International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 297823, 11 pages

http://dx.doi.org/10.1155/2015/297823

## Estimation of Sidelobe Level Variations of Phased Codes in Presence of Random Interference for Bistatic Wideband Noise Radar

^{1}The Signal Theory and Communication Department, University of Vigo, 36310 Vigo, Spain^{2}The Klipsch School of Electrical and Computer Engineering, New Mexico State University, Las Cruces, NM 88001, USA^{3}Texas Instruments Inc., Dallas, TX 75243, USA

Received 22 July 2014; Accepted 3 November 2014

Academic Editor: Yong Bae Park

Copyright © 2015 Ana Vazquez Alejos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We discuss the importance of using the sidelobe level of the cross-correlation function as a criterion to implement a noise radar based on the transmission of wideband binary waveforms. Theoretical expressions are introduced for the parameters Peak-Sidelobe, Secondary-Sidelobe, and Integrated-Sidelobe levels for both Golay and pseudorandom binary sequences in presence of additive white Gaussian noise, relating the sequence length to the spectral power of the interfering noise. These expressions offer a valuable method for adaptive radar waveform design in order to determine sequence requirements which allow facing the noise present in the frequency band of interest. We also show a comparison of the ambiguity functions for Golay and PRBS sequences to analyze their performance in terms of Doppler and range accuracy. We describe a practical implementation of a pseudonoise waveform-based bistatic radar with reduced sidelobe level due to the use of Golay codes in combination with single side band modulation and operation at UHF band. Experimental measurements were performed in actual scenarios for ranging test of single and double targets. Linear polarizations were combined with different length sequences to determine their influence on the sounder performance under field test conditions.

#### 1. Introduction

Radar data, consisting of returns from several objects, might result easily corrupted [1–4] because of the presence of noise and interferences, scattered signal components, and frequency dispersion [5–7] due to the random nature of the propagation medium. As a result of those impairment propagations, the target detection process is further complicated due to the problem of weak signals, which carry information about subtle changes that are buried in the sidelobes of stronger reflections.

At present, widely used noise radar systems operate with either very short pulses or linear frequency modulated waveforms and are based on either mono- or bistatic configurations [8]. These systems suffer from having strong sidelobes, thereby masking weaker returns from subtle changes and making it difficult to detect those variations due to a target presence.

In order to overcome the sidelobe problem, various coding techniques have been proposed with different degrees of success in [1–4]. One such technique is based on the transmission of pseudonoise (PN) waveforms, such as pseudorandom binary sequences (PRBS), and the system using them is known as noise radar [9–14]. Although PRBS are considered a good option in terms of their autocorrelation function, these sequences are not optimal if sidelobe level is taken into account. This problem can be overcome if the transmitting process is composed of codes showing good autocorrelation properties, mainly estimated in terms of sidelobe level amplitude. This is the case of the complementary binary series of sequences known as Golay series [9–14].

Golay complementary codes are a pair of equal length sequences that have the property of canceling the sidelobes when the autocorrelation functions corresponding to each sequence are algebraically added. As a consequence of this addition, the correlation peak is double to the one corresponding to the PRBS case, thereby providing a significant enhancement in the output signal-to-noise ratio. Also, once the individual autocorrelation functions are added, they provide zero sidelobes. These improvements are important when dealing with large attenuation and/or with stronger sidelobes, as is generally the case of subsurface, through-wall or through-dispersive media detections, or in applications that require the use of large frequency bandwidth.

Due to a priori knowledge of the real-time cross-correlation function (CCF) properties of the transmitted binary sequences, an adaptive-on-transmit (AT) system can be derived for wideband radar systems using the information given by the Peak-Sidelobe (PSL), Secondary-Sidelobe (SSL), and Integrated-Sidelobe (ISL) as a design criterion.

This means that we can know the theoretical value of PSL, SSL, and ISL parameters at any instant for the transmitted code; besides, the generating conditions of the transmitted codes could be changed to improve the sidelobe values under the detection of a certain noise level presence. By adapting the sidelobe properties of the transmitted waveform to minimum levels, the overall performance of the system will achieve enhanced performance features to face anomalous or extreme operation conditions [15–18].

In this paper, we introduce a formal analysis of the sidelobe level trend for the phase codes PRBS and also for the complementary phase codes named Golay series. The ISL, SSL, and PSL parameters from their CCFs have been parameterized as functions of code length and interfering white Gaussian random noise power.

Additionally to the sidelobe issue, the noise radar technique presents some implementation requirements that often turn these systems into technical- or cost-unaffordable sounders. At the transmitter end, high bit rates and large sequence lengths are needed to achieve large amplitude and spatial resolution, respectively. This feature implies an analogue-digital conversion stage of great bandwidth and large amplitude resolution at the receiver end if a digital implementation is selected to build the sounder. This SDR (software defined radio) architecture may not be always easy to achieve and it usually results in very costly hardware.

In this paper, we introduce a solution to the problem caused by a large bandwidth requirement based on the use of single side band transmission that offers a double benefit: firstly, only half bandwidth will be required at the analogue-digital conversion stage of the receiver end, which will simplify the hardware and reduce costs; secondly, the traveling waveform will be exposed to less noise (interferences) levels, an especially important feature if the frequency band is radio electrically polluted, as the UHF band case.

Section 2 presents software simulations to illustrate a comparison of the robustness of PRBS and Golay sequences against noise interferences. Theoretical expressions are derived for PSL, SSL, and ISL terms, for both Golay and PRBS cases. Section 3 briefly describes the hardware implementation of the prototype system, followed by the experimental results in Section 4. Experimental measurements were carried out to perform ranging tests for single and double target identification for both sequences, demonstrating the viability of a phase code based noise radar in the UHF band. The influences of the sequence length, as well as the linear polarization used, have been analyzed in order to determine the behavior of this radar sounder under field test conditions. Finally, conclusions are offered in Section 5.

#### 2. Noise Radar Techniques Based on Phase Coded Binary Sequences

The noise modulated radar technique offers a large number of advantages mainly due to its robustness to interferences [8, 18, 19], and the wideband version received importance especially in the last decades [13, 14, 17–19]. Nevertheless, until not long ago, it was very difficult to find practical implementations of these systems. One of the main problems with them is that they show detection ambiguity zones and the presence of sidelobes that can mask weak reflections [8]. Another key element of the noise radar technique is the waveform generation that is mostly based on the transmission of a wideband signal that usually consists of monopulsed transmissions.

Other implementations of the wideband random noise technique use waveforms based on pseudorandom binary sequences with maximum length, also named PRBS sequences with length given in bits or chirps. This technique [8] offers great advantages regarding high resolution of targets as well as its great immunity to detection in hostile surroundings, as well as in presence of natural or man-made caused interferences.

Nevertheless, the radar technique by transmission of PRBS sequences presents a limitation in the offered dynamic range which goes bound to length of the transmitted sequence [12, 13]. Thus, detecting weaker echoes is difficult, which may be confused with noise in some cases due to the large attenuation undergone by the propagated signal. In addition, PRBS sequences present a serious problem of large power sidelobes presence [10], which worsens the problem of false echoes detection that is usual in radar applications.

The sidelobe amplitude level is directly proportional to length of the sequence, so that if the length is increased with the purpose of increasing the dynamic range, the sidelobe amplitude level will be increased in counterpart. However, by increasing the length of the transmitted sequence, the speed of target detection is decreased, thus limiting the response speed of the radar device.

In this paper, we considered a solution to the problem produced by increasing the length of the transmitted PRBS sequence by considering the use of Golay series [9–11] which lead to a twofold dynamic range with respect to the one corresponding to a PRBS sequence with the same length . This allows the use of smaller length sequences to increase the target detection speed. This feature compensates the need of transmitting two sequences in the Golay case that would increase the time needed for measurement.

In Section 2.1, the capabilities of PRBS and Golay sequences are measured in terms of PSL, SSL, and ISL levels. The effect of noise is presented in Section 2.2. This comparison also shows better understanding of advantages provided by reduced sidelobe levels. The results indicate which parameters of these binary sequences used in noise radar can be easily adapted depending on the operation requirements according to the idea of an AT system.

##### 2.1. Theoretical Expressions: PSL, SSL, and ISL

The theoretical expressions have been derived for PSL, SSL, and ISL parameters definition, sequence length , and the noise statistics mean and variance ., for unitary amplitude level of the pulses ±1 V. The theoretical definition of the sidelobe level parameters for a signal is given by

For the Golay case, the pair of sequences composing the code are denoted as and , with . As we explained above, each of them has been added with the same noise signal and later correlated with the original sequence. These operations can be expressed according to (2)–(4) where indicates correlation:

Taking into account (2)-(3), (1) can be written for the Golay case as follows:

The discrete CCFs and are given by the following expressions:

From (7) we infer that the cross-correlation between a sequence of the pair and random noise is not dependent on index . Finally, we reach the following expressions (8) for PSL, SSL, and ISL involving and :

For the PRBS case, only one sequence composes the code and it is denoted as , with . The same noise signal is added and the resulting noisy signal is correlated with the original sequence. These operations can be expressed according to (9) where indicates correlation:Taking into account (8), (1) can be written for the PRBS case as follows:Finally we reach the following expressions:

The first observation to be inferred, when comparing PSL/SSL/ISL expressions for both types of codes, is that the PSL for the Golay case is not influenced by the AWGN as much as for the PRBS case. Moreover, the SSL in the Golay case depends only on the noise parameters, whereas it also depends on the inherent autocorrelation noise in the PRBS case. So, we conclude that an irreducible noise is present in the ACF for a PRBS sequence, the so-called code noise [18]. The same trend is observed for the ISL parameter.

##### 2.2. Robustness against Sidelobe Presence

Software simulations using MATLAB have been performed to illustrate the robustness of PRBS and Golay sequences against noise interferences. For this purpose, two 4096-bit-length Golay sequences and one 8192-length PRBS sequence with amplitude level of ±1 V and chip period s were generated using software [14–16]. Additive white Gaussian noise (AWGN) was added to each sequence with power level within the range dBW. The added noise has the same bit rate as sequences used, thus offering identical bandwidth conditions.

Cross-correlation functions between noisy and original sequences were obtained. Later, PSL, SSL, and ISL levels were measured without performing any average that would aim to reduce the added noise. From the plots shown in Figure 1 the following conclusions can be inferred.(i)For larger than 3 dB, PSL levels in Golay and PRBS are the same.(ii)SSL level in Golay sequences is almost 50 dB down compared to that in PRBS.(iii)As the ratio increases, the SSL level difference between Golay and PRBS sequence decreases.(iv)ISL level in the Golay case is almost 50 dB lesser than the ISL level for PRBS.(v)As the ratio increases, the ISL level difference between the Golay and PRBS sequences decreases.(vi)For equals 16 dB, PSL level is zero. At this point the AWGN power is larger than the sequence power, so the noise masks the signal. This fact would correspond to a negative signal-to-noise ratio region.