Adaptive Lattice Filters for CDMA Overlay DSP 2 Project Presentation By Rajat Kapur & AdityaKiran Jagannatham

CDMA Technology CDMA is a Multiple Access wireless technique. Uses the idea of Spread Spectrum Benefits of CDMA: 1.Capacity increases of 8 to 10 times that of an AMPS analog system 2. Improved call quality, 3.Simplified system planning through frequency reuse. 4.Enhanced privacy and Bandwidth on demand 5. Possibility of fewer cell sites

The Overlay Concept: Motivation: Increasing demand for BW in Mobile Comm. Establishment of PCN in the GHz Band (‘92) Previously occupied by Narrow-band Microwave Signals This situation of “Spectrum Sharing” CDMA Overlay. Initial experiments in Houston, Orlando, San Diego using Broad-Band CDMA Goals: 1. Overlay would not excessively interfere with N-Band 2. PCN users can operate efficiently in the overlay environment 3. Conform to PCN philosophy (100  W in 183m cell radius)

Adaptive Filtering in CDMA Overlay LMS Filtering employed in N-Band interference rejection (’96) Lattice Filtering suggested as an alternative by J.Wang and V.Prahatheesan (2K) Lattice shown to outperform LMS

Overlay Receiver BP Filter Lattice Filter Hard Decision Channel CDMA Receiver Nband Filter

P represents Signal Power f 0 is the CDMA Carrier Frequency b k – k th user binary information N = T b /T c Processing Gain  k = Rayleigh Fading Parameter ( E(  k 2 ) = 2  )  k – Random Phase ~ [0,2  ]  k – Path Delay ~ [0, T b ] ( Rayleigh Flat Fading Channel) B c = 2/ T c - CDMA Signal Bandwidth j(t) = Narrow-Band Interference Signal n(t) = Band-Limited AWGN (PSD ~ N 0 /2)

j c (t), j s (t) – Inphase and Quadrature Narrow-Band Components  = frequency offset from CDMA Carrier p = B j /B c q =  T c

Lattice Filter Structure

Lattice Recursive Equation Cleaned CDMA Signal ….which is the final stage lattice output

Analysis Almost EXACT analysis !!! Reflection Coefficient Update Equation is given as: T a - Update Interval T a  2/B j, 2/B j ~ Input Correlation Time  - Step Size Signal T c (Chip Time) Input Signal independent at update intervals No need to ASSUME Independence ! Central Limit Principle applied

Input at sample time intervals is given as: Correlation of input samples: It can be derived…. Observation: Correlation at T c, 2T c exclusively from N-Band Signal T c  Correlation Time of CDMA Signal Hence is analogous to “White Noise” Analysis Cont’d…

Reflection Coefficient at j th iteration… The Product term indicates dependence on past data For a large number of co-channel users ( K ~ 30 or >), the term… Can be simplified as… …using CLP To yield…

Analysis Cont’d… Which in the limit yields… …clearly showing E[R 1 ] depends on step size  !!! Observe : If  = 0 … … the optimal Wiener Filter Coefficient Similarly, it can shown that

Analysis Cont’d… Where A is given by… … pretty complicated !!!

Analysis Cont’d… SNR Calculation: The Despreader O/P is given as… b i (  ) -  th bit of i th user J – NBand interference, N – Interference from Noise I – Co-Channel User Interference

Analysis Cont’d… where this FINALLY concludes our analysis !!! † Precise Details can be found in references…

Simulations: System Specs. : K = 30 (No. of Co-Channel Users),  = 0.1 (-7 dB Fading) p = B j /B c = 5% (0.05)  T a = 20 T c q =  T c = 0 (  =0) N = T b /T c Processing Gain = 750 J/S = 17,20,23 dB b – 32 Kbps, BPSK Signal Link Specs. : f 0 : GHz (B-M), GHz (M-B) Chip Rate = 24 Mchips/sec  T c = 1/24E6 48 MHz BW for each DS Waveform N-Band Interference Mbps † Specs. taken from “On the Feasibility of a CDMA Overlay for PCN (’92)

Simulation Results: Convergence behavior of R 1…

Results Cont’d: Convergence behavior of R 1…

Results Cont’d: LMS Vs Lattice SNR Performance … †F rom: Adaptive Lattice Filters for CDMA Overlay (Trans. Comm., 2K)

Sim. Log.: Simulations done in Base-Band Iterations of the order 750 X 30 X X 30 X 40 Random Binary Sequences used as PN Sequences  = 1 for user  no attenuation on Direct Path White Noise used

Conclusions… CDMA Overlay effective for frequency re-use Each stage of the Lattice Converges independent of others Lattice Filter provides faster rate of convergence compared to LMS Filter Lattice Filter has good capability of Narrow Band Interference Suppression References… 1.“Adaptive Lattice Filters for CDMA Overlay”- Trans. Comm., 2K 2.“Adaptive LMS Filters for Cellular CDMA Overlay”- Select Areas in Comm., ‘96 3.“On the Feasibility of CDMA Overlay for PCN”- Select Areas in Comm.,’92 4.“Cellular CDMA Overlay Systems”- IEE Proc. Comm., ‘96