Joint suppression method for range-Doppler ambiguity sidelobes in DTMB-based passive bistatic radar

Abstract

To mitigate the impact of the suboptimal ambiguity function of digital television terrestrial multimedia broadcasting (DTMB) signal, used as the illuminator of opportunity in passive bistatic radar, this paper provides a detailed analysis of the ambiguity function characteristics based on the physical structure of the DTMB signal frame. It elucidates the mechanisms behind intra-frame and inter-frame range sidelobes, as well as Doppler sidelobes. Building on this analysis, a novel joint method for suppressing range-Doppler ambiguity sidelobes is proposed to achieve unambiguous target detection. The proposed method effectively removes various types of ambiguity peaks while minimizing mainlobe loss. Simulations and experimental data validate the accuracy of the analysis and demonstrate the effectiveness of the proposed method.

Introduction

Passive bistatic radar (PBR) does not emit electromagnetic signals itself, but instead utilizes existing third-party illuminators of opportunity (IOs) in the environment for target detection^1,2,3. Compared to traditional active radars, PBR offers unparalleled detection advantages such as simple structure, low cost, stealth and anti-stealth capabilities, as well as being environmentally friendly and pollution-free. As a result, it has garnered widespread attention from both academia and commercial fields in recent years^4,5,6,7,8. However, waveforms from third-party IOs are not specifically designed for target detection and remain beyond the control of radar designers. Consequently, the emitted signal’s ambiguity function often exhibits an undesirable spike-shaped profile. This specific data structure may result in higher sidelobe responses or generate a series of ambiguity sidelobes in the range or Doppler domain^9,10. These sidelobes during target detection may be mistaken for real target echoes or obscure weak target signals, thereby increasing the probabilities of false alarms and missed detection. Therefore, the selection of IOs is a crucial factor influencing the performance of PBR. Parameters such as coverage area and waveform characteristics need to be carefully evaluated in combination^11,12.

Digital television terrestrial multimedia broadcasting (DTMB) is a ground-based digital television broadcasting standard developed independently by China, utilizing time-domain synchronous-orthogonal frequency division multiplexing (TDS-OFDM) technology. Its physical frame comprises time-domain pseudorandom noise (PN) synchronization sequences and OFDM data symbols, resulting in DTMB signal exhibiting pseudo-random noise-like characteristics and excellent main lobe resolution properties. However, due to periodic features in the DTMB physical signal frame such as the PN sequence frame header, system transmission parameter symbols (TPS), pre/postambles, and power differences between frame headers and payloads, its ambiguity function exhibits a main peak and multiple two-dimensional range-Doppler ambiguity sidelobes^13,14. These ambiguity sidelobes can be misidentified as false targets during the target detection, leading to the phenomenon known as “stronger signal masks weaker signal”. This occurs when the sidelobes of strong targets obscure the main peak of weaker targets, significantly degrading the PBR’s ability to estimate target parameters accurately¹⁵.

In addressing the issue of suboptimal ambiguity function in the DTMB signal, three primary methods are currently employed^16,17,18,19: PN zeroing, randomization, and truncation. Specifically, PN zeroing aims to eliminate sidelobes in the range domain by nullifying periodic sequences. However, this method effectively imposes a periodic rectangular window in the time domain, which introduces additional periodic characteristics in the Doppler domain, resulting in more pronounced Doppler sidelobes. Moreover, due to the periodic PN sequence in the DTMB signal having twice the power of the data frame, PN zeroing can lead to significant degradation in signal-to-noise ratio (SNR) during target detection. Randomization involves replacing the original periodic PN sequence with a random sequence or directly multiplying it to eliminate ambiguity side lobes. Similar to PN zeroing, this approach may introduce additional periodic Doppler peaks. Truncation aims to achieve ambiguity-free target detection by discarding specific periodic signals from the reference signal. However, truncation may introduce non-uniform sampling issues, resulting in increased computational complexity.

To effectively address the issue of suboptimal ambiguity function in the DTMB signal caused by the presence of periodic information, this paper begins with an introduction to the physical frame structure of the DTMB signal. It then provides a theoretical analysis of the mechanisms and locations of range and Doppler ambiguity peaks under different PN header patterns. Furthermore, a novel joint suppression method for range-Doppler ambiguity sidelobes in DTMB-based PBR is proposed. In this method, the received reference signal undergoes rapid and precise synchronization processing to accurately separate the periodic PN header sequences from the data frames. Subsequently, selective zeroing of the periodic PN sequences and energy balancing operations are applied to suppress ambiguity sidelobes in both the range and Doppler dimensions. Finally, the effectiveness and feasibility of the proposed method are validated through analysis of simulated and experimental data. This method aims to mitigate the impact of periodic information on the ambiguity function of the DTMB signal, thereby enhancing the accuracy and reliability of target detection in practical applications. Compared to existing research, the main novelty of this paper lies in:

• The proposed method employs multi-frame accumulation to achieve precise estimation of carrier offset, thereby significantly enhancing the quality of channel response estimation. This approach also mitigates mismatches between the reference and echo channels that can arise from coarse estimation.

• The proposed method achieves effective joint suppression of range and Doppler ambiguity sidelobes through selective zeroing of PN sequences and energy balancing processing. This approach not only mitigates additional Doppler peaks introduced by traditional zeroing methods but also further reduces the SNR loss suffered by target echoes.

• The effectiveness of the proposed method has been validated not only through simulation analysis but, more importantly, also through field experimental data, providing valuable insights for the development of DTMB-based PBR.

The rest of this paper is organized as follows. The Section on the “DTMB signal model and analysis” comprises the DTMB signal frame structure and the analysis of the signal ambiguity function. Detailed specifics of the proposed method are presented in the “Joint suppression method for range-doppler ambiguity sidelobes” Section. This is followed by a Section on “Simulations and analysis”, which includes Section on “Single-target ambiguity-free detection”, “Multi-target ambiguity-free detection”, and “Performance loss analysis”. Next, the processing and analysis of measured data are addressed. Finally, the conclusions of this paper are presented.

DTMB signal model and analysis

DTMB signal frame structure

The formation process of the DTMB physical layer transmission signal is as follows²⁰. First, the input bitstream undergoes randomization, forward error correction (FEC), and quadrature amplitude modulation (QAM) constellation mapping to form basic information blocks. Subsequently, TPS and basic data blocks undergo frequency domain interleaving, followed by OFDM modulation to generate time-domain frame symbols. Next, the frame symbols are combined with PN headers to construct basic physical layer signal frames, which are then processed through shaping filtering (e.g., square root raised cosine, SRRC) to convert into baseband output signals. Finally, the baseband signals are up-converted orthogonally to generate radio frequency signals for broadcasting services.

The DTMB physical layer signal is carried by a complex frame composed of a series of basic signal frames, structured into four layers of data frames: the daily frame (length of 24 h), sub-frame (length of 1 min), super-frame (length of 125 ms), and signal frame. The composite frame structure of the DTMB signal is illustrated in Fig. 1. The signal frame serves as the fundamental data unit in the DTMB system frame structure, comprising a concatenation of frame headers and frame bodies in the time domain. The frame header is filled with a PN sequence, which possesses excellent auto-correlation characteristics to ensure efficient codeword synchronization and robust channel estimation. In addition, to adapt to the complex and variable urban and rural communication environments, the DTMB signal defines three frame header modes of different lengths: PN420, PN595, and PN945, which correspond to varying capabilities in mitigating multipath effects. The frame body is formed by multiplexing TPS and data blocks in the frequency domain, which are then interleaved in the frequency domain and modulated into the time domain frame body signal using C subcarriers. The TPS identifies parameters such as the constellation mapping format, LDPC code rate, and single/multi-carrier mode of the frame body. Figure 2 depicts the time-frequency resource grid of DTMB signals under multi-carrier modulation. It shows that TPS consists of frame mode identification and modulation rate identification, occupying 36 symbols, while the frame body data information occupies 3744 symbols.

Fig. 1

Structure of the DTMB signal frame.

Fig. 2

Time-frequency resource grid of the DTMB signal.

The DTMB signal operates within the frequency range of 470–860 MHz, with a channel effective bandwidth of 7.56 MHz. When utilizing $C = 3780$ multi-carrier modulation, each subcarrier is spaced at intervals of 2 kHz, corresponding to a frame’s time-domain signal length of 500 $\mu$s. The baseband representation of the DTMB signal frame can be expressed as:

$$\begin{aligned} w(t) = \left\{ {\begin{array}{*{20}{c}} {p{n_l}}& {(m - 1){T_e}< t \le (m - 1){T_e} + {T_p}}\\ {{\mathbf{{s}}_b}(t)}& {(m - 1){T_e} + {T_p} < t \le m{T_e}} \end{array}} \right. \end{aligned}$$

(1)

where l denotes the phase identification of the PN sequence. When it is necessary to identify the frame sequence within a superframe, $l = (m - 1)\% L$, where % denotes the modulo operator, and L represents the total number of PN sequences with different phases within each superframe. Under PN420 mode, $L = 225$; under PN945 mode, $L = 200$. Conversely, when frame sequence identification is not required within the superframe, $L = 0$, indicating that the phase of the PN sequence remains fixed with only the PN sequence starting at phase 0 used. $T_e$ denotes the duration of a signal frame, $T_p$ represents the duration of the PN frame header. $m = 1, \cdots , M$ represents different signal frame indices within the accumulated total of M frames over time. $\mathbf{{s}}(t)$ represents the frame signal comprising TPS and the transmission data block. The $C = 3780$ modulation mode is expressed as:

$$\begin{aligned} {\mathbf{{s}}_b}(t) = \sum \limits _{c = 0}^{C - 1} {{a_c}\exp (j2\pi c\Delta ft)} \end{aligned}$$

(2)

where c denotes the index of the subcarrier carrying information, where C represents the total number of subcarriers, set to 3780. ${a_c}$ denotes the complex symbol conveying frame information. $\Delta f$ signifies the frequency spacing between subcarriers, set to 222 kHz. Typically, the average power of the PN frame header is twice that of the frame body. Figure 3 presents the time-domain waveform and spectrum of measured DTMB signals, with a carrier frequency ${f_c} = 666$ MHz, observed over a duration of 120 ms at a sampling rate ${f_s} = 8$ MHz. From the figure, it is observed that the physical frame characteristics of DTMB signals correspond to theoretical analysis. Each individual signal frame consists of a PN frame header and a signal frame body, with noticeable energy differences between the header and the body signals. The signal spectrum exhibits an effective bandwidth of 7.56 MHz, which remains stable over time, providing consistent range resolution.

Fig. 3

Time-domain waveform and spectrum of the real DTMB signal (a) time-domain waveform (b) spectrum of the real DTMB signal.

DTMB signal ambiguity function analysis

In radar signal processing, the width of the peak at the position of the ambiguity function $(\tau = 0, {f_d} = 0)$ characterizes the range and Doppler resolution of the detection signal. The specific modulation scheme of the transmitted signal waveform can introduce random sidelobes and periodic ambiguity side peaks in the ambiguity function. The ambiguity function is defined as the output of the matched filter for the transmitted signal^21,22, given by:

$$\begin{aligned} {{\chi }}(\tau ,{f_d}) = \int _{ - \frac{T}{2}}^{\frac{T}{2}} {\mathbf{{r}}(t){\mathbf{{r}}^*}(t - \tau )} \exp ( - j2\pi {f_d}t)dt \end{aligned}$$

(3)

where $\mathbf{{r}}(t)$ represents the complex envelope of the DTMB reference signal, T denotes the signal accumulation time, and $f_d$ represents the Doppler shift. Figure 4 presents the measured ambiguity function of the synchronized DTMB signal, where the carrier frequency $f_c$ is 666 MHz, the accumulation time is 0.2 s, and the frame header mode is PN945 (no phase rotation). Near the main peak at position (0, 0), a series of range and Doppler sidelobes are observed. Figure 4b,c respectively show the zero Doppler and zero range cut results of the ambiguity function. The positions of the range sidelobes are [67.6, 557.4, 625, 653.7] $\mu$s, corresponding to range bins [511, 4214, 4725, 4942]. The positions of the Doppler sidelobes are [± 1.6, ± 3.2] kHz, with the largest sidelobe peak being 7.5 dB lower than the main peak. In practical target detection, these sidelobes may generate false targets, thereby complicating the accurate estimation of target range and Doppler information. When employing multi-carrier modulation, the frame header can be selected in either PN420 or PN945 mode to provide guard intervals, with their average power being twice that of the signal frame. Under this modulation scheme, the ambiguity function of the signal exhibits three types of sidelobes: PN ambiguity sidelobes, TPS ambiguity sidelobes, and energy difference ambiguity sidelobes.

Fig. 4

Ambiguity function of the DTMB signal: (a) two-dimensional results of the ambiguity function; (b) zero Doppler profile; (c) zero range profile.

PN ambiguity sidelobes

For the PN420 frame header sequence, it consists of 420 symbols with a total duration of 55.56 $\mu$s. PN420 comprises three parts: PN255 sequence, preamble, and postamble. The PN255 sequence is an 8th-order m-sequence, which, after cyclic extension, forms the preamble and postamble with symbol lengths of 82 and 83, respectively. The PN420 frame header structure is illustrated in Fig. 5. Specifically, by varying the initial state of the PN255 sequence, 255 different PN sequences can be generated with initial phases ranging from 0 to 254, represented as:

$$\begin{aligned} p{n_l} = \left\{ {\begin{array}{*{20}{c}} {p{n_0}{{((n - 1/2))}_N}{R_N}(n),}& {l = 0,2,...,112}\\ {p{n_0}{{((n + (l + 1)/2))}_N}{R_N}(n),}& {l = 1,3,...,111}\\ {p{n_{224 - l}},}& {l = 113,114,...,224} \end{array}} \right. \end{aligned}$$

(4)

where $p{n_0}{(n)_N}$ represents the periodic extension of the zero-phase PN420 sequence and ${R_N}(n)$ denotes a rectangular window function of length $N = 255$. From (4) and the structure of this frame header mode, it is evident that within one superframe, the ambiguity sidelobes caused by the PN420 sequence consist of leading code double sidelobes $P_{420-dpr}$, trailing code double sidelobes $P_{420-dpo}$, and double main sidelobes $P_{420-dm}.$ Their respective positional information is as follows:

$$\begin{aligned} & {P_{420 - dpr}} = \left\{ {\left( {l{T_e} + \frac{{l{T_d}}}{2} + 255T,\frac{i}{{2{T_e}}}} \right) \cup \left( {l{T_e} - \frac{{l{T_d}}}{2} + 255T,\frac{i}{{2{T_e}}}} \right) |l = 2,...,110;i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(5)

$$\begin{aligned} & {P_{420 - dpo}} = \left\{ {\left( {l{T_e} + \frac{{l{T_d}}}{2} - 255T,\frac{i}{{2{T_e}}}} \right) \cup \left( {l{T_e} - \frac{{l{T_d}}}{2} - 255T,\frac{i}{{2{T_e}}}} \right) |l = 2,...,112;i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(6)

$$\begin{aligned} & {P_{420 - dm}} = \left\{ {\left( {l{T_e} + \frac{{l{T_d}}}{2},\frac{i}{{2{T_e}}}} \right) \cup \left( {l{T_e} - \frac{{l{T_d}}}{2},\frac{i}{{2{T_e}}}} \right) |l = 2,...,110;i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(7)

where $T_d$ represents the sampling interval of baseband symbols, where $T_d = 1/7.56$ $\mu s$. $T_e$ denotes the signal frame length under PN420 frame header mode, with $T_e = 555.65$ $\mu s$. Specifically, when $l = 0$, $P_{420-dpr}$ represents intra-frame sidelobes. $\textbf{Z}$ denotes the set of integers. Figure 6 illustrates the range and Doppler slices of the ambiguity function of measured DTMB signals using the phase modulation PN420 mode. Upon observation of the figure, it is evident that apart from the intra-frame ambiguity sidelobes, the remaining peaks appear in a double-peak form due to the influence of phase cyclic extension. These peaks occur at intervals that are integer multiples of the length of a single signal frame, confirming the accuracy of the analysis described above. Furthermore, when the DTMB system does not require frame identification, all PN sequences within one superframe maintain a constant phase. Specifically, the PN420 sequence with index 0 is used as the frame header. The ambiguity sidelobes under this phase configuration are represented as:

$$\begin{aligned} {P_{420}} = \left\{ {\left( {255{T_d},\frac{i}{{{T_e}}}} \right) \cup \left( {l{T_e} + 255{T_d},\frac{i}{{{T_e}}}} \right) |l \ne 0;l,i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(8)

For the PN945 frame header sequence, it consists of 945 symbols with a duration of 125 $\mu$s. The frame header comprises three parts: PN511 sequence, a preamble of length 217, and a postamble of length 217, as schematically shown in Fig. 7. By varying the initial state of PN511, 200 PN sequences with phase shifts ranging from 0 to 199 can be generated. Therefore, the PN945 frame header sequence in each superframe can be represented as:

$$\begin{aligned} p{n_l} = \left\{ {\begin{array}{*{20}{c}} {p{n_0}{{((n - 1/2))}_N}{R_N}(n),}& {l = 0,2,...,100}\\ {p{n_0}{{((n + (l + 1)/2))}_N}{R_N}(n),}& {l = 1,3,...,99}\\ {p{n_{100 - l}},}& {l = 101,102,...,199} \end{array}} \right. \end{aligned}$$

(9)

where $p{n_0}{(n)_N}$ represents the periodic extension of the zero-phase PN945 sequence and $R_{N}(n)$ denotes a rectangular window function of length $N = 511$. Based on (9) and the structure of this frame header, it is known that within one superframe, the ambiguity sidelobes caused by the PN945 sequence exist in three types: leading code double sidelobes $P_{945-dpr}$, trailing code double sidelobes $P_{945-dpo}$, and double main sidelobes $P_{945-dm}$. Their respective positional information is expressed as:

$$\begin{aligned} & {P_{945 - dpr}} = \left\{ {\left( {l{T_e} + \frac{{l{T_d}}}{2} + 511{T_d},\frac{i}{{2{T_e}}}} \right) \cup \left( {l{T_e} - \frac{{l{T_d}}}{2} + 255{T_d},\frac{i}{{2{T_e}}}} \right) |l = 2,...,98;i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(10)

$$\begin{aligned} & {P_{945 - dpo}} = \left\{ {\left( {l{T_e} + \frac{{l{T_d}}}{2} - 511{T_d},\frac{i}{{2{T_e}}}} \right) \cup \left( {l{T_e} - \frac{{l{T_d}}}{2} - 511{T_d},\frac{i}{{2{T_e}}}} \right) |l = 2,...,100;i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(11)

$$\begin{aligned} & {P_{945 - dm}} = \left\{ {\left( {l{T_e} + \frac{{l{T_d}}}{2},\frac{i}{{2{T_e}}}} \right) \cup \left( {l{T_e} - \frac{{l{T_d}}}{2},\frac{i}{{2{T_e}}}} \right) |l = 2,...,100;i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(12)

Here, $T_e$ represents the signal frame length under PN945 frame header mode, where $T_e = 625$ $\mu$s. When $l = 0$, $P_{945-dpr}$ denotes intra-frame sidelobes. When the DTMB system does not require frame identification, the ambiguity sidelobes under this phase configuration consist of intra-frame and inter-frame sidelobes. The Doppler sidelobe period is $1 / T_e$, represented as:

$$\begin{aligned} {P_{945}} = \left\{ {\left( {511{T_d},\frac{i}{{{T_e}}}} \right) \cup \left( {l{T_e} \pm 511{T_d},\frac{i}{{{T_e}}}} \right) |l \ne 0;l,i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(13)

The ambiguity function of the signal under this frame header mode is depicted in Fig. 4, showing complete alignment with theoretical analysis results.

Fig. 5

Frame header structure of the DTMB signal in PN420 mode.

Fig. 6

Ambiguity function of real DTMB signal in PN420 frame header mode (a) zero Doppler profile (b) zero range profile.

Fig. 7

Frame header structure of the DTMB signal in PN945 mode.

TPS ambiguity sidelobes

The role of TPS is to provide essential parameter information required for signal frame demodulation, such as carrier mode, bitrate selection, mapping way, and interleaving depth. Within one superframe, except for the first frame, the inserted TPS information in each signal frame remains identical. Specifically, after frequency domain interleaving, TPS is distributed throughout the entire signal frame. Therefore, the position of sidelobes $P_{TPS}$ caused by TPS (only referring to range sidelobes) is represented as:

$$\begin{aligned} {P_{TPS}} = \left\{ {\left( {l{T_e},0} \right) |l \in \mathbf{{Z}}} \right\} \end{aligned}$$

(14)

where the value of the signal frame length $T_e$ depends on the frame header mode, which equals to either 555.56 $\mu$s or 625 $\mu$s.

Energy difference ambiguity sidelobes

In the DTMB standard, to ensure rapid symbol synchronization and robust channel estimation, the average power of both PN420 and PN945 frame header sequences is twice that of the time-domain frame body signal, represented as:

$$\begin{aligned} & w(t) = g(t){h_g}(t) \end{aligned}$$

(15)

$$\begin{aligned} & {h_g}(t) = \left\{ {\begin{array}{*{20}{c}} {\sqrt{2} }& {(m - 1){T_e}< t \le (m - 1){T_e} + {T_p}}\\ 1& {(m - 1){T_e} + {T_p} < t \le m{T_e}} \end{array}} \right. \end{aligned}$$

(16)

where g(t) represents the DTMB signal where the power of the frame body equals the power of the frame header. According to (16), the energy difference between the time-domain frame header and frame body signals is equivalent to a windowing effect, where the window length is $T_p$ and the period is $T_e$. Therefore, the position of sidelobes $P_d$ caused by this energy difference is represented as:

$$\begin{aligned} {P_d} = \left\{ {\left( {0,\frac{i}{{{T_e}}}} \right) |i \ne 0,i \in \mathbf{{Z}}} \right\} \end{aligned}$$

(17)

From (17), it can be deduced that sidelobes caused by energy differences only appear at zero distance positions, meaning these sidelobes are Doppler ones.

Joint suppression method for range-doppler ambiguity sidelobes

Based on the analysis in the previous section, it is evident that the occurrence of range ambiguity sidelobes in the DTMB signal arises from the correlation characteristics between different signal frames, which are characterized by the periodicity of the PN frame header sequence and TPS. The appearance of Doppler sidelobes is attributed to the energy difference between the time-domain frame header and the frame body signals, which acts as a windowing effect, leading to velocity ambiguity. To overcome the inherent disadvantages of the DTMB signal ambiguity function and achieve unambiguous target detection, a novel method for joint suppression of two-dimensional range-Doppler ambiguity sidelobes is proposed, and with its flowchart is shown in Fig. 8. The core steps of this method include high-precision signal synchronization, selective zeroing of the PN frame header, energy equalization, and joint cross-ambiguity processing.

Fig. 8

Flowchart of the proposed joint range-Doppler ambiguity sidelobe suppression method.

High-precision signal synchronization

To separate the PN frame header sequence from the frame body, precise symbol and carrier frequency synchronization of the received signal is essential. In this subsection, a joint time-frequency synchronization method based on multi-frame signal accumulation is proposed, which enables robust parameter estimation for both time-domain symbol positions and carrier frequency offsets.

As depicted in Fig. 9, the core idea of this method is to treat the direct-path signal with time delay and frequency offset as the signal echo of a moving target, and estimate its parameters in the matched filtering manner. Specifically, the sampled reference signal is first preprocessed into subframes, dividing it according to the length of a single signal frame and arranging it into a two-dimensional matrix of intra-frame and inter-frame signal. Then, cross-correlation processing is performed between the local PN sequence and all subframes within the frame to obtain the starting position information of the time-domain symbols within the subframe. This process can be represented as:

$$\begin{aligned} {\xi _m}[d] = \sum \limits _{n = 0}^{{L_{pn}} - 1} {p{n^*}[n]{r_m}[n + d]} \end{aligned}$$

(18)

where ${L_{pn}}$ represents the length of the PN sequence, m signifies the subframe number, r[n] refers to the discrete sampled form of the reference signal, and pn[n] denotes the local PN420/PN945 sequence. Subsequently, coherent processing between frames is performed using the fast Fourier transform to form a unique accumulation peak, thereby obtaining an estimate of the symbol frequency offset, which can be expressed as:

$$\begin{aligned} \psi [d,v] = \sum \limits _{m = 0}^{M - 1} {{\xi _m}[d]{e^{ - j2\pi mv/M}}} \end{aligned}$$

(19)

where d and v represent the time-domain starting position of the symbol and the carrier frequency offset, respectively. After processing with the aforementioned method, the precise symbol starting position can be obtained, thereby achieving the separation of the PN frame header and the OFDM frame body data block. Further, Fig. 10 presents the synchronization results of this method applied to the measured DTMB signal. It can be observed that the maximum correlation peak of the signal appears at the 3184th sample point, indicating that the starting position of the signal frame is 3184.

Fig. 9

Flowchart of multi-frame signal time-frequency synchronization estimation.

Fig. 10

Time-frequency synchronization results based on measured data from the DTMB signal.

Selective zeroing of the PN frame header

The PN frame header sequence consists of three parts: a preamble, an m-sequence, and a postamble. Its periodicity can lead to the appearance of both intra-frame and inter-frame sidelobes in the range dimension. As analyzed in the previous section, within the detection region of interest, range sidelobes include both intra-frame and inter-frame types, arising from the correlation of the preamble/postamble and their cyclic extension sequences. Therefore, zeroing out the preamble/postamble and their corresponding cyclic extension sequences for each signal frame can eliminate the impact of range sidelobes. Specifically, the selective zeroing of the PN frame header involves two steps: a) zeroing the cyclic extension sequences of the preamble and postamble to eliminate intra-frame range sidelobes; b) zeroing the cyclic extension sequences of the postamble and preamble to eliminate inter-frame range sidelobes. For clarity, these steps are referred to as preamble zeroing and postamble zeroing.

Since the zeroing operation is equivalent to applying a periodic rectangular window to the reference signal, The form of the reference signal after selective zeroing (windowing) of the PN frame header in PN945 mode is shown in Fig. 11. In practical applications, the specific mathematical form of the periodic rectangular window can be written as:

$$\begin{aligned} {h_r}(t) = \left\{ {\begin{array}{*{20}{c}} 0& {(m - 1){T_e}< t \le (m - 1){T_e} + 2{T_{pr}}}\\ 1& {(m - 1){T_e} + 2{T_{pr}} < t \le m{T_e}} \end{array}} \right. \end{aligned}$$

(20)

where ${T_{pr}}$ represents the time length of the preamble. By performing cross-ambiguity processing between the reference signal, with the preamble sequence zeroed, and the target echo signal s(t), the target accumulation result without intra-frame range ambiguity, denoted as $CA{F_z}$, can be obtained. It is expressed as:

$$\begin{aligned} CA{F_z}(\tau ,{f_d}) = \int _{ - T/2}^{T/2} {s(t){r^*}(t - \tau ){h_r}(t)} \exp ( - j2\pi {f_d}t)dt \end{aligned}$$

(21)

Similarly, by performing cross-ambiguity processing between the reference signal, with the postamble sequence windowed, and the target echo signal s(t), the target accumulation result without inter-frame range ambiguity, denoted as $CA{F_p}$, can be obtained. It is noteworthy that after the Fourier Transform, the presence of the window function introduces additional ambiguity sidelobes in the frequency domain due to its time-domain periodicity. The positions of these sidelobes are distributed as follows:

$$\begin{aligned} {P_z} = \left\{ {\left( {0,\frac{i}{{{T_e}}}} \right) |i \in N;i \ne 0} \right\} \end{aligned}$$

(22)

Based on the method proposed in the previous subsection, the identification of the impure component within the reference signal can be achieved. The subsequent focus of this subsection revolves around the reconstruction of the signal and the subsequent purification of the reference signal through subtraction from the original reference signal. This purification process aims to mitigate the adverse impact of impurities on target detection.

Fig. 11

Illustration of the reference signal after selective zeroing of the PN frame header in PN945 mode (a) preamble zeroing (b) postamble zeroing.

Energy equalization

As mentioned in the previous section, the energy difference between the frame header and frame body signal is equivalent to a windowing effect, leading to the appearance of periodic peaks in the Doppler domain. Therefore, this paper employs energy equalization of the PN frame header sequence to eliminate the impact of Doppler sidelobes. The specific equalization response can be written as:

$$\begin{aligned} {h_e}(t) = \left\{ {\begin{array}{*{20}{c}} {1/2}& {(m - 1){T_e}< t \le (m - 1){T_e} + {T_p}}\\ 1& {(m - 1){T_e} + {T_p} < t \le m{T_e}} \end{array}} \right. \end{aligned}$$

(23)

Figure 12 shows the time-domain waveform of the reference signal after energy equalization processing. Compared to Fig. 3, the energy of the PN frame header sequence is significantly reduced, with its average power equaling that of the frame body signal, effectively eliminating the windowing effect. Similarly, by performing cross-ambiguity processing between the energy-equalized reference signal and the target echo signal s(t), the target accumulation result without Doppler ambiguity, denoted as $CA{F_n}$, can be obtained as:

$$\begin{aligned} CA{F_n}(\tau ,{f_d}) = \int _{ - T/2}^{T/2} {s(t){r^*}(t - \tau ){h_e}(t)} \exp ( - j2\pi {f_d}t)dt \end{aligned}$$

(24)

Fig. 12

Time-domain waveform of the reference signal after energy equalization.

Joint cross-ambiguity processing

The two operations described above are independent and can be processed in parallel. After the reference signal undergoes selective zeroing with the PN sequence, the periodic characteristics within and between signal frames are alleviated. Consequently, cross-ambiguity processing between the selectively zeroed reference signal and the target echo signal effectively suppresses range sidelobes. Specifically, in the accumulation results $CA{F_z}$ and $CA{F_p}$, additional peaks appear in the Doppler dimension, with amplitudes greater than the original peaks. Meanwhile, the reference signal, after energy equalization, compensates for the energy difference effect. The cross-ambiguity processing with the echo signal eliminates the influence of the original Doppler sidelobes, yielding the result $CA{F_n}$. However, due to the specific periodic characteristics within and between signal frames not being completely eliminated, range sidelobes still exist in $CA{F_n}$ compared to $CA{F_z}$ and $CA{F_p}$. To effectively suppress both range and Doppler sidelobes, further joint processing of $CA{F_z}$, $CA{F_p}$, and $CA{F_n}$ is required. This involves taking the intersection of different accumulation results and selecting the maximum peak as the final detection result for the target, thereby eliminating additional ambiguous sidelobes and achieving an accumulation result $CA{F_m}$ without range and Doppler ambiguity. This procedure can be expressed as:

$$\begin{aligned} CA{F_m}(\tau ,{f_d}) = \left\{ {\begin{array}{*{20}{c}} {\max \{ \left| {CAF_m^{'}(\tau ,{f_d})} \right| ,\left| {CA{F_n}(\tau ,{f_d})} \right| \} }& {\left| {CAF_m^{'}(\tau ,{f_d})} \right|> \gamma and \left| {CA{F_n}(\tau ,{f_d})} \right| > \gamma ,}\\ {\min \{ \left| {CAF_m^{'}(\tau ,{f_d})} \right| ,\left| {CA{F_n}(\tau ,{f_d})} \right| \} }& {other} \end{array}} \right. \end{aligned}$$

(25)

where $\gamma$ is the detection threshold, and $CAF_m^{'}$ is calculated by:

$$\begin{aligned} CAF_m^{'}(\tau ,{f_d}) = \left\{ {\begin{array}{*{20}{c}} {\max \{ \left| {CA{F_z}(\tau ,{f_d})} \right| ,\left| {CA{F_p}(\tau ,{f_d})} \right| \} }& {\left| {CA{F_z}(\tau ,{f_d})} \right|> \gamma and\left| {CA{F_z}(\tau ,{f_d})} \right| > \gamma ,}\\ {\min \{ \left| {CA{F_z}(\tau ,{f_d})} \right| ,\left| {CA{F_p}(\tau ,{f_d})} \right| \} }& {other} \end{array}} \right. \end{aligned}$$

(26)

Simulations and analysis

This section uses simulation data to validate the proposed method’s performance in suppressing ambiguity sidelobes. The simulated DTMB signal is generated in strict accordance with the national standard physical frame definitions. The simulation parameters for the DTMB signal are detailed in Table 1, with a signal length of 125 ms. Specifically, this section presents multiple simulation experiments, including single-target ambiguity-free detection, multi-target ambiguity-free detection, and performance loss analysis. Additionally, the simulations assume that the maximum detection range and velocity interval of the PBR are 90 km and 360 m/s, respectively, focusing on ambiguity-free detection within 4500 range cells and ± 4 kHz for targets.

Table 1 Simulation parameters.

Single-target ambiguity-free detection

This subsection compares the single-target detection performance of conventional range-Doppler (RD) processing method, reference signal zeroing method, reference signal randomization method, and the proposed method. The moving target has an initial range cell of 100, a Doppler frequency of 210 Hz, and an initial SNR of − 25 dB before detection. The target accumulation results using the conventional RD method are shown in Fig. 13a. As observed, in addition to the main peak, a series of sidelobes appear in both the range and Doppler dimensions. The minimum energy difference between these sidelobes and the main peak is 16.1 dB, and these sidelobes may be misinterpreted as real targets during detection, thereby increasing the false alarm rate. Therefore, it is necessary to remove these two-dimensional false peaks to improve target detection performance. Figure 13b shows the target processing results using the reference signal zeroing method. It is evident that zeroing the PN sequence disrupts the signal’s periodic characteristics, effectively suppressing the range dimension sidelobes. However, zeroing, which is equivalent to windowing in the time domain, results in more severe ambiguity sidelobes in the Doppler frequency domain. Figure 13c illustrates the target processing results using the reference signal randomization method. Similar to the zeroing operation, this method only suppresses range sidelobes caused by the PN sequence’s periodic characteristics and cannot eliminate the periodic Doppler peaks.

Fig. 13

Single-target processing results of three existing methods (a) results of traditional RD method (b) results of zeroing method profile (c) results of randomization method.

Figure 14 presents the target accumulation results of the proposed method. Specifically, Fig. 14a displays the target accumulation results after selectively zeroing the PN sequence’s preamble in the reference signal. Within the region of interest, this approach effectively eliminates the intra-frame range ambiguity peaks. Figure 14b presents the target accumulation results following the selective zeroing of the PN sequence’s postamble in the reference signal. This method effectively suppresses the inter-frame range dimension ambiguity peaks within the region of interest. Figure 14c displays the target accumulation results after equalizing the energy difference between the PN frame header sequence and the frame body signal in the reference signal. Compared to Fig. 14a,b, it is clear that the Doppler dimension’s periodic peaks are completely suppressed, leaving only the range peaks. Figure 14d illustrates the results of joint cross-ambiguity processing of the ambiguity-free detection results from Fig. 14a–c. The simulation results show that both range and Doppler sidelobes, caused by the signal’s inherent periodic and energy difference characteristics, are effectively suppressed. The target appears with a unique detection peak, significantly reducing the false alarm rate for the DTMB-based PBR.

Fig. 14

Single-target processing results of the proposed method (a) intra-frame ambiguity peaks suppression (b) inter-frame range ambiguity peaks suppression (c) Doppler ambiguity peaks suppression (d) results of joint cross-ambiguity processing.

Multi-target ambiguity-free detection

This subsection evaluates the multi-target detection performance of the proposed method through simulation experiments, focusing on the problem of “large target masking small targets.” The motion parameters of the targets are detailed in Table 2. Figure 15a illustrates the target detection results using the conventional RD method. It is evident from the figure that, in addition to the main peak of the target, significant range and Doppler ambiguity sidelobes, caused by the strong target A, appear in the detection results. These sidelobes not only create false alarms but also obscure the main peaks of targets B and C, making it challenging to accurately resolve the range and Doppler information for all three targets. To detect target without ambiguity, the proposed method is used to suppress the two-dimensional ambiguity sidelobes. Initially, the preamble of the reference signal is selectively zeroed, and the accumulation result is shown in Fig. 15b. Next, zeroing of the postamble is applied to address inter-frame range dimension ambiguity, with the resulting accumulation shown in Fig. 15c. Combining the results from Fig. 15b,c yields a detection result free of range ambiguity, revealing three distinct target peaks in the range dimension. Subsequently, energy equalization is applied to the reference signal, followed by RD processing with the echo signal to achieve Doppler ambiguity-free detection, as shown in Fig. 15d. This figure demonstrates that the periodic peaks in the Doppler dimension caused by the large target A are completely removed, allowing clear observation of the Doppler frequencies for the three simulated targets. Finally, joint processing of the detection results from Fig. 15b–d provides multi-target parameter information free from both range and Doppler ambiguities, as depicted in Fig. 15e. This result shows three distinct target peaks on the detection plane, with parameter information consistent with theoretical simulations. The simulation results confirm that the proposed method effectively suppresses two-dimensional ambiguity sidelobes, resolves the “large target masking small targets” issue in multi-target detection scenarios, and improves the detection probability of DTMB-based PBR.

Table 2 Target motion parameters.

Fig. 15

Multi-target processing results of different methods (a) results of traditional RD method (b) intra-frame ambiguity peaks suppression (c) inter-frame range ambiguity peaks suppression (d) Doppler ambiguity peaks suppression (e) results of joint cross-ambiguity processing.

Performance loss analysis

The previous two subsections provided a detailed analysis of the two-dimensional sidelobe suppression performance of the proposed method under single-target and multi-target conditions. This subsection further explores the performance loss associated with the proposed method. In the DTMB signal frame under the PN945 mode, the PN preamble sequence occupies $20\%$ of the total frame length, with the preamble and postamble sequences each accounting for $4.6\%$ of the effective length. Additionally, the TPS occupies $0.8\%$ of the effective signal length. Employing the conventional zeroing method to eliminate range dimension sidelobes results in approximately 1 dB of target energy loss and introduces severe periodic Doppler sidelobes. In this section, considering the specific target detection intervals for the DTMB signal, it is sufficient to selectively remove the preamble and postamble sequences to suppress range ambiguity peaks. Consequently, the SNR loss of the target main peak is reduced to only 0.4 dB.

Verification with real-world DTMB-based PBR data

This section validates the target detection performance of the proposed method using real-world data from a DTMB-based passive radar system. The experimental setup includes a receiving station located in Xingping, and a transmitting station at the Xi’an TV Tower, operating at a frequency of 666 MHz. The frame head mode is the non-phase-rotated PN945, and other system parameters remain consistent with those listed in Table 1. The signal accumulation time is 100 ms. As shown in Fig. 8, the process begins by purifying the original reference signal to obtain the clean direct-path signal. Adaptive filtering methods are then employed to suppress complex clutter²³, resulting in the target echo signal. Finally, the proposed method is used to achieve unambiguous target detection. Particularly, before performing target detection, this section first presents the ambiguity functions of the original reference signal and the reference signal processed by the proposed method, as illustrated in Fig. 16. It is evident that, after applying selective zeroing of the PN sequence and energy equalization, the DTMB signal’s ambiguity function exhibits a single dominant peak in both the range and Doppler dimensions. This confirms the effectiveness of the theoretical and simulation analyses discussed earlier.

Fig. 16

Comparisons of ambiguity functions between the original reference signal and the reference signal after processing by the proposed method (both based on the real DTMB signal) (a) zero Doppler profile (b) zero range profile.

Figure 17 presents the target accumulation results processed by different methods. Figure 17a shows the result of the traditional RD method. It is evident that in the two-dimensional detection plane, in addition to the prominent target peak at (9, 29.5 Hz), a series of ambiguity peaks are present. These include intra-frame range ambiguity peaks, inter-frame range ambiguity peaks, Doppler periodic peaks, and co-frequency interference peaks, which can be removed through secondary interference cancellation. After constant false alarm rate (CFAR) detection, these peaks will be output as real targets, severely degrading the detection performance of the PBR. Figure 17b shows the results after zeroing the reference signal. It can be seen that although the main peak of the target in the range dimension can be effectively resolved, more severe periodic peaks appear in the Doppler dimension, with a maximum value being 13.4 dB. This indicates a high probability of false alarms. Finally, Fig. 17c describes the target accumulation result processed by the proposed method (selective zeroing of the PN sequence and energy equalization), showing no range or Doppler ambiguity. It can be seen that there is only one moving target in this batch of measured data, with all range and Doppler ambiguity peaks completely suppressed. The target echo signal forms a single peak at (9, 29.5 Hz) in the detection plane, improving the target detection performance of the PBR.

Fig. 17

Comparisons of results obtained by processing field data using different methods (a) results of traditional RD method (b) results of zeroing method (c) results of the proposed method.

Conclusions

This paper investigates the use of the DTMB signal as the IO for PBR and addresses the challenge of target detection caused by its suboptimal ambiguity function. An analysis of the physical frame structure of the DTMB signal reveals the mechanisms and locations of range and Doppler ambiguity peaks under different PN header modes. Based on this analysis, a joint suppression method for two-dimensional ambiguity peaks is proposed to achieve unambiguous target detection. This method effectively removes range and Doppler ambiguity peaks through selective zeroing of the PN sequence and energy equalization. Additionally, a joint time-frequency synchronization method based on multi-frame signal accumulation is presented, facilitating rapid and accurate signal synchronization estimation and further ensuring effective suppression of two-dimensional range-Doppler ambiguity. Analysis of a series of simulations and field test data demonstrates the feasibility of the proposed method.