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## Adaptive Lattice Filters for CDMA Overlay

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**Adaptive Lattice Filtersfor 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 1.85-1.99 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 (100W 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**CDMA Receiver Nband Filter Channel Hard Decision Lattice Filter BP Filter**P represents Signal Power**• f0 is the CDMA Carrier Frequency • bk – kth user binary information • N = Tb/Tc Processing Gain • k = Rayleigh Fading Parameter ( E(k2) = 2 ) • k – Random Phase ~ [0,2] • k – Path Delay ~ [0, Tb ] (Rayleigh Flat Fading Channel) • Bc = 2/Tc - CDMA Signal Bandwidth • j(t) = Narrow-Band Interference Signal • n(t) = Band-Limited AWGN (PSD ~ N0/2)**jc(t), js(t) – Inphase and Quadrature Narrow-Band**Components • = frequency offset from CDMA Carrier • p = Bj/Bc • q = Tc**Lattice Recursive Equation**• Cleaned CDMA Signal ….which is the final stage lattice output**Analysis**• Almost EXACT analysis !!! • Reflection Coefficient Update Equation is given as: • Ta - Update Interval • Ta 2/Bj, 2/Bj ~ Input Correlation Time • - Step Size • Signal Sampled @ Tc (Chip Time) • Input Signal independent at update intervals • No need to ASSUME Independence! • Central Limit Principle applied**Analysis Cont’d…**• Input at sample time intervals is given as: • Correlation of input samples: • It can be derived…. • Observation: Correlation at Tc , 2Tc exclusively from N-Band Signal • Tc Correlation Time of CDMA Signal • Hence is analogous to “White Noise”**Analysis Cont’d…**• Reflection Coefficient at jth 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[R1] 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… • bi() - th bit of ithuser • 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 = Bj/Bc = 5% (0.05) Ta = 20 Tc • q = Tc = 0 (=0) • N = Tb/Tc Processing Gain = 750 • J/S = 17,20,23 dB • b – 32 Kbps, BPSK Signal • Link Specs. : • f0 : 1.884 GHz (B-M), 1.956 GHz (M-B) • Chip Rate = 24 Mchips/sec Tc = 1/24E6 • 48 MHz BW for each DS Waveform • N-Band Interference - 64 QAM @ 45 Mbps • †Specs. taken from “On the Feasibility of a CDMA Overlay for PCN (’92)**Results Cont’d: LMS Vs Lattice SNR Performance…**†From: Adaptive Lattice Filters for CDMA Overlay (Trans. Comm., 2K)**Sim. Log.:**• Simulations done in Base-Band • Iterations of the order 750 X 30 X 30 + 750 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… • “Adaptive Lattice Filters for CDMA Overlay”- Trans. Comm., 2K • “Adaptive LMS Filters for Cellular CDMA Overlay”- Select Areas in Comm., ‘96 • “On the Feasibility of CDMA Overlay for PCN”- Select Areas in Comm.,’92 • “Cellular CDMA Overlay Systems”- IEE Proc. Comm., ‘96