simulations Paper #2

37. Preview of Results • Mutual coupling leads to capacity loss • Intrinsic capacity • NLOS capacity gains higher than LOS • Capacity not just a function of min(NT,NR) • Dipoles outperform multimode (premature) • Subset selection of arrays • Cube and 6-degree polarization diversity Paper #2

38. Preview: Mutual Coupling • Fix array size and vary element count • Capacity decreases for increased array density • Required study of Janaswamy’s original paper Capacity

39. Mutual Impedance ** • Energy coupled from one antenna to another • Sources “see” more impedance due to “competition from other driving voltages, Vsj (**) Taken from the original source cited in Jensen’s review.

40. Impedance • Infinite array assumption (ignore edge effects) • Voltage at antenna formed via voltage divider of source, mutual impedance network: ZT = ZT(ZT+Zs)-1 • Radiated power smeared via coupling from one channel into another (ZT is not diagonal) • Noise stays constant • SNR for any channel deteriorates

41. SNR degradation ** • SNR ~ Trace( ZT ZT†) Trace( ZR†ZR) • When element count > 10 (spacing < λ/2) SNR decays • Capacity is optimized when radiated power is held constant [**] SNR

42. Additional modeling assumptions • (v) separable Kronecker product of spatial correlation (transmitter and receiver widely separated and uncoupled) • Spatial correlation, J0 Bessel

43. Mutual Coupling • Significance: Capacity actually decreases for tightly spaced arrays (due to lowered effective SNR) • Cap ~ log2( 1+ SNR ) ~ log2( I + det((ZTΨTHZRΨR)2) )

44. Intrinsic capacity result ** Significance: • capacity levels off • Here, 16 elements may suffice • Intrinsic capacity helps identify L Capacity

45. Intrinsic capacity method • Integration over receive & transmit volumes • Using basis elements **

46. Conclusions:Significance of results • Avoid mutual coupling (dense arrays) where possible • Intrinsic capacity gives upper bound • NLOS capacity gains higher than LOS • Diversity can improve on min(NT,NR) • Subset selection of arrays adequate • Polarization diversity should be exploited

47. Conclusions:Significance of the work • Survey • Excellent tutorial • Wide range of sources • Relevance • Antenna & propagation focus perfect • Intrinsic capacity will be my next step

48. Conclusions:Extending on Jensen’s research • 3G wireless standards • Mutual coupling result reliability (Kronecker spatial model errors of 70%) • Interrelation of antenna and coding (i.e. DIV-2X suited to BLAST [Monogioudis]) • Extensibility to wideband or multi-user MIMO systems • Limits of practical systems (subset switching losses, LNA count, etc.) • Exploiting less glamorous LOS systems • Randomly thinned antenna arrays • Achieving Intrinsic capacity systematically

49. Synthesis

50. Synthesis: all three papers • Good fit to my study plan in RF, advanced communications, inversion, numerical methods • Good fit to my research plan in antenna system optimization for MIMO channels • Achieving intrinsic capacity will be a measure of my success • Mutual coupling, diversity, polarization, etc. must all be considered • Signal processing and adaptive methods will help evaluate time-variant channels