On the Design of RAKE Receivers with Non-uniform Tap Spacing By K. B. Baltzis and J. N. Sahalos RadioCommunications Lab., Department of Physics, Aristotle University of Thessaloniki, Greece. July 2006  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

CONTENTS 1. Abstract. 2. Introduction. 3. Transmitter and Channel Model. 4. Proposed Receiver Model. 5. The Maximum Power Minimum Correlation (MPMC) Criterion. 6. Numerical Examples. 7. Conclusions.  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

ABSTRACT The effect of Non-Uniform tap spacing on the performance of a RAKE receiver is studied. A new RAKE receiver, the MPMC RAKE, is suggested. Taps positions optimization is done according to the MPMC criterion. MPMC criterion considers the total received signal autocorrelation properties at the correlators outputs of the receiver. Numerical results, comparisons and discussions are provided.  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

DS/SS (WCDMA) Used in 3G Communication Systems. INTRODUCTION DS/SS (WCDMA) Used in 3G Communication Systems. RAKE diversity Used to combat Multipath Fading. Maximal Ratio Combining, MRC Equal Gain Combining, EGC (Generalized) Selection Combing, (G)SC Maximum Likelihood criterion, ML Implementation Strategies  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

xi, ith-correlator output Z, decision variable RAKE receiver model INTRODUCTION r(t), received signal W, signal bandwidth L, number of branches xi, ith-correlator output Z, decision variable RAKE receiver model  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

Usually taken equal to chip period. INTRODUCTION TAP SPACING: Usually taken equal to chip period. MRC is optimum under the assumption of independent branch signals, Dong and Beaulieu, [2002]. ML criterion is optimal when tap spacing is set less than chip duration, Kim et al., [2000].  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

ASSUMPTIONS The modulation scheme is a BPSK one. TRANSMITTER AND CHANNEL MODEL ASSUMPTIONS The modulation scheme is a BPSK one. Signal energy per bit Eb is assumed equal for all users. Channel is modeled as a WSSUS frequency-selective Rayleigh fading one. Transmitted pulses are time-limited rectangular. Power Delay Profile (PDP) is uniform or exponential.  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

EQUIVALENT LOWPASS TRANSMITTED SIGNAL OF THE kth–USER: TRANSMITTER AND CHANNEL MODEL EQUIVALENT LOWPASS TRANSMITTED SIGNAL OF THE kth–USER: bit energy processing gain binary data sequence of the kth user PN signature sequence of the kth user the largest integer not greater than chip duration normalized chip waveform  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

TOTAL RECEIVED EQUIVALENT LOWPASS SIGNAL TRANSMITTER AND CHANNEL MODEL TOTAL RECEIVED EQUIVALENT LOWPASS SIGNAL AT THE RECEIVER FROND END (K ACTIVE USERS): channel impulse response of the kth user’s link at delay τ and time instant t time of arrival of the kth user’s signal low pass equivalent process of AWGN Complex zero-mean Gaussian random process It is related to the PDP function g(t) with the expression: Delay depends on the time instant t:  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

ASSUMPTIONS Desired user channel impulse response can be estimated. PROPOSED RECEIVER MODEL ASSUMPTIONS Desired user channel impulse response can be estimated. Amplitude, phase and timing of the desired user’s signal are known. Chip waveform shaping filters in transmitter and receiver are known. Average received signal energy is the same for all users (power control).  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

CORRELATOR OUTPUT: DESIRED SIGNAL COMPONENT: ISI COMPONENT: PROPOSED RECEIVER MODEL CORRELATOR OUTPUT: DESIRED SIGNAL COMPONENT: ISI COMPONENT: MAI DUE TO THE kth USER COMPONENENT: AWGN COMPONENT: Symbol denotes the convolutional operator  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

the first bit of the desired user data sequence PROPOSED RECEIVER MODEL the first bit of the desired user data sequence the discrete crosscorrelation function between the desired and the kth user the autocorrelation function of the chip waveform. DESIRED USER CHANNEL IMPULSE RESPONSE:  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

PROPOSED RECEIVER MODEL ITS MAIN CHARACTERISTIC IS THE NON-UNIFORM TAP SPACING  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

Block diagram of Correlation Coefficients Estimator (CCE) Unit PROPOSED RECEIVER MODEL Block diagram of Correlation Coefficients Estimator (CCE) Unit  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

Block diagram of SUM1 and SUM2 Units PROPOSED RECEIVER MODEL Block diagram of SUM1 and SUM2 Units  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

Multi-objective optimization problem THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION DEFINITION OF MPMC CRITERION Optimum receiver performance is gained when a simultaneous maximization of the sum of squares of average received signal power in each branch and minimization of the sum of squares of autocorrelation between each pair of branches takes place Multi-objective optimization problem  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

the taps settings vector THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION DEFINITIONS: the taps settings vector the total signal average power coefficients vector the total signal autocorrelation coefficients matrix It is: the autocorrelation function of X(t) given b1,0  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

PROBLEM: Euclidean norm of Applied in the Decision Unit THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION PROBLEM: Euclidean norm of Applied in the Decision Unit Hilbert-Schmidt norm of Created in CCE Unit Calculated in SUM1 and SUM2 Units  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

LEXICOGRAPHIC method has been adopted for the optimization THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION Finally MPMC criterion is defined as: the antiderivative function of g(t) the inverse function of g(t) LEXICOGRAPHIC method has been adopted for the optimization  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

SIMULATION CHARACTERISTICS: NUMERICAL RESULTS SIMULATION CHARACTERISTICS: Processing gain N = 256 Constant tap spacing in MRC RAKE Tr = Tc Constant tap spacing in ML RAKE, (Kim et al.), Tr = 0.7Tc  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

tmax = 2Tc K = 10 Uniform PDP NUMERICAL RESULTS INTERFERENCE LIMITED SYSTEM TAPS SETTINGS: MPMC 3RAKE: 0.28, 0.98, 1.69 (Tc ) MPMC 4RAKE: 0.28, 0.65, 1.3, 1.7 (Tc ) MPMC 4RAKE: 40 – 50% smaller Pe compared to ML 4RAKE at Eb/N0 = 15dB 60 – 80% smaller Pe compared to ML 4RAKE at Eb/N0 = 30dB  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

Pe<10-3 tmax = 2Tc NUMERICAL RESULTS Uniform PDP INTERFERENCE LIMITED SYSTEM MPMC RAKE: 40 – 50% increase in the number of users compared to MRC RAKE 20 – 30% increase in the number of users compared to ML RAKE  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

Uniform PDP NUMERICAL RESULTS 3rd tap 2nd tap 1st tap OPTIMUM TAPS POSISTIONS MPMC 3RAKE  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

ARE NOT AFFECTED FROM THE NUMBER OF USERS NUMERICAL RESULTS ARE NOT AFFECTED FROM THE NUMBER OF USERS OR THE VALUE OF SIGNAL TO NOISE RATIO. EXAMPLE (MPMC 3RAKE, tmax = 2Tc): OPTIMUM TAPS POSITIONS ONLY CHANNEL CHARACTERISTICS HAVE AN IMPACT ON THEM.  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

MORE SIGNIFICANT IMPOVEMENT IN PERFORMANCE FOR THE CASES OF: NUMERICAL RESULTS Exponential PDP, tspr = Tc Exponential PDP, tspr = 2Tc MORE SIGNIFICANT IMPOVEMENT IN PERFORMANCE FOR THE CASES OF: UNIFORM PDP LARGER CHANNEL SPREAD Uniform PDP, tmax = Tc  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

MORE SIGNIFICANT IMPOVEMENT IN PERFORMANCE FOR THE CASES OF: NUMERICAL RESULTS Exponential PDP, tspr = Tc Exponential PDP, tspr = 2Tc MORE SIGNIFICANT IMPOVEMENT IN PERFORMANCE FOR THE CASES OF: UNIFORM PDP LARGER CHANNEL SPREAD Uniform PDP, tmax = Tc  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

NUMERICAL RESULTS IMPERFECT CHANNEL IMPULSE RESPONSE ESTIMATION OR / AND PARTIAL KNOWLEDGE OF CHANNEL PDP DEGRADES RECEIVER PERFORMANCE TWO CASES ARE STUDIED: THE “OPTIMIZED TAPS” 1. IMPERFECT DESIRED USER CHANNEL IMPULSE RESPONSE ESTIMATION THE “NON-OPTIMIZED TAPS” ESTIMATION. 2. TAPS OPTIMIZATION IS DONE ACCORDING TO THE AVERAGE AND NOT THE INSTANTANEOUS PDP VALUE. TAPS POSITIONS DO NOT CHANGE. THIS IS ALSO THE CASE BEFORE THE TAPS ACQUIRE THEIR OPTIMIZED VALUES (TRAINING PERIOD)  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

K = 10 MPMC 3RAKE Uniform PDP NUMERICAL RESULTS MPMC 3RAKE Uniform PDP K = 10 OPTIMIZED TAPS: ITS PERFORMANCE COMPENSATES FOR THE COMPLEXITY NON-OPTIMIZED TAPS : SIMPLE – LOW COMPUTATIONAL COST  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

CONCLUSIONS A RAKE receiver with non-uniform taps distribution has been proposed. Determination of the optimum taps positions is based on the correlation properties of the signal components in each branch. The Maximum Power Minimum Correlation (MPMC) criterion has been proposed for the optimization of taps distribution (multi-objective optimization problem).  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

CONCLUSIONS Comparisons with other implementations have exhibited the improved performance of the proposed receiver especially at higher values of signal to noise ratio. Optimum taps settings depend only on channel characteristics. Channel estimation errors does not affect significantly receiver performance.  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

On the Design of RAKE Receivers with Non-uniform Tap Spacing By K. B. Baltzis and J. N. Sahalos RadioCommunications Lab., Department of Physics, Aristotle University of Thessaloniki, Greece. July 2006  RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki