International Journal of Antennas and Propagation

Volume 2018 (2018), Article ID 2301052, 9 pages

https://doi.org/10.1155/2018/2301052

## Space-Time-Frequency Adaptive Processor for Multiple Interference Suppression in GNSS Applications

College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Correspondence should be addressed to Lian-gang Qi; nc.ude.uebrh@gnagnailiq

Received 23 August 2017; Revised 9 January 2018; Accepted 17 January 2018; Published 24 April 2018

Academic Editor: Sotirios K. Goudos

Copyright © 2018 Qiang Guo 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

To enhance the multiple interference suppression performance of global navigation satellite system (GNSS) receivers without extra antenna elements, a space-time-frequency adaptive processor (STFAP) is investigated. Firstly, based on the analysis of the autocorrelation function of the multicomponent signal, we propose a common period estimation and data block technique to segment the received signal data into blocks. Secondly, the signal data in each block are short-time Fourier transformed into time-frequency (TF) domain, and the corresponding TF points with similar frequency characteristics are regrouped to structure space-time-frequency (STF) data matrixes. Finally, a space-time-frequency minimum output power- (STF-MOP) based weight calculation method is introduced to suppress multiple interfering signals according to their sparse characteristics in TF and space domains. Simulation results show that the proposed STFAP can effectively combat more wideband periodic frequency-modulated (WBPFM) interferences even some of them arriving from the same direction as GNSS signals without increasing the number of antenna elements.

#### 1. Introduction

In recent years, with the rapidly increasing complexity of the electromagnetic environment, interference suppression techniques for global navigation satellite system (GNSS) receivers have become an increasingly prominent role [1]. Many researchers have been devoting themselves in the study of interference mitigation to ensure the reliability and continuity of GNSS services, and much progress have been already achieved. According to the required number of antenna elements, existing interference suppression methods can be classified into single-antenna interference suppression techniques and multiple-antenna interference suppression techniques. The single-antenna interference suppression methods, such as frequency-domain filtering [2], adaptive time-domain filtering [3, 4], and time-frequency (TF) filtering [5], have the advantages of small volume and low hardware complexity; however, they can only deal with the interferences with sparse characteristics in time and frequency domains (such as narrowband interferences and linear chirp interferences) and are not able to cope with multiple interferences [6] effectively. The space processing based on an antenna array, such as power inversion technology and space-only MPDR (S-MPDR) beamformer, can nullify wideband interferences (WBI) and narrowband interferences (NBI) regardless of their time and frequency characteristics [7]. But the number of interferences coped with by space-only-based methods is limited to the number of antenna elements. To deal with this shortcoming, the space-time adaptive processing (STAP) is introduced in GNSS applications and widely studied [8–10]. By combining time and spatial processing, it increases the number of suppressed NBI without extra elements in the array; nevertheless, it still cannot deal with the scenario in which the number of WBI exceeds that of antenna elements. With the rapid development of jamming technology and the increasingly complex electromagnetic environment, how to effectively deal with more interferences with a limited number of antenna elements has aroused the concern of people [11]. Recently, [12] drew the attention on suppressing the multiple interferences according to their direction of arrival (DOA) and power by using an open-loop antijam approach. The key idea is to suppress the strong interferences (interference-to-signal ratio (ISR) 30 dB) by spatial processing and ignore the weak interferences. Obviously, it failed when the number of strong interferences exceeds that of antenna elements. In addition, the methods mentioned above are not able to cope with the WBI arriving from the same direction as GNSS signals very well. Reference [13, 14] drew the attention on cascaded interference suppression methods based on sparse decomposition and spatial filtering. In the first stage, the interfering signals whose waveform characteristics are known are detected and canceled by utilizing their sparsity in the overcomplete dictionary, and the residual interferences are suppressed by spatial filtering in the second stage. However, they need the prior information of interfering signals dealt with by sparse decomposition.

In view of the above problems, this paper proposes a space-time-frequency adaptive processor (STFAP) by combining TF analysis and spatial processing. More specifically, our main contributions are as follows: firstly, in order to avoid the repeated consumption of the spatial degree of freedom (DoF), we propose a common period estimation and data block technique which can obtain the common period of generalized periodic signals and segment received signal data into blocks; then, the signal data in each block are short-time Fourier transformed (STFT) into TF domain, and the corresponding TF points with similar frequency characteristics are regrouped to structure space-time-frequency (STF) data matrixes. Secondly, to avoid the degradation of interference suppression performance when the number of interferences falling into a TF point exceeds the limitation that an antenna array can cope with, we propose a space-time-frequency minimum output power- (STF-MOP) based interference suppression method to modify the conventional weight calculation formula by using a reference TF point.

#### 2. Signal Model

The analog signals received by an -element antenna array can be expressed as follows: where is the array signal, each row corresponding to one antenna, and “” represents the transpose; represents the number of interfering signals; and denote the steering vector of the GNSS signal and the th interfering signal, respectively; , and are defined as the GNSS signal, the th interfering signal, and the receiver thermal noise, respectively.

According to their frequency characteristics, interferences can be divided into NBI (e.g., single-tone (S-T) interfering signals) and WBI (e.g., wideband periodic frequency-modulated (WBPFM) and Gaussian noise (WBGN) interfering signals). The WBPFM interfering signal is one of the most efficient interferences due to its wideband and nonstationary characteristics in the frequency domain, and the WBGN interference is considered to be the most costly interference because of the requirement of large transmit power [15, 16]. Reference [17] pointed out that using different combinations of multiple WBPFM and S-T interfering signals and fewer WBGN interferences, we can effectively disable the STAP with lower costs. Therefore, this paper focuses on the research of mixed interference suppression in the presence of these interfering signals. In general, the S-T and WBPFM interfering signals can be expressed as follows: where is the frequency-modulated (FM) function with the period , where represents the number of WBPFM interfering signals; , , and are the amplitude, the carrier frequency, and the phase, respectively.

#### 3. The Proposed STFAP

From [1], we have known that, in a relatively short time, the bandwidth of the WBPFM signal is narrow; however, since its frequency is rapidly varying compared to the receiver integration time, it acts like a WBI. And as we have known, the time domain finite impulse response (FIR) filter in the conventional STAP is not able to make full use of the time-frequency sparse characteristics of interference signals because it only has frequency-resolving ability. Then, the WBPFM interference is treated as a global WBI. It results in the waste of the spatial DoF.

It is aware that since WBPFM interfering signals have significant concentrated energy distribution and periodicity in the time-frequency domain, there are a few TF points affected by the interferences. For the convenience of expression, an analysis is carried out by taking two linear frequency-modulated continuous wave (LFMCW) interfering signal as an example, and their spectrogram is shown in Figure 1, where and are the carrier frequency and bandwidth, respectively; , , denotes the frequency bins; and represent the integer multiple of two modulation period of the two LFMCW interfering signals and a positive integer, respectively; and is the number of signal data in time domain. And the TF point () is named as the ()th TF point belonging to the th block, and we defined that the “th TF point” represents the “th TF point” belonging to all blocks. From it, we can find out that although the bandwidth of the two interfering signals are the same, their frequencies are different at most times due to their different modulation periods and initial frequencies. In theory, WBPFM interferences can be treated as NBI by using a single TF point data, and the number of interferences falling into one TF point may be less than the total number of interferences in the receiving environment. However, we need huge amounts of snapshot data to ensure the performance of interference suppression due to the unknown nature of interferences and the thermal noise. Looking closely at Figure 1, the frequency characteristics of the two interfering signals in TF points () and (), such as () and (), are consistent, where is a positive integer. In other words, all of the th TF points consist the same WBPFM interferences. Then, we are able to regroup the TF points with similar TF characteristics to obtain the required number of snapshot data.