Single Correlator Based UWB Receiver Implementation through Channel Shortening Equalizer By Syed Imtiaz Husain and Jinho Choi School of Electrical Engineering and Telecommunications University of New South Wales, Sydney.

Why Channel Shortening in UWB Receivers? UWB channel impulse responses have following features: 1.Very long as compared to UWB pulse width. 2.Dense in multipaths. 3.Quasi-static. Due to fine resolution of UWB pulses, multipaths are resolvable and receiver is implemented through RAKE. Complexity and cost of UWB receiver depends upon the number of fingers in the RAKE. Channel shortening can help in reducing the number of fingers in RAKE and eventually simplify the complexity and reduce the associated cost.

Channel Shortening – Introduction and Existing Applications Introduction: It is an equalization technique to reduce the channel impulse response within a desired window of time. It is also known as Time Domain Equalization (TEQ). Existing Applications: Channel shortening was first introduced in 1970s to reduce the complexity in sequence estimation – Reduced State Sequence Estimation (RSSE). In 1990s, this technique reappeared for MCM/DMT systems to reduce the channel delay spread as compared to the length of CP. A similar idea has been proposed to suppress scalar channels in a multiuser environment for effective detection. Most of the recent applications for MCM/DMT systems are developed for wired line channels with less multipaths and intend to maximize bit rate or channel capacity.

Channel Shortening – Our Approach In this paper, we design and apply a new channel shortening algorithm for wireless UWB channels with dense multipaths. We show that the proposed algorithm can shorten any UWB channel to just one significant tap. We also prove that the proposed algorithm performs better than its existing variants in terms of energy capture and SINR improvement.

System Model Standard channel models suggested by IEEE Study Group 3a, namely CM 1 to CM 4, are used for performance evaluation. A time hopping pulse position modulated (TH-PPM) UWB system is considered. Following realistic system parameters are assumed for comparative analysis: Table 1: System Parameters Pulse Width2 nSec No. of Repetitions ‘N’3 Pulse Repetition Period ‘T f ’30 nSec Modulation Index ‘  ’ 5 nSec Sampling Rate2 GHz Centre Frequency1.5 GHz Bandwidth> 2 GHz Power Spectral Density< -40 dBm

System Model (Continued….) The impulse response of the channel is ‘h’ whereas channel shortening equalizer (CSE) weight vector is ‘w’. Hence, the combined channel-CSE response ‘x’ is: x = h*w or x = Hw where H is channel convolution matrix. We assume that the receiver has complete knowledge of channel through a channel estimator.

Previous Approaches Maximum Shortening Signal to Noise Ratio (MSSNR) Algorithm: In this algorithm, a window within combined channel-CSE response vector ‘x’ is defined. This window represents the shortened channel. The energy within and outside the window can be given as: Energy within shortened channel window = E r = w T H r T H r w = w T H 1 w Energy outside shortened channel window = E s = w T H s T H s w = w T H 2 w The algorithm works to maximize the energy within shortened channel window with constrained outside window energy, i.e. max (w T H 1 w)such that w T H 2 w = 1 Hence, the optimum CSE can be obtained as follows: w opt = {H 2 1/2 } -1 a where ‘a’ is the eigenvector corresponding to maximum eigenvalue ‘a max ’ of the matrix: A = (VD 1/2 ) -1 H 1 (D 1/2 V) -1 where V and D are the matrices containing eigenvectors and eigenvalues of H 2 respectively.

Previous Approaches (Continued….) Target Impulse Response (TIR) Based Minimum Mean Squared Error (MMSE) Algorithm: This algorithm generates the optimum CSE by exploiting the error statistics between a predefined TIR and combined channel-CSE response. It defines the following optimization problem: min (w T [R yy – R T xy R xy ]w)such that w T R T xy R xy w = 1 where R xy is the input-output cross correlation matrix and R yy is the output auto correlation matrix. This optimization can be solved to yield optimum CSE. The performance of this algorithm is same as that of previous one.

Proposed Algorithm In our proposed algorithm, we define an unconstrained optimization problem. This algorithm works to maximize the energy of a single tap in the combined channel-CSE response. Hence, the optimization problem can be stated as: max (w T h L T h L w) where h L is the L th row of H and represents the tap to be maximized. Hence, the optimum CSE is the eigenvector ĥ associated to maximum eigenvalue h max of h L T h L.. w opt = ĥ This CSE is less complicated to evaluate and shortens the channel to just single tap.

Simulation Results and Comparative Analysis Simulations are performed in a multiuser environment with 50 simultaneous active users for CM1, CM2, CM3 and CM4 scenarios. Length of the shortened channel is assumed to be 10 taps maximum. Higher values contradict to the problem definition. Performance of each algorithm is evaluated and compared on the basis of Captured Energy, SINR Improvement and BER. Standard deviation in captured energy is used to determine the consistency of each algorithm in successfully shortening the channel. Extensive simulations provided following results:

Energy Capture Performance in CM 1

Energy Capture Performance in CM 2

Energy Capture Performance in CM 3

Energy Capture Performance in CM 4

Comments MSSNR/MMSE algorithms gather slightly more energy as compared to the proposed one only in CM 1 environment, but: –They are more inconsistent as shown by the higher standard deviation values. –Shortened channel is 10 taps long and they are completely unsuccessful in shortening the channel to below this limit. –Whereas proposed algorithm shortens the channel to one significant tap only. –And it can be implemented with less number of equalizer weights and involves less computations. In case of dense multipath environments, like CM 3 and CM 4, the proposed algorithm performs well above MSSNR/MMSE algorithms in any aspect.

SINR Improvement

BER Analysis

Conclusion BER analysis shows that MSSNR/MMSE algorithms are not suitable for UWB environment. The proposed algorithms outperforms both of these algorithms. The proposed algorithm enables a simple, cost effective and single correlator based implementation of UWB receiver. Due to single correlator design, transmitted pulse shape can be used as receiver template which further reduces the burden of on-line template evaluation from the receiver. Future targets include testing of this algorithm in further dense multipath environments and modifying it to a blind and adaptive design. –Note: For theoretical BER analysis, please refer to section IV(D) of the paper.

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