A SIMULATOR FOR DIFFERENTIAL MSK DIRECT SEQUENCE SPREAD SPECTRUM SYSTEMS OPERATING IN A MULTIPATH AWGN ENVIRONMENT WITH APPLICATIONS TO ACOUSTIC TRAVEL-TIME MEASUREMENT Yair Linn Department of Electrical and Computer Engineering, University of British Columbia 2356 Main Mall, Vancouver, BC, Canada V6T-1Z4 [email protected]

Matthew J. Yedlin Department of Electrical and Computer Engineering, University of British Columbia 2356 Main Mall, Vancouver, BC, Canada V6T-1Z4 [email protected]

Abstract

In this poster we shall present a simulator developed for complete simulation of a D-MSK DSSS (Differential Minimum Shift Keying Direct Sequence Spread Spectrum) system which operates in a multipath AWGN (Additive White Gaussian Noise) channel. The simulator is “complete” in the sense that it simulates the transmitter, the channel, and the receiver. This includes precise simulation of the various synchronization loops in the receiver, ability to simulate a virtually unlimited number of multipath interferers with arbitrary amplitudes, and complete control over the parameters of the communications link. The simulator is operated through a Matlab GUI (Graphical User Interface) which runs proprietary code written in Matlab. In addition to discussing the simulator itself, we shall also outline one of the unique applications of the simulation program, which is in the development of a novel technique for acoustic travel-time measurement in geophysical exploration.

Keywords:

spread spectrum, multipath, minimum shift keying, channel modeling

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Introduction Spread Spectrum (SpSp) systems are rapidly becoming a mainstay of modern wireless communications due to the many advantages which they afford. These include, for example, resistance to multipath interference and a lower spectral footprint. MSK DSSS (Minimum Shift Keying Direct Sequence Spread Spectrum) is one of the primary SpSp methods currently used[1]. Our simulator models such an MSK DSSS system which operates in the presence of multipath interferers and AWGN. We furthermore choose to use Differential MSK (D-MSK) because use of differential detection allows us to avoid the need to implement a carrier synchronization loop (see [2] Chap. 5), which would have had poor performance in a multipath environment. In our work at the University of British Columbia (UBC), D-MSK DSSS systems have been a subject of particular interest due to possible application of this modulation technique to acoustic travel-time measurement in geophysical systems. The travel-time is an indication of the geological properties of the medium through which the acoustic waves propagate, so travel-time measurement is a widely used tool in oil and gas exploration surveys. The conventional approach to travel-time measurement in geophysical acoustic surveys involves generating a “one-shot” disturbance at the source and measuring its arrival time at the destination. This is prone to error due to various types of reflected and refracted waves which arrive at the destination point along with the direct-path wave. Our approach is different: instead of trying to send and receive a one-shot signal, we establish a continuous spread spectrum acoustical communications link between the source and destination. We then send, over this link, framed data which contains timestamps taken at the transmitter. The receiver then subtracts those transmission timestamps from the receiver’s clock, hence computing the travel-time. The problem of overcoming interference by indirect-path waves is hence transformed into the task of overcoming multipath interference in a spread spectrum communications system, which is a well-known problem to which solutions are readily available[1]. Although our simulator was developed with this geophysical application in mind, it can be used without modification to simulate any wireless D-MSK DSSS system in a multipath AWGN environment. As we shall discuss in this poster, our simulator is completely configurable and allows for specification of nearly every channel and system parameter. Moreover, it has the ability to carry out automated Bit Error Rate (BER) measurements as well as complete endto-end simulations of the geophysical travel-time measurement application.

1.

System Model

A simplified diagram of the system model is shown in Fig. 1. There are two general operation modes of the simulator: (a) end-to-end simulation of the

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travel-time measurement application, and (b) BER simulations. The switch configuration shown in Fig. 1 is configured for operation in mode (a). For mode (b), the switch positions should be toggled. It should be noted that mode (b) would have the most widespread application as it corresponds to performance evaluation of the general case of a D-MSK DSSS system in a multipath AWGN environment.

Figure 1.

System Model

Our simulator accurately simulates the closed-loop tracking behaviour of the Spread Spectrum synchronization loop as well as that of the Symbol Synchronization loop. The former is implemented as an Early-Late tracking loop ([1] Chap. 4). The latter is implemented as a PLL (Phase Locked Loop) which uses the timing error detector of [3]. It should be noted that by simulating the PLLs’ behaviour our simulator differs from many channel simulation programs, which assume perfectly locked chip synchronization and symbol timing synchronization loops. Hence, by incorporating these closed-loop PLL simulations our model provides a much more realistic indication of system performance which includes the degradation caused by the necessarily imperfect synchronization loop behaviours.

2. 2.1

Overview of the D-MSK DSSS System Why MSK?

We chose to use MSK because: (a) MSK is a constant envelope modulation (which is less susceptible to degradation due to transmitter and channel nonlinearities) (b) MSK is a Continuous Phase Modulation (CPM) (which is a necessary requirement in order to efficiently drive certain acoustic transducers)

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(c) MSK can be treated as a special case of Offset QPSK (Quaternary Phase Shift Keying) with half-sinusoidal baseband pulses, which simplifies transmitter and receiver design.

2.2

Example of MSK Transmission

As an example of the transmission of MSK, consider the transmitted baseband I-channel waveform, as shown in Fig. 2. Each of the half-sinusoid pulses represents one transmitted chip. After transmission the downconverted signal is passed through filters matched to the chip pulse shape. In the absence of noise, the signal is as in Fig. 3. Lamentably, in the actual operating environment, the signal which appears at the receiver the signal is corrupted both by noise and by multipath interference. An example of this is shown in Fig. 4. As easy to conjecture by comparing Fig. 3 and Fig. 4, the noise and multipath interference will have a detrimental effect upon the receiver’s error rate. For this reason, spread-spectrum modulation has been employed. The purpose of our simulator is to quantitatively evaluate the performance of such a spreadspectrum link.

Figure 2.

I-channel baseband Tx signal.

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Figure 3.

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I-channel post chip-matched filter signal, no noise, no multipath.

Figure 4. I-channel post chip-matched filter signal, chip SNR = 5 dB, 2 multipath interferers with amplitudes of 0.1 and 0.3, delays of 10 and 20 chips (relative to primary signal).

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3.

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Simulator Overview

The simulator is named CARESS, an acronym for Coordinated Acoustic Radiography Employing Spread Spectrum. This is a reference to the original application of acoustic travel-time measurement. However, as noted, the simulator can be used without modification for wireless channel simulations. CARESS was developed using the Matlab GUI toolbox. However it is emphasized that the simulator does not use Simulink; rather, all the simulation routines have been indigenously developed by the authors and implemented as Matlab code. This was a deliberate design choice which affords us two important advantages: (a) Speed - good Matlab code is significantly faster than Simulink, and (b) Control - since we control the inner workings of our simulator, we are assured exact control of every minute detail in the simulation process; this is nearly impossible to achieve using Simulink, and allows us to optimize the simulator for speedy and lean performance. The disadvantage of writing the code ourselves (rather than using Simulink blocks) was that, obviously, a significant amount of complicated code needed to be written and debugged. However, the speed and control advantages outlined above were deemed significant enough to warrant this extra effort. The GUI allows the user seamless control of system parameters. Using Matlab also allows the simulator to run on the many operating systems which support Matlab.

3.1

Simulator Parameters and Operation

Some of the simulator’s user-configurable parameters are summarized below. Configurable Transmitter Parameters - Number of symbols to be simulated - Chip duration - Samples/chip - Chips/bit (from which the SpSp processing gain is determined) - Chip PN sequence which is completely configurable in terms of PN-generator register length, feedback tap configuration, and PN register initial value. - Coding: choice between Viterbi Coding (K=7, rate=1/2) or Uncoded - Data waveform: choice between frames (for travel-time measurement application), configurable PN sequence (for BER measurements), as well as auxiliary engineering testing modes. Configurable Channel Parameters - SNR of primary signal - Multipath interferers: number, amplitudes, and delays vs. primary signal Configurable Receiver Parameters - Carrier frequency and phase errors

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- Modeling of AGC loop - Hard Viterbi, Soft Viterbi, or Uncoded reception

Figure 5.

3.2

Screenshot of CARESS main window.

Diagnostic Plots

The simulator is capable of generating a multitude of graphs for diagnosis and verification purposes. This includes (but is not limited to) the following plots: The transmitted signal before and after modulation The modulated signal with effects of multipath & noise The I and Q signals throughout the receiver’s datapath Various internal receiver variables Many of the plots can be generated both in the time and frequency domains. All of the plots shown in the poster were generated using the CARESS simulator.

4.

Spread Spectrum Removal

The Spread Spectrum synchronization loop is responsible for removing the chip PN sequence and recovering the underlying bit waveform. To do this,

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it employs an Early-Late (EL) tracking loop. A portion of the unfiltered Ichannel post EL-loop waveform is shown in Fig. 6. Note that the abrupt transitions to 0 in Fig. 6 correspond to transitions in the chip PN sequence. In actual fact, when the symbol synchronization loop is locked the samples used are only those at the peaks of the chips. This, combined with post-EL filtering, ensures that no degradation is incurred due to this phenomenon. We see in Fig. 6 that the equivalent bit pulse shape is very nearly rectangular. This is interesting, since this implies that the overall system will behave like an D-OQPSK system and not an D-MSK system, something which BER measurements verify. The filtered, downsampled, post-EL-loop I-channel waveform when the symbol synchronization loop is locked is shown in Fig. 7; this is the input waveform to the symbol synchronization PLL.

Figure 6.

5.

Unfiltered I-channel post-EL-loop, noiseless conditions, no multipath

BER Simulation

In BER simulation mode, the simulator operates in an automated fashion to simulate the system over a variety of user specified SNRs. Examples of such graphs are given in Fig. 8. In that figure we see BER measurement results which were obtained in a system experiencing no multipath interference (Fig. 8a) and 3 multipath interferers (Fig. 8b,c,d). The system has 10 chips/(coded bit). As seen in Fig. 8a, with no interference the performance of the spread spectrum system approximates that of a D-OQPSK (Differential Offset-QPSK) system; as explained earlier, this is due to the fact that the effective transmitted bit pulse shape is approximately rectangular. When multipath interference is added (Fig. 8b) the multipath-combating advantages of using SpSp are readily

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Figure 7. I-channel post-EL-loop after filter matched to the (rectangular) bit shape and downsampling, noiseless conditions, no multipath.

apparent. Further improvement is possible via Hard Viterbi decoding (Fig. 8c) and Soft Viterbi decoding (Fig. 8d). However, as seen in Fig. 8c and Fig. 8d, meaningful improvement is only possible if spread-spectrum modulation is used in conjunction with the coding; merely adding coding still results in unacceptable error rates in the presence of multipath interference. In Fig. 8, the theoretical curve for D-MSK is taken from [4] (see [4] Fig. 9 with M=1), and the theoretical curve for D-OQPSK is taken from [5] eq. (4).

6.

Application to Acoustic Travel-Time Measurement in Geophysical Exploration

As noted in the introduction, the motivation for this research has been the development of a new method for acoustic travel-time measurement, with special emphasis on geophysical applications such as oil and gas exploration. In this section we shall show how the geophysical problem which we are investigating results in an equivalent multipath channel response. A common multipath situation occurs in a tomographic, seismic exploration situation. In Fig. 9, a compressional acoustic wave propagates through the oil-bearing shale layer, traveling from the source S to the receiver R. We are interested in estimating the travel time corresponding to the direct path, path (0). Travel-times collected from multiple source-receiver pairs placed at multiple locations form the input to a travel-time inversion algorithm, which estimates seismic wave velocity over a 3-D grid. This data can in turn can be related to the layer’s geological properties. An incorrect choice of the travel times may thus result in an incorrect determination of the geological medium.

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Figure 8. BER results for (a) uncoded, no multipath; (b) uncoded, multipath; (c) Hard Viterbi, multipath; (d) Soft Viterbi multipath. The multipath systems have multipath interferers at delays of 10, 20, and 30 chip intervals, with relative amplitudes of 0.1, 0.3, and -0.4, respectively. For all systems PN sequence length is 63 chips; carrier frequency 16 KHz; chip length 1msec; 10 chips/(coded bit).

In Fig. 9 the primary acoustic wave, path(0), is contaminated by four reflections, shown as ray paths (1) to (4). The objective, as previously described, is to estimate the travel time corresponding to the direct path in the presence of the foregoing multiple reflections and noise (note that this example is the simplest approximation of multiple arrivals due to the presence of the layering above and below the target oil-bearing shale layer. In practice, the multipath problem is more severe, as there can many multiple reflections, diffracted waves and guided waves). The wave propagation model is that of spherical waves. For example, for the direct arrival (path(0)), the signal at the receiver g 0 (t) will be written as g0 (t)=f(t-d0 /α 1 )/d0 , where f(t) is the transmitted signal (at S), d0 is the distance from S to R, and α 1 is the acoustic wave speed for the modeled direct arrival.

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Figure 9. Simple model of multipath propagation in a geological survey. This three layer model is parameterized by the oil bearing shale layer of thickness h, compressional and shear waves speeds α1 and β1 and density ρ1 . The overlying and underlying sedimentary layers have the wave propagation parameters, α2 , β2 and ρ2 . The source is at S and the receiver is at R.

Similarly, for a given path i, the corresponding signal at the receiver will be written as gi (t)= Γi f(t-di /α 1 )/di where di is the distance traveled along the reflected ray path, and Γi is the effective reflection coefficientbetween the sedimentary layer and the oil-bearing shale layer. A good approximation[6] to the total channel response at R can be written as the sum of g0 (t) and all the multipath contributions {gi (t)}. This corresponds to the multipath communications model that has been studied in this paper.

7.

Conclusions and Future Work

In this poster we have presented a simulator which we have developed in order to simulate Differential MSK Direct Sequence Spread Spectrum systems operating in a multipath AWGN environment. Sample BER results, which highlight the effects of the spread spectrum modulation with and without coding, have been shown. While this research was motivated by the possibility of using D-MSK DSSS in geophysical surveys, it has the potential to be of use to other researchers which are interested in the same modulation for other purposes. As for future work, research is proceeding in parallel tracts. First, regarding the CARESS simulator, it is being continuously improved in order to allow for more parameters to be modeled and to make its operation even more userfriendly. Secondly, research is continuing into the application of the simulator to the geophysical problem of interest, namely travel-time measurement. Fu-

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ture work in this respect will include: (1) theoretical and empirical derivation of the equivalent geophysical multipath propagation models, (2) conducting simulations of the proposed travel-time measurement procedure upon realistic geophysical propagation models, and (3) comparison of the results obtained using our method to results obtained using other methods, in particular with regards to the necessary transmission power, achievable accuracy, and measurement speed.

References [1] R. L. Peterson, R. E. Ziemer, D. E. Borth, Introduction to Spread Spectrum Communications, New Jersey: Prentice-Hall, 1995. [2] J. G. Proakis, Digital Communications, 4th ed., New York: McGraw-Hill, 2001. [3] Y. Linn, “A new NDA timing error detector for BPSK and QPSK with an efficient hardware implementation for ASIC-based and FPGA-based wireless receivers,” in Proc. IEEE Intl. Symp. on Circuits and Systems (ISCAS 2004), May 23-26, 2004, Vancouver, BC, Canada, vol. 4, pp. 465-468. [4] G. K. Kaleh, “A differentially coherent receiver for minimum shift keying signal,” IEEE Journal on Selected Areas in Communications, vol. 7, no. 1, pp. 99-106, Jan. 1989. [5] G. Ferrari and G. E. Corazza, “Tight bounds and accurate approximations for DQPSK transmission bit error rate,” IEE Electronic Letters, vol. 40, no. 20, 30th Sept. 2004. [6] V. Cerveny, Seismic Ray Theory, New York: Cambridge University Press, 2001.