Multipath Resolution Effects in Wideband CDMA Transmission Rodger E. Ziemer Electrical and Computer Engineering Dept. University of Colorado at Colorado Springs Colorado Springs, CO 80933

2 The Challenge 3G wideband: Mixed traffic, some of which demands wide bandwidth Finer resolution of multipath:  Wider spread bandwidth  Directive antennas Statistics/spectra of multipath:  Envelope component partially specular - Ricean model?  Phase distributions for tracking loops (Tikonov?)  Bathtub Doppler power spectrum no longer valid Fundamental question: Resolve more paths – power decreases per resolved path When is additional diversity gain provided by finer path resolution negated by phase/timing errors?

3 A Related Challenge Where does bandwidth come from to do this finer resolution? cdma2000 hedges on this by having an RTT option that allows noncontiguous chunks of bandwidth to be used (multicarrier spread spectrum, MC-SS) Kondo & Milstein (1996) showed that for equal bandwidths, W-CDMA and MC-SS give same diversity gain under ideal conditions (maximal ratio combining, etc.)

4 Well Known Diversity Result Proakis; Diversity reception in context of RAKE (L = no. fingers; = Ave. SNR in kth finger;  r  for FSK and -1 for BPSK): Flat Rayleigh channel; says to resolve multipath as as much possible (BEP versus L monotonically decreases for any E b /N 0 )

5 The Two Issues of This Talk First Issue: W-CDMA for finer resolution of multipath with diversity combining by RAKE Second Issue: Wideband achieved by multicarrier spread spectrum

6 RAKE Receiver Structure

7 Model for Fine Resolution Resolution increases (chip duration decreases): Multipath reflections are from smaller patches or include smaller “bundles” of rays A model for envelope of multipath components: Model for tracking loop phase (e.g., RAKE finger):

8 Decision Statistic: RAKE Receiver Adapting from Proakis: Given    and    U 1 is a Gaussian RV (drop Re). Its moment generating function is Average of exp( ) sum becomes product of averages

9 Ricean Envelope; Tikonov Phase Again, from Proakis: Laplace transform of the detection statistic pdf is The  k ’s are assumed Ricean distributed; make integrand of average look like Ricean pdf with additional factors outside integral.

10 Laplace Transform of Detection Statistic Average over  k : Can’t get a closed form for the average over  k with respect to a Tikonov phase pdf: For given s carry out the average numerically; do product Use numerical technique of Biglieri, et al., Elec. Letters, Feb. 1, 1996, pp , to get probability of error

11 Gauss-Chebyshev Quadrature to Get BEP from MGF of Decision Statistic G-C formula from Biglieri, et al. c affects the number of nodes necessary to achieve a desired accuracy A recommendation in Biglieri, et al is the value minimizing   (c) Or else 1/2 the smallest real part of the poles of   (s)

12 More Practical Case: Internal Noise in Phase Tracking Device Generalize to the signal-to-noise ratio, SNR(k), in the kth finger of the RAKE receiver being Typically, by minimizing phase jitter due to external and internal noise,

13 P b versus E b /N 0 ; Ricean fading with K = 0 dB; loop SNR 20 dB above E b /N 0 = 0 dB; L = no. of RAKE fingers; constant PDP

14 P b versus E b /N 0 ; various orders of diversity, L; Ricean fading, K = 6 dB; σ int 2 /N 0 B L = 1; R b /B L = 15 dB; expon. PDP

15 P b vs. L; Ricean fading, K = -6, 0, 6 dB, E b /N 0 = 7 dB; σ int 2 /N 0 B L = 1; R b /B L = 15 dB; expon. PDP; opt. L values: 37, 34, and 26

16 P b versus L; Ricean fading, K = 6 dB; E b /N 0 = 5, 7, & 9 dB; σ int 2 /N 0 B L = 1; R b /B L = 15 dB; exp. PDP; Opt. L values: 18, 26, & 41 for E b /N 0 = 5, 7, & 9 dB, respectively

17 Summary – RAKE Phase Tracking An optimum number of paths exists, giving a minimum bit error probability Finer multipath resolution, through wider spread bandwidth, buys improved performance The majority of this improvement is obtain for a few RAKE fingers combined (say five or so) It is less dramatic as the number of fingers goes beyond 10 or 15.

18 Next: MC-SS Have L channels (carriers) to be combined at receiver. For simplification assume Equal gain combining DPSK modulation Follow same procedure as before: Obtain MGF of single carrier MGF of sum is product of separate MGF’s Use G-C integration to obtain bit error probability Can obtain closed form result for Rayleigh fading

19 Results for f d T b = (  1)

20 Moderate Doppler Spread; Nearly Rayleigh

21 Higher Doppler Spread; Ricean; Uniform power across carriers

22 BEP versus L; K = 10 dB, and f d T b = 0.04 for uniform power profile

23 Summary Have an optimum number of paths Nonoptimum, equal gain combining used to simplify analysis DPSK modulation exhibits error floor due to Doppler spread

24 References R. E. Ziemer, B. R. Vojcic, L. B. Milstein, and J. G. Proaki s, “Effects of Carrier Tracking in RAKE Reception of Wide-Band DSSS in Ricean Fading,” vol. 47, no. 6, pp , June T. B. Welch, Analysis of Reduced Complesity Direct-Sequence Code-Division Multiple-Access Systems in Doubly Spread Channels, Ph. D. Dissertation, University of Colorado at Colorado Springs, 1997 R. E. Ziemer and T. B. Welch, “Equal-Gain Combining of Multichannel DPSK in Doppler- Spread Ricean Fading,” IEEE Veh. Tech. Transactions, Vol. 49, pp , Sept S. Kondo and L. G. Milstein, “Performance of Multicarrier DS CDMA Systems,” IEEE Trans. on Commun., Vol. 44, pp , Feb. 1996