ISWCS’06, Valencia, Spain 1 Blind Adaptive Channel Shortening by Unconstrained Optimization for Simplified UWB Receiver Design Authors: Syed Imtiaz Husain and Jinho Choi Presenter: Syed Imtiaz Husain

ISWCS’06, Valencia, Spain 2 Presentation Outline Problem Statement Solution and Motivation System Architecture Proposed Channel Shortening Algorithm Simulation Results Conclusions

ISWCS’06, Valencia, Spain 3 Problem Statement UWB channels are very dense in multipaths. To maintain a good SNR, a RAKE receiver with large number of fingers must be used. This makes the receiver structure and the rest of the signal processing very complex. Difficult from analysis and design perspectives and involves higher manufacturing costs. A simple and cost effective receiver structure is needed.

ISWCS’06, Valencia, Spain 4 The proposed solution is Channel Shortening: An equalization technique which compresses the channel impulse response (CIR) within a small desired temporal window. Mainly in use for MCM/OFDM systems. It is used to eliminate just few channel taps beyond the cyclic prefix (CP) length. Available algorithms are MCM/OFDM system specific, not general, except few. Mostly developed for wired line slowly varying scenarios. Solution and Motivation

ISWCS’06, Valencia, Spain 5 Solution and Motivation UWB systems are different in: Working principles Architecture Channel models and many other things Channel shortening appears in its extreme sense in UWB in contrast to MCM/OFDM systems: CIRs must be compressed to just few multipaths eliminating a large number of channel taps. Rapidly varying wireless scenarios.

ISWCS’06, Valencia, Spain 6 Solution and Motivation New and modified channel shortening algorithms are needed to: Address specific needs of UWB systems. Make use of UWB parameters. Can work in dense multipath channels. Can handle the extreme nature of channel shortening needed in UWB CIRs. Must be capable to adapt to channel variations.

ISWCS’06, Valencia, Spain 7 System Architecture Assuming time hopping pulse position modulated (TH-PPM) UWB system. Standardized UWB channel models (CM 1 to CM 4) for performance evaluation. A multiuser AWGN environment with N u simultaneous active users.

ISWCS’06, Valencia, Spain 8 Proposed Channel Shortening Algorithm Fundamental assumptions: In a single user AWGN environment, if a single pulse is received, it quite accurately reveals the channel information. This assumption is not quite valid in a multiuser environment, but still provides a basis to develop channel shortening equalizer (CSE). A CSE which can shorten the received signal is also capable to shorten the channel, a property explicitly available in UWB systems.

ISWCS’06, Valencia, Spain 9 Proposed Channel Shortening Algorithm Fundamental assumptions (continued): We propose block by block data transmission. Two consecutive blocks should be separated by at least 600 nS. A single pulse is transmitted between the two blocks to calculate and update/adapt CSE. The length of data block is variable and can be adjusted according to channel coherence time.

ISWCS’06, Valencia, Spain 10 Proposed Channel Shortening Algorithm We assume:, is the received signal vector and, is the channel shortening equalizer, such that b<<q. The effective channel (channel-CSE) is:, where is the convolution matrix of.

ISWCS’06, Valencia, Spain 11 Proposed Channel Shortening Algorithm Now we define using a row vector in as follows: where such that. To obtain the optimum CSE, we define the following unconstrained optimization:

ISWCS’06, Valencia, Spain 12 Proposed Channel Shortening Algorithm Hence, the optimum CSE is: where is the maximum eigenvalue of and is the corresponding eigenvector. The effective channel can now be given as: where ‘n’ is the length of CIR.

ISWCS’06, Valencia, Spain 13 Proposed Channel Shortening Algorithm If: S ignal bandwidth = W Time between maximum and minimum pulse amplitude = τ p then the shortened channel window length is This shortened window occurs from: to where ‘p’ is odd and represent the length of transmitted signal vector.

ISWCS’06, Valencia, Spain 14 Simulation Results Following simulation parameters were used: CSE Length = 50 N u = 1 (Single User) and 20 (Multi User) Channel Models = CM 1 to CM 4 Length of Shortened Channel = 2 taps Performance of the proposed algorithm is evaluated in terms of: BER Vs. SINR Captured Energy Vs. SINR BER Vs. No. of users

ISWCS’06, Valencia, Spain 15 Simulation Results BER performance degrades as the channel becomes more dense in multipaths or the number of interfering users increases.

ISWCS’06, Valencia, Spain 16 Simulation Results As BER performance, the energy capture also exhibits the similar trends.

ISWCS’06, Valencia, Spain 17 Simulation Results At a constant SINR of nearly 8 dB, increasing number of users does not show any significant effect. Only dense multipath channels degrade the performance.

ISWCS’06, Valencia, Spain 18 Conclusions The proposed channel shortening algorithm: 1. Exploits the UWB channel and system characteristics to address the specific needs of UWB systems. 2. This algorithm can blindly shorten the dense multipath channels to just two significant taps with a CSE length of 50 and can still capture 55% of the channel energy. 3. The algorithm can be updated via proposed mechanism periodically at channel coherence time. 4. It greatly simplifies the UWB receiver structure, associated signal processing and reduces the manufacturing cost.