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This work analyses the effect of the receiver movement on the detection by pulse compression of different families of codes characterizing the emissions of an Ultrasonic Local Positioning System. Three families of codes have been compared: Kasami, Complementary Sets of Sequences and Loosely Synchronous, considering in all cases three different lengths close to 64, 256 and 1,024 bits. This comparison is first carried out by using a system model in order to obtain a set of results that are then experimentally validated with the help of an electric slider that provides radial speeds up to 2 m/s. The performance of the codes under analysis has been characterized by means of the auto-correlation and cross-correlation bounds. The results derived from this study should be of interest to anyone performing matched filtering of ultrasonic signals with a moving emitter/receiver.

Local Positioning Systems (LPS), intended to locate people and/or objects in indoor environments, constitute one of the core elements of the so-called Intelligent Environments (IE). The interest to develop this type of systems has significantly grown in the last years, with the appearance of proposals based on different technologies that include ultrasonic [

Yet during the first years of the former decade, some systems were proposed that achieved centimetric precision through the emission of ultrasonic pulses, both centralized, where the object to be located acts as the emitter [

Many authors have already pointed out the problems that the receiver movement could cause on the detection of ultrasonic encoded signals, since the Doppler effect undergone by these signals could make them completely unrecognizable to the matched filter installed in the receiver [

This work represents a significant extension of the work carried out by the authors in those papers, since three different families of binary codes are compared in terms of their bound values when detected by pulse compression with a moving receiver. The analysis is first performed with a high versatility simulator that allows the user to choose among different families of codes and modulation schemes, as well as to model the effect of various phenomena that characterize the propagation of ultrasonic signals in air: geometrical spreading, atmospheric absorption and the filtering associated with the transducers. Next, the results obtained with this simulator for a particular family of codes and modulation scheme are experimentally validated making use of an electric slider with which the speed of the ultrasonic emitter/receiver can be accurately controlled. These results are finally discussed in the last section, where the main conclusions of this work are also outlined.

As stated before, three different codes already used in the design of ultrasonic LPS are compared in this work. The main features of these codes are briefly described in this section, where also the modulation scheme and the parameters used to characterize the comparative analysis are presented.

Kasami sequences [_{1} is a maximal sequence of length ^{N−1} with _{2} is the sequence obtained from the decimation of _{1} with a decimation factor of ^{N/2} + 1 and the concatenation of the result ^{l}m_{2} is the sequence obtained by cyclically shifting _{2} sequence. Three different families of four sequences with lengths of 63, 255 and 1,023 bits have been generated following this procedure. With this number of sequences in a family, a usual 4-beacon LPS architecture is being assumed in this work.

A set of _{i}_{xixi}_{i}_{i}_{1}, _{2}, _{3}, _{4}} with lengths of 16, 64 and 256 bits. The four sequences composing a set are finally interleaved to generate three different emission sequences

LS codes can be generated from Golay [_{0}, where _{0} is the number of zeros inserted in the center of the LS code, that determines the total length of the IFW as min(2_{0} + 1) (_{0} is usually chosen as _{k}_{xy}_{0}). Three families of four LS codes with lengths of 71, 271 and 1,087 bits have been generated in this work from Golay codes of 8, 16 and 64 bits respectively, following the procedure proposed in [

In order to adapt the spectral features of the emissions to the frequency response of the ultrasonic transducer, these codes are binary phase modulated (BPSK). This modulation scheme has been widely used to transmit binary codes in matched filtering-based sonar systems. Every bit in the code

A common measure for the performance of a family of _{sp}

These parameters have to be slightly modified when dealing with LS sequences, since only the correlation values obtained inside the IFW are of interest in this case. Taking into account that this window is limited by two correlation peaks with half the height of the main AC peak, and to avoid the effects derived from the correlation of the modulation symbol, the new bounds are defined as:
_{0} is half the size of the IFW as defined in Section 2.1.3.

This section shows the results obtained by the simulator when only the effect of the receiver movement is modeled, and no further phenomena characterizing a particular system are considered. This effect can be easily simulated by assuming a virtual sampling frequency _{s}_{s}_{r}_{e}_{r}

_{AC}_{r}_{AC}

_{AC}

As pointed out in the Introduction, one of the main advantages of encoding the ultrasonic signals of a LPS is the capability to perform simultaneous emission of all beacons whose signals will be distinguished by the receiver despite their possible overlapping. For this reason, it is important to analyze the effect of the receiver movement not only in the auto-correlation of the emitted codes but also in the cross-correlations between all the codes in the family. As stated before, we have supposed that our LPS is composed of four beacons performing the simultaneous emission of different codes with good correlation properties, and thus, families of four members (codes) have been generated.

_{CC}_{CC}_{CC}

It is important to remark that the families of binary codes chosen to conduct the study presented in this work are those with the best correlation properties among all the families that can be generated from the same algorithms with the same number of members and lengths. If other families are used, similar trends to those observed in

Prior to obtaining experimental data with the equipment that will be described in Section 4, two phenomena characterizing this particular experimentation must be included in the model employed in Section 3.1, since they could have a strong influence on the simulated results. These phenomena are:

The frequency response of the ultrasonic transducer, with a nominal bandwidth of 10 kHz at −6 dB according to the manufacturer.

Atmospheric absorption of ultrasound in air at the laboratory temperature and humidity conditions. This absorption coefficient is strongly dependent on frequency.

To model the first phenomenon, an accurate experimental analysis of the frequency response of the the emitter (driver + transducer) has been carried out in the range 20–80 kHz, obtaining the results shown in

With respect to the atmospheric absorption of ultrasound in air, it has been modeled as dictated by the ISO 9613-1 (1993) standard [

_{AC}_{AC}

This section presents the experimental analysis carried out to validate the simulated results obtained in the previous section. A picture of the experimental equipment employed in this analysis is shown in

Computer: from where a software application controls the emission, the movement of the platform supporting the emitter, and the acquisition parameters. The received data are stored in a text file for their latter processing.

Electric slider: two meters long conveyor belt where the ultrasonic transducer is fixed. A rigid metallic platform has been built to separate the emitter from the base and avoid undesired echoes. This slider is capable to reach a maximum speed of 2 m/s, with maximum acceleration values of ±3 m/s^{2}, thus providing an analysis window of about 800 ms of constant velocity.

Two DC sources: one providing 24 V and 7 A for the electric slider, and the second providing 24 V and 3 A for the controller.

NI USB-6212 data acquisition card, to transmit the modulated code to the emitter and acquire the signal received by the microphone at a sampling frequency of 400 kS/s.

Prowave 400WB160 ceramic ultrasonic transducer, with a central operation frequency of 40.0 ± 1.0 kHz, a nominal bandwidth of 10 kHz at −6 dB, and a SPL of 105 dB min with respect to 20 μPa at 30 cm. A driver module has been specifically designed for this transducer, based on a TL082 operational amplifier in inverting configuration, providing a gain of −3 V/V.

G.R.A.S. 40BE free-field pre-polarized ultrasonic microphone, with a sensitivity of 4 mV/Pa, a dynamic range of 3—166 dB with respect to 20 μPa, and a flat frequency response in the range 4 Hz–100 kHz.

G.R.A.S. 12AK power module, that provides a signal amplification of 40 dB in the range of frequencies of interest and performs a high-pass filtering with a cutoff frequency of 20 Hz.

In order to test the functionality of this equipment, a proof 40 kHz carrier signal has been continuously emitted during the following 4-stage trajectory:

Acceleration at 3 m/s^{2} for 666 ms, until the maximum nominal speed of 2 m/s is reached.

Constant speed movement at 2 m/s for 300 ms.

Deceleration at −3 m/s^{2} until stop.

Static emission until a total emission time of 2 s is completed.

The experimental analysis has been carried out by increasing the emitter velocity from 0 to 2 m/s in steps of 0.1 m/s for all sequences and code lengths under consideration. During each trial, every code is emitted once when the platform has reached the constant velocity regime, and these trials are repeated ten times to provide average values of the auto- and cross-correlation bounds. _{AC}^{2}, that is also represented in this figure as a continuous line. This quadratic fit, whose coefficients are presented in _{AC}

Finally,

This work has presented a detailed study of the influence that the receiver velocity can have on the matched filtering of the signals emitted by a particular ultrasonic LPS. Families of four BPSK modulated Kasami, LS and CSS sequences with different lengths have been considered in this study, establishing for each one of them the range of admissible receiver velocities in terms of the auto-correlation and cross-correlation bounds of the corresponding family. These results have been experimentally validated with the help of an electric slider, and these experimental data have been fitted to a second order polynomial that can be used to easily determine the worsening of the bound as a function of the receiver velocity.

Both the simulated and the experimental results confirm that Complementary Set of Sequences are not the best choice when dealing with a moving receiver, since the auto-correlation bound of this family has a high value over the entire range of velocities. Also, the cross-correlation bound of this family exhibits a range of velocities where it increases significantly with respect to its static value. As expected, LS codes present the lowest values of auto- and cross-correlation bounds with a static receiver for all lengths, although these values increase with the receiver velocity exceeding those obtained with Kasami sequences at a certain point. Furthermore, the range of admissible velocities is reduced in this case due to the presence of large sidepeaks at the bounds of the Interference Free Window, peaks that can exceed the main peak of the auto-correlation long before the bound reaches values close to 1.

Kasami sequences seem to be a good choice when matched filtering of ultrasonic signals is used with a moving emitter/receiver. Although the static value of their auto-correlation bound is greater than that of LS sequences, the worsening of this bound with increasing receiver velocity is relatively slow, thus providing the largest range of admissible velocities. Also, conversely to the behavior obtained with the other families of binary codes, the cross-correlation bound of Kasami sequences remains at a relatively constant value throughout all the range of velocities analyzed.

Some work is still to be done in this interesting field of research. For example, only one modulation scheme has been considered in our study (BPSK), but other possibilities should be explored. Even more interesting, new encoding sequences are currently being developed with promising performances against Doppler shift, such as the use of Multilevel Complementary Sequences [

This work has been partially supported by the Spanish Ministry of Science and Innovation, through the project LEMUR-UEx (TIN2009-14114-C04-04), and the Regional Government of Extremadura, through the European Regional Development Funds (FEDER - GR10097)

Spectral features of the longest BPSK modulated codes.

Simulated auto-correlation bound for the sequences with lengths close to

Simulated cross-correlation bound for the sequences with lengths close to

Emitter frequency response: experimental values (blue dotted) and IIR filter model (red solid).

Simulated auto-correlation bound for the sequences with lengths close to

Simulated cross-correlation bound for the sequences with lengths close to

Experimental setup.

Features of the proof 40 kHz carrier signal.

Simulated and experimental auto-correlation bounds for the sequences with lengths close to

Simulated and experimental cross-correlation bounds for the sequences with lengths close to

Receiver velocities (m/s) whose θ_{AC}

∼ 64 bits | 4.9 | 4.2 | 4.3 |

∼ 256 bits | 1.4 | 1.1 | 1.1 |

∼ 1,024 bits | 0.6 | 0.3 | 0.3 |

Receiver velocities (m/s) whose θ_{AC}

∼ 64 bits | 3.0 | 3.0 | 3.5 |

∼ 256 bits | 1.0 | 0.9 | 1.0 |

∼ 1,024 bits | 0.3 | 0.2 | 0.3 |

Polynomial coefficients of the quadratic fit for all sequences.

Kasami | 63 bits | 0.1941 | −0.0007 | 0.0299 |

255 bits | 0.1200 | 0 | 0.4083 | |

1,023 bits | 0.1796 | 0 | 2.0547 | |

| ||||

LS | 71 bits | 0.1026 | −0.0578 | 0.0446 |

271 bits | 0.2882 | −0.6773 | 1.0550 | |

1,087 bits | 0.2340 | −2.1490 | 12.8500 | |

| ||||

CSS | 64 bits | 0.3588 | 0.0081 | 0.0067 |

256 bits | 0.3879 | −0.5263 | 0.7246 | |

1,024 bits | 0.2371 | 0.1860 | 4.8540 |