CDMA CODE SYNCHRONIZATION USING SEGMENTED MATCHED FILTER WITH ACCUMULATION AND BEST MATCH

SELECTION

AMREEN SYEDA, A.CHAITANYA LAKSHMI,

IV-ECE, DR.K.V.S.R.I.T, IV- ECE, DR.K.V.S.R.I.T,

EMAIL ID:syeda_amreen29@yahoo.com EMAIL ID:sweety.amy29@gmail.com

ABSTRACT

This paper investigates code phase acquisition in direct-sequence spread spectrum (DS-SS) systems under conditions of high co-user noise and significant carrier frequency offset (Doppler). While conventional serial search acquisition is tolerant of these conditions, the process is quite slow. Conventional matched filters can provide fast acquisition but are unable to handle significant carrier frequency offset. This paper describes a segmented matched filter (SMF) that provides rapid acquisition under conditions of frequency offset and high noise. An accumulation and best match selection scheme is introduced and its performance is compared to the segmented matched filter with threshold detection and also to a conventional non-coherent correlator with serial search. Expected acquisition time is shown as a function of multiple access interference in the presence of carrier Doppler. Example calculations are based on GPS transmission parameters. In addition to calculated probability density functions (PDFs), the paper presents measured PDFs from a mixed-signal ASIC that implements a 512 chip SMF with half-chip code phase resolution. With this acquisition method, the receiver carrier is assumed to be non-coherent, data modulation of the DS-SS signal is allowed and prior chip synchronization is not required.

INTRODUCTION

Code division multiple access (CDMA) using direct-sequence spread spectrum (DS-SS) modulation is a modern trend in mobile communication systems. Before a spread spectrum communication link can function, three levels of synchronization must be attained in the receiver. These are carrier synchronization, code phase synchronization, and data bit timing. Determination of the time phase of the spreading code sequence is referred to as

code phase acquisition and is typically a difficult and time-consuming process. At the receiver, the overall received signal will have three components. These are the useful signal, multiple access interference (MAI) due to co-users, and Gaussian noise. We assume a high noise environment dominated by multiple access interference with the useful signal power as much as 20 dB lower than the noise power. We also assume substantial frequency offset that might be due to Doppler or to frequency error in the receiver. A non-fading channel is assumed and it is modeled as a single transmission path with Doppler shift together with co-user noise and additive white Gaussian noise (AWGN). High Doppler applications include low-earth orbit (LEO) satellite personal communication systems and high microwave frequency mobile communication systems.

The received CDMA signal is represented by

r( t ) = d( t )c( t + β Tc )√2 S cos(2π f 0 t θ ( t )) n( t )(1)

where d(t) is the transmitted data sequence (with amplitude ±1), c(t) is the binary spreading code of length L chips, β is the relative delay of the spreading code, TC is the chip duration, S is the signal power of the desired user, f0 is the receiver carrier reference frequency (local oscillator), θ (t) is the phase of the received signal carrier relative to the local oscillator and n(t ) is the sum of co-user noise and AWGN. We assume co-user noise to be the dominant source of noise. A receiver must determine the value of β such that the code phase of the dispreading sequence in the receiver can be aligned with the code phase of the spreading sequence c(t) at the transmitter. The receiver uses correlation with the desired code sequence in order to detect the correct code phase. However, this detection process is impeded by transitions in the data signal d(t) and by rotations in θ (t) , the received signal phase.

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The detection process is also impeded by signals from other co-users that use the same transmission bandwidth. These co-users are differentiated only by their individually unique spreading code sequences.

Low orbits and high carrier frequencies used in LEO satellite systems create severe Doppler shift and this presents a difficult problem with carrier synchronization. Because of the high co-user and background noise in the satellite channel, carrier synchronization cannot be attempted until code phase acquisition is complete.

CONVENTIONAL ACQUISITION METHODS

We begin with a review of the serial search and transversal matched filter acquisition schemes. Serial search uses a ‘trial and error’ approach to determine the correct code phase [1]. The “correctness” is evaluated by a non-coherent correlator composed of a band-pass filter, an envelope or square law detector and an integrator as illustrated in Fig. 1. In this “active” correlator, the received signal is multiplied by a locally generated spreading code and, when the code phase is aligned with the transmitter code phase, the signal is dispread and its power falls within the range of a band-pass filter. If the code phase is incorrect, the received signal remains spread, little signal power reaches output and the post-detection integrator, (with “dwell” time Td) yields a small value for the decision variable z at the output of the integrator.

Fig. 1 Serial search with non-coherent correlator [1]

With each trial, the input signal is correlated with a replica of the desired user’s code that has a specific delay (i.e., a new code phase). In high co-user noise environments, the dwell time must be increased to improve averaging. The decision to accept a specific code phase or to move on to the next code phase is made by testing the decision variable z against a threshold. In a recent paper by J.H.J. Iinatti [2] the principles of threshold setting in serial search are discussed. The code sequence length determines the number of possible code phases that must be tested, and since each test involves a dwell time, a lengthy serial search must be performed before the communication link is usable. To its credit, serial search acquisition with non-

coherent detection can handle transitions in the data signal d(t) and modest carrier frequency shift.

In this non-coherent correlator, part of the signal averaging occurs prior to the detector (in the BPF) and part of the averaging occurs after the square-law detector (in the dwell integrator). Hopkins [1] has developed expressions for the nonaligned mean, m0, the aligned mean, m1, the non-aligned standard deviation, s0, and the aligned standard deviation, s1, of the decision variable z. These distributions are used to calculate transition probabilities that can then be used to predict the mean synchronization time.

Matched filters compute correlation on a parallel basis and offer faster acquisition performance than a serial search correlator [3]. A new code phase candidate can be tested with each new received chip. Most matched filters operate at baseband and are sensitive to phase error between the signal carrier and the receiver’s local oscillator (LO). Static phase offset is addressed by using an in-phase and quadrature (I-Q) structure [3].

Large carrier frequency mismatches, resulting from Doppler shift or oscillator frequency offset, cause the relative phase to change over the length of the matched filter. This results in amplitude modulation of the demodulated sequence and produces periodic polarity inversions in the received sequence. Under these conditions, even the aligned code phase condition will result in approximately zero output. Shorter filters are less susceptible to Doppler shift but less tolerant of co-user noise. Conventional matched filters are therefore impaired by frequency offset.

Code Doppler is impairment in MF detection. The problem occurs when the rate of entering samples into the shift register of the matched filter is slightly different than the arrival rate of signal chips. In practical situations, the effect of code Doppler is several orders of magnitude less severe than for carrier Doppler and, in this paper, it will not be considered further.

A segmented matched filter (SMF) is a solution to the frequency offset problem. By segmenting the matched filter, Doppler tolerance can be increased while maintaining sufficient tolerance to co-user noise. Segment outputs are squared before being combined so that inverted sequence portions add to the correlation sum. As a consequence of segmentation, code phase alignment can be detected even when there are transitions in the data signal d(t). The structure was initially proposed in [4] and is illustrated in Fig. 3.

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We describe a 512 sample SMF structure split into 16 segments of 32 sequence bits (chips). The SMF operates at baseband where phase or frequency offset in the demodulator can be addressed by an in-phase/quadrature (I-Q) structure [5]. Since correlation is performed separately in each segment, allowable Doppler shift is 16 times greater than for an unsegmented 512 chip matched filter. This segmentation increases the allowable Doppler shift from 480 Hz to 7.8 kHz. For reference, GPS satellite systems operating at 1.5 GHz have Doppler shifts as high as 15 kHz.

Fig. 2 Segmented Matched Filter [4]

This increase in Doppler tolerance, comes at a cost. From a noise averaging point of view, the matched filter effectiveness is less when the summation/averaging occurs after non-coherent detection (i.e., the square law devices). As developed in [5] the effective length of the matched filter is decreased by a factor of 4 when the filter is divided into 16 segments.

BEST MATCH SELECTION

We now introduce a “pick the best” approach to detecting the aligned code phase. This results in much faster acquisition than a threshold based method, but it requires more hardware. In the simplest implementation, the SMF output is stored during one complete cycle of the code sequence and the code phase with the highest correlation is selected. This is assumed to coincide with the aligned code phase. The probability that the correct code phase is actually chosen can be assessed from the probability density functions (pdfs) at the output of the SMF.

In a sample calculation, we use GPS system parameters together with 25 co-users and 5 kHz Doppler shift. In order for the correct code phase to be selected, the SMF output at code phase alignment must exceed the maximum of all non-aligned SMF outputs during the entire code cycle. If Pd is the probability of a correct decision and OA

and ONA are the output samples from the SMF for thealigned and non-aligned conditions respectively, then

Pd POA max(ONA )(2)

To calculate this probability, the new random variable M is introduced and given the value M = max (ONA). The pdf for M must be found so

that it can be compared to the pdf of the aligned case. Since different non-aligned samples within each code cycle are essentially uncorrelated, the cumulative distribution function (cdf) for M is determined using Papoulis [6].

( L−1)

FM ( x) FONA ( x)(3)

where L is the length of the code sequence and L-1 is the number of non-aligned samples per cycle. In this example, the code sequence length L = 1023 as in the GPS system.

Fig. 3 Cumulative Density Function, FM

The cdf of the non-aligned SMF output is differentiated to yield the pdf of the maximum non-aligned sample within the code cycle. The cdfs and pdfs for this example are shown in Figs. 3 and 4, respectively.

Fig. 4 Max (Non-Aligned) probability density

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To determine Pd another random variable, D, is introduced to represent the difference D = OA – max (ONA). This allows Equation 2 to be simplified to

Pd P D 0

(4)

Fig. 5 Probability of detecting correct code phase, Pd

The difference pdf is found by performing a convolution of the non-aligned maximum pdf with the aligned pdf. This pdf is shown in Fig. 6 where Pd corresponds to the area of the difference pdf for difference values greater than zero.

For this example, Pd is relatively small and there is a high probability of detecting an incorrect code phase (false alarm). Pf is clearly related to the amount of pdf overlap between the aligned and non-aligned output pdfs, and it is particularly sensitive to the upper tail of the non-aligned pdf because of the large number of non-aligned samples per cycle.

To improve the probability of correct detection, the SMF output samples at each code phase can be accumulated over several code cycles. If n code cycles are tested, the means of the two pdfs become n times greater, and the standard deviations only increase by a factor of n . This results in a greater separation between the two pdfs and a better probability of correct code phase detection. As the SMF output is accumulated for several code cycles, the difference between the maximum non-aligned case and the aligned case becomes much larger as illustrated in Fig. 6. For this example, the pdf is almost completely positive and the correct detection probability, Pd is nearly 100% once the outputs from 10 code cycles are accumulated.

Accumulating and storing the code phase samples does require additional hardware, however in many applications this hardware is readily available. For instance, the processor in a cellular telephone is available to help with CDMA synchronization because the call processing software is idle at that time.

ACQUISITION TIME CALCULATION

In the preceding method, the acquisition time depends on how many code cycles must be accumulated before the true code phase is found. Calculation of the average acquisition time requires evaluation of the correct detection probability (as in Fig. 6) as a function of the number of accumulated code cycles.

For the example of 25 co-users and 5 kHz Doppler offset, the top graph in Figure 7 shows the cdf of Pd as a function of the number of code cycles that are accumulated. The lower graph in Fig. 7 shows the corresponding pdf along with the calculated mean () and standard deviation (σ ). From this distribution, the mean acquisition time (time for detecting the correct code phase) is estimated to be 2.5 code cycles (2.5 ms).

Fig. 7 Detection with accumulation and best selection

For the purpose of comparison, we have determined the expected acquisition time of the serial search and matched filter synchronizers under the same conditions. Analysis is based on flow graphs similar to those shown in [3]. In the calculation of acquisition time, the uncertainty region of the correct code phase is assumed to extend over the entire sequence length which is composed of q = 2L phase positions where L is the sequence length. The expected acquisition time is calculated assuming that the search has started from a random starting position and, in the case of the SMF, it is assumed that the matched filter registers filled prior to the start of the process. Using flow graph techniques we obtain the mean acquisition time as

1 1− 1 T1 (q − 1)P T

1− 1T qT (5)

acq 1 f fa

P

2

2 2

2

2P P

dd d

where each time step T1 = TC / 2 (where TC is the chip duration) and where the false alarm time, Tfa, includes verification time plus time

spent in false lock. In (5), the first term is the time required to test all q

possible

code phases times a factor that includes1

1 to accountPd Pd

2

for missing the true code phase (and recycling through all q tests again). The final term accounts for time spent in the false alarm state rejecting code phases that were incorrectly accepted. In the case when Pfa is very small Tfa is only slightly greater than one code cycle [5]. The final term also includes a factor 1 Pd

2 to account for recycles. Finally, the terms -1/2 adjust for a random starting position that is, on average, at (q-1)/2.

A comparison of acquisition time for the three synchronization methods is given in Fig. 8. In performance calculations for serial search and for the segmented matched filter, we assumed two dwell times: 512 chips for search and 1023 chip times for verification. The fixed threshold was set for 0.001 probability of false alarm at each code phase test. Evaluations were performed with 10, 25, 50 and 100 co-users which corresponded to –10, -14, -17 and –20 dB SNR at the received chip level. Performance results for the SMF with fixed threshold detection can be compared with Fig. 6 in the paper by Corazza [7]. Although the performance results are similar, it should be noted that the SMF presented here allows for data modulation and for substantial Doppler shift.

Serial 5 kHz Doppler

1.0E+06 Search L = 1023Fixed

1.023 Mchip/sThresh.

Code cycle =1ms1.0E+05

(ms) T1 = 512 chip

VariableT2 = 1023 chip

Tim

e 1.0E+04 Thresh.Pfa = 0.001

Acq

uisi

tion

1.0E+03Fixed

ThresholdSMF

1.0E+02

Mea

n1.0E+01

SMF with1.0E+00

Accumulation

-20 -18 -16 -14 -12 -10 -8 -6 -4-22

SNR per chip (dB)

Fig. 8 Acquisition Time vs SNR

SEGMENTED MF INTEGRATED CIRCUIT

Considerable effort has gone into the design and fabrication of a circuit to implement the ideas presented in this paper. Since significant signal processing is required for an effective filter length (512 chips), an all-digital implementation of the SMF did not seem practical using current technology. The adopted mixed-signal approach used digital elements for storage and analog elements for signal processing such as summing and squaring. Relative to an all-digital approach, this resulted in a significant reduction in the required IC die area (2 mm x 2.5 mm using a 0.5 m CMOS process). The inaccuracy of analog processing was not significant when compared with the extremely high noise levels in the received signal.

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As in any mixed-signal design, a significant portion of the design effort is aimed at mitigating interference between signals in the digital and analog circuitry. A common problem is digital switching noise that couples through the substrate, power supply connections or the circuitry itself to interfere with the analog signals. The fabricated IC was successfully clocked beyond the target clock rate of 2 MSamples/s, and it exhibited minimal switching noise. More details on the circuit are in [5].

A large number of pdfs, similar to those shown in Fig. 5 have been obtained in three different ways. The first was through theoretical development using binomial distributions and approximations based on the central limit theorem. The second was through computer simulation of the signal sources and of the segmented matched filter. The third involved measurement of a VLSI prototype of the SMF circuit. The performance testing was carried out using the same test sequences that were applied to a simulation model. The theoretical, simulation and test results for the SMF agreed closely [8].

CONCLUSION

Code division multiple access (CDMA) has gained widespread popularity in mobile communication systems. This work focused on the challenges presented to code phase acquisition in a LEO satellite environment that includes high levels of co-user noise and large Doppler shift. A segmented matched filter (SMF) acquisition method was validated with three approaches. First, a theoretical framework was developed and calculations were made to estimate the SMF performance. Second, these calculations were verified with simulation of the circuit and development of circuit output pdfs. Finally, a VLSI implementation of the SMF was designed, fabricated and tested. Performance in CDMA code phase acquisition was determined by measuring output pdfs with data sequences developed from a system model.

When compared with serial search methods, the segmented matched filter retains the ability to operate in the presence of large Doppler shift and to withstand data modulation during the acquisition process. Since the SMF performs correlation on a parallel basis, its operation is much faster than the serial search method and, for the system parameters selected here and with fixed threshold detection, the SMF method is about 300 times faster than conventional serial search. The accumulation and best match selection method described in this paper offers a further improvement in acquisition time with a relatively modest increase in hardware complexity. Accumulation is

particularly useful as the number of co-users becomes large.

ACKNOWLEDGEMENTS

This research was made possible with support from TRLabs, equipment and design tools from the Canadian Microelectronics Corporation, and funding from the National Science and Engineering Research Council. This work is an outgrowth of a project funded by Industry Canada and the authors thank Mike Moher, formerly of the Communications Research Center, for his guidance.

REFERENCES

[1] P.M. Hopkins, “A Unified Analysis of Pseudonoise Synchronization by Envelope Correlation,” IEEE Trans. Commun., vol. 25, no. 8, pp. 770–778, Aug. 1977.

[2] J.H.J. Iinatti, “On the Threshold Setting Principles in Code Acquisition of DS-SS Signals,” IEEE J. Select. Areas Commun., vol. 18, no. 1, pp. 62–72, Jan. 2000.

[3] A. Polydoros and C.L. Weber, “A Unified Approach to Serial Search Spread-Spectrum Code Acquisition–Part II: A Matched-Filter Receiver,” IEEE Trans. Commun., vol. 32, no. 5, pp. 550–560, May 1984.

[4] D. Dodds and M. Moher, “Spread Spectrum Synchronization for a LEO Personal Communications Satellite System,” Proc. of IEEE Canadian Conf. on Elec. and Comp. Eng., Montreal, Sept. 1995, pp. 20–23

[5] B. Persson, D.E. Dodds, and R.J. Bolton, “A Segmented Matched Filter for CDMA Code Synchronization in Systems with Doppler Frequency Offset” Proceedings IEEE Globecom, San Antonio, Texas, Nov 2001, Session BWS07-1.

[6] A. Papoulis, Probability, Random Variables and Stochastic Processes, New York: McGraw-Hill 1991

[7] G. E. Corazza, “On the MAX/TC criterion for code acquisition and its application to DS-SSMA systems,” IEEE Trans. Commun. , vol. 44, pp.1173–1182, Sept. 1996

[8] B. Persson, “A Mixed Signal ASIC for CDMA Code Synchronization,” M.Sc. Thesis, Dep. Elect. Eng., Univ. Saskatchewan, Saskatoon, Canada, Aug. 2001

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