A synchronization module, receiver, and signal processing method for an integrated communication and navigation receiver.

Abstract

This invention belongs to the field of communication and navigation, and relates to a synchronization module, receiver, and signal processing method for an integrated communication and navigation receiver. The synchronization module has two signal paths: one for synchronizing received signals for communication services; the other is a navigation tracking loop, including a delay-locked loop and a frequency-locked loop, for estimating time delays for navigation services; the delay-locked loop includes an instantaneous branch, a lead branch, and a delay branch. The received signal is mixed with a local carrier and filtered to obtain an intermediate frequency (IF) signal; the IF signal is multiplied by a reference signal and then coherently integrated to obtain the integral result; the autocorrelation function values ​​of the three branches are calculated based on the integral result; the time delay is then calculated; the calculated time delay estimate is passed to the time synchronization module and the reference signal generation module; the frequency offset estimate is obtained based on the integration result and passed to the frequency synchronization module and the carrier generation module. This solves the problem that existing synchronization modules cannot be compatible with communication and navigation synchronization.

Description

Technical Field

[0001] This invention belongs to the field of communication and navigation, and specifically relates to a synchronization module, receiver, and signal processing method for an integrated communication and navigation receiver. Background Technology

[0002] In today's era of rapid information technology development, communication and navigation technologies play a vital role in numerous fields. Whether in aerospace, transportation, military applications, or everyday communications, the demand for high-precision, high-reliability communication and navigation equipment is constantly increasing.

[0003] Traditional communication and navigation systems are typically designed and operated independently, resulting in large, expensive devices and limiting overall system performance and resource utilization. For example, in complex applications, devices requiring both precise navigation and efficient communication capabilities are often unsuitable for standalone systems. With technological advancements, the concept of Integrated Communication and Navigation (ICAN) has emerged. It aims to organically integrate communication and navigation functions into a single system, enabling resource sharing and collaborative operation, thereby improving overall system performance and efficiency.

[0004] As a crucial component of an integrated communication and navigation system, the design of the receiver's synchronization module is particularly important. The synchronization module is the core element ensuring the receiver's accurate signal reception and processing. It needs to rapidly and accurately acquire, track, and synchronize signals in complex electromagnetic environments to guarantee communication stability and navigation accuracy. However, due to differences in characteristics and modulation methods between communication and navigation signals, designing a synchronization module that can accommodate both presents numerous challenges, such as signal interference suppression, improving synchronization accuracy, and balancing algorithm complexity with real-time performance. Summary of the Invention

[0005] The purpose of this invention is to provide a synchronization module, receiver, and signal processing method for an integrated communication and navigation receiver, which solves the problem that the synchronization module in existing receivers cannot be compatible with communication and navigation synchronization.

[0006] This invention is achieved through the following technical solution:

[0007] This invention discloses a synchronization module for an integrated communication and navigation receiver. The synchronization module has two signal paths: one for synchronizing the reception of signals for communication services; and the other is a navigation tracking loop for estimating the time offset and frequency offset of the received signals and estimating the time delay for navigation services.

[0008] The navigation tracking loop includes a delay-locked loop that acts as a code tracking loop and a frequency-locked loop;

[0009] The delayed-locked loop consists of three branches: an immediate branch, a leading branch, and a delayed branch;

[0010] The signal path for synchronously received signals includes a time synchronization module and a frequency synchronization module;

[0011] Each of the three branches is connected to a reference signal generation module and a carrier generation module.

[0012] Furthermore, the outputs of the three branches are connected to time delay discriminators, and the outputs of the time delay discriminators are connected to DLL filters; the output of the instantaneous branch is connected to an FLL filter.

[0013] The DLL filter connects to the time synchronization module and the reference signal generation module;

[0014] The FLL filter connects the frequency synchronization module and the carrier generation module.

[0015] This invention also discloses a signal processing method for the synchronization module of an integrated communication and navigation receiver, comprising the following steps:

[0016] The received signal is mixed with a local carrier and then filtered to obtain an intermediate frequency signal;

[0017] The intermediate frequency signal is multiplied by the locally replicated reference signal, and then coherently integrated to obtain the integral results on the in-phase and quadrature components.

[0018] The autocorrelation function values ​​of the three branches were calculated using the integration results;

[0019] The time delay is calculated based on the autocorrelation function value;

[0020] The time delay is filtered and calculated to obtain an estimated time delay value; the estimated time delay value is then passed to the time synchronization module and the reference signal generation module.

[0021] Meanwhile, the frequency offset value is calculated based on the integration result. After filtering, the frequency offset value is used to obtain the frequency offset estimate, which is then transmitted to the frequency synchronization module and the carrier generation module.

[0022] Furthermore, the received signal is mixed with a local carrier and then filtered to obtain an intermediate frequency signal, as expressed by:

[0023]

[0024] in, t Indicates time, The real part of the complex number is represented by j, and the imaginary unit is represented by j. It is the frequency of the local carrier. and These represent the in-phase and quadrature components of the intermediate frequency signal, respectively.

[0025] Furthermore, the integral results on the in-phase and quadrature components are specifically expressed as follows:

[0026]

[0027] in, This indicates the time delay between the received signal and the locally copied signal. This represents the autocorrelation function of the reference signal on the in-phase and quadrature components. Indicates the frequency offset between the received signal and the local carrier. This indicates the phase offset between the received signal and the local carrier. It is the integration period. This represents the sinc function. This represents the integral result over the in-phase components; This represents the result of the integral over the orthogonal components.

[0028] Furthermore, the time offset of the reference signal corresponding to the instantaneous branch is The reference signal time offset ratio corresponding to the leading branch The time offset of the reference signal corresponding to the delay branch is less than 1 correlator spacing. One larger correlation spacing;

[0029] The autocorrelation function values ​​of the three branches are calculated using the integration results, i.e., the autocorrelation function values ​​of the branches. The expression is:

[0030]

[0031] Similarly, the autocorrelation function value of the leading branch is obtained. Autocorrelation function values ​​of delay branches ;

[0032] The time delay is calculated based on the autocorrelation function value, expressed as follows:

[0033] .

[0034] Furthermore, the process of obtaining the estimated time delay by filtering the time delay is as follows:

[0035] First, obtain the filtered time delay. Calculate using the following formula:

[0036]

[0037] in, and These are the filtering time delay and the measurement time delay in the previous integration cycle, respectively.

[0038] This represents the natural frequency that determines output accuracy and dynamic response performance;

[0039] Finally, the filtered delay Delay estimate in the previous integration period Calculate the estimated time delay. :

[0040] ;

[0041] in, It is the integration period.

[0042] further, Based on the noise bandwidth of the DLL The calculation shows that:

[0043] .

[0044] Furthermore, the process of measuring the frequency offset value based on the integration result is as follows:

[0045] The integral value is first calculated from the integral results on the in-phase and quadrature components. :

[0046]

[0047] The phase change between adjacent integration cycles is obtained by multiplying the integral value from the previous integration cycle with the integral value corresponding to the current integration cycle. The expression is as follows:

[0048]

[0049] in, express The conjugate of complex numbers, The modulus of a complex number, Indicates the integration period Phase changes in the middle;

[0050] The frequency offset value is calculated based on this phase change. :

[0051]

[0052] The range of frequency measurement is , It is the integration period;

[0053] The frequency offset value is filtered to obtain the frequency offset estimate. .

[0054] The present invention also discloses an integrated communication and navigation receiver containing the aforementioned synchronization module.

[0055] Compared with the prior art, the present invention has the following beneficial technical effects:

[0056] This invention proposes a synchronization module for an integrated communication and navigation receiver, which integrates navigation tracking loop and communication synchronization functions. It has a time synchronization module and combines it with a delay-locked loop (DLL). By utilizing its three branches of instantaneous, lead, and delay, it can accurately identify signal time delay and precisely correct time errors through a DLL filter, allowing the receiver to accurately locate the time point of the received signal. This is extremely important for subsequent accurate data demodulation and positioning calculation.

[0057] A frequency-locked loop (FLL) works in conjunction with a frequency synchronization module to accurately estimate and compensate for frequency offsets in the received signal. Precise frequency synchronization avoids distortion and bit errors caused by frequency deviations during signal demodulation, ensuring the reliability of the communication link and the accuracy of data transmission.

[0058] Two distinct signal paths are configured: one for basic synchronization reception and the other focused on navigation and tracking, with a clear division of labor. This architecture allows for targeted optimization and debugging of the synchronization process and navigation and tracking parameter estimation in complex and variable signal environments, enhancing the system's adaptability to different operating conditions.

[0059] The delay-locked loop and the frequency-locked loop work together to continuously track and adjust the signal when it changes dynamically, whether it is the Doppler frequency shift of the signal or the fluctuation of the transmission delay. This maintains a stable and reliable lock on the signal, reduces the probability of signal loss, and ensures the continuity of communication and navigation functions.

[0060] The connections between the modules are clear, so if a module malfunctions, it can be quickly located and troubleshooted. Replacing the corresponding module will fix the problem, reducing maintenance costs and difficulty, and also facilitating subsequent system upgrades and functional expansion.

[0061] This invention proposes an ICAN receiver that integrates a navigation tracking loop and a communication synchronization module. The synchronization module can be used for both synchronizing communication signals and estimating the time delay of navigation services. Compared to separate communication and navigation receivers, this ICAN receiver improves signal processing efficiency and reduces cost and power consumption. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the synchronization module of an ICAN receiver;

[0063] Figure 2 Application of synchronization modules in OFDM systems;

[0064] Figure 3 The curve showing the change in BER as a function of satellite transmission power;

[0065] Figure 4 The curve showing how the estimation error of the time delay changes over time;

[0066] Figure 5 This shows the variation of ranging accuracy with LEO satellite transmission power. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of the present invention clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the present invention, and not all of them.

[0068] The detailed description of the embodiments of the present invention provided in the following figures is not intended to limit the scope of the claimed invention, but merely to illustrate one selected embodiment of the invention. All other embodiments obtained by those skilled in the art based on the figures and embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0069] The features and performance of the present invention will be further described in detail below with reference to embodiments.

[0070] This invention proposes an ICAN receiver that integrates a navigation tracking loop and a communication synchronization module. The synchronization module can be used for both synchronizing communication signals and estimating the time delay of navigation services. Compared to separate communication and navigation receivers, this ICAN receiver improves signal processing efficiency and reduces cost and power consumption.

[0071] First, the working principle of the ICAN receiver synchronization module proposed in this invention is described in detail. Then, taking an Orthogonal Frequency Division Multiplexing (OFDM) system as an example, the transmitter and receiver processing flow of integrated communication and navigation signals is illustrated, in which the signal synchronization module utilizes the method proposed in this invention. Finally, the performance of the ICAN receiver synchronization module proposed in this invention is compared with that of traditional receiver synchronization modules, demonstrating the advantages of this method.

[0072] The synchronization module of the integrated communication and navigation receiver designed in this invention has two functions: (1) to receive signals synchronously for communication services; and (2) to estimate time delays for navigation services. Generally, integrated communication and navigation signals contain a reference signal, which can be reproduced in the receiver and used to achieve synchronization of the integrated communication and navigation signals.

[0073] Figure 1 This diagram shows the synchronization module of an ICAN receiver, which has two signal paths: one for synchronizing the received signal. The other is the navigation tracking loop, used for estimation. The navigation tracking loop consists of a delay lock loop (DLL) that acts as a code tracking loop and a frequency lock loop (FLL). The DLL contains three branches: an immediate branch, a lead branch, and a delay branch.

[0074] The signal output by the instantaneous branch is the square of the autocorrelation function value. The signal output by the leading branch is the square of the autocorrelation function value. The signal output by the delayed branch is the square of the autocorrelation function value. .

[0075] The three branches are connected to the reference signal generation module and the carrier generation module. The output of the three branches is connected to the time delay discriminator, and the output of the time delay discriminator is connected to the DLL filter. The output of the instantaneous branch is connected to the FLL filter.

[0076] The signal path for synchronously received signals includes a time synchronization module and a frequency synchronization module.

[0077] The DLL filter connects to the time synchronization module and the reference signal generation module.

[0078] The FLL filter connects the frequency synchronization module and the carrier generation module.

[0079] The following details the processing procedure of the Delayed Locked Loop DLL.

[0080] To better understand the principle of delay-locked loops, we will use an instantaneous branch as an example. Figure 1 As shown, first, the signal is received. It is mixed with a local carrier and then filtered to obtain an intermediate frequency signal. :

[0081] (1)

[0082] in, t Indicates time, The real part of the complex number is represented by j, and the imaginary unit is represented by j. It is the frequency of the local carrier. and These represent the in-phase (I) component and the quadrature (Q) component of the intermediate frequency signal, respectively.

[0083] Subsequently, the intermediate frequency signal Multiplying the product with the locally replicated reference signal, the result is fed to the Integrator & Discard (I&D) filter for coherent integration. The integration results on the in-phase and quadrature components are as follows:

[0084] (2)

[0085] in, This indicates the time delay between the received signal and the locally copied signal. This represents the autocorrelation function of the reference signal on the in-phase and quadrature components. Indicates the frequency offset between the received signal and the local carrier. This indicates the phase offset between the received signal and the local carrier. It is the integration period. This represents the sinc function. This represents the integral result over the in-phase components; This represents the result of the integral over the orthogonal components.

[0086] To avoid phase shift The influence of the autocorrelation function is calculated using the coherence integral results. :

[0087] (3)

[0088] Similarly, the autocorrelation function values ​​of the leading branch can be generated. Autocorrelation function values ​​of delay branches The difference between the three branches lies in the time offset of the locally copied reference signal; that is, the time offset of the reference signal corresponding to the branch is... The reference signal time offset ratio corresponding to the leading branch is... The time offset of the reference signal corresponding to the delay branch is less than 1 correlator spacing. The difference in the correlator spacing (one step larger) results in different local reference signals. These reference signals are multiplied by the intermediate frequency signal and then coherently integrated, leading to different autocorrelation function values.

[0089] The non-coherent early-minus-late power (NELP) method is used as a time delay discrimination method. The calculation formula for the time delay discriminator is as follows:

[0090] (4)

[0091] Then, the calculated time delay The signal is fed to a DLL filter to reduce the impact of noise. Because the time delay of the received signal varies linearly with time, this invention uses a second-order DLL loop to accurately track the time delay. This invention uses a first-order DLL filter, and the time delay after filtering by the DLL filter... Calculate as follows:

[0092] (5)

[0093] in, and These are the filtering time delay and the measurement time delay in the previous integration cycle, respectively. These are parameters of the DLL filter, representing the natural frequencies that determine output accuracy and dynamic response performance. They can be determined based on the noise bandwidth of the DLL. The calculation shows that:

[0094] (6)

[0095] Finally, the filtered delay Delay estimate in the previous integration period Calculate the estimated time delay in the current integration period. :

[0096] (7)

[0097] Then, the time delay estimate It is passed to the time synchronization module and the reference signal generation module to mitigate the time offset of the received signal.

[0098] also, It can also be used to calculate the pseudorange of navigation services. Notably, the proposed synchronization method simultaneously estimates the time delays of communication and navigation services. Compared to processing communication and navigation separately, this ICAN receiver eliminates the need for a carrier tracking loop in navigation and a traditional synchronization module in communication, reducing cost and power consumption.

[0099] The following section details the processing procedure of a frequency-locked loop (FLL).

[0100] Due to the influence of the Doppler frequency and the low-stability oscillator, there is a frequency offset between the received signal and the locally replicated signal in the receiver. The frequency-locked loop (FLL) tracks the intermediate frequency (IF) signal based on adjacent integral values ​​in the instantaneous branch. (Integral value) It is derived from the integration of the I and Q components:

[0101] (8)

[0102] Similarly, This represents the integral value in the previous integration cycle. By multiplying these two integral values, the phase change in adjacent integration cycles can be obtained, expressed as:

[0103] (9)

[0104] in, express The conjugate of complex numbers, The modulus of a complex number, Indicates the integration period The phase change in the frequency range. Therefore, the frequency offset can be calculated based on this phase change. :

[0105] (10)

[0106] The range of frequency measurement is .

[0107] Similar to the DLL process, the calculated frequency offset value The frequency offset estimate is obtained after passing through an FLL filter. ,Then It is passed to the frequency synchronization and carrier generation module.

[0108] The following section details the application of the synchronization module in OFDM systems.

[0109] OFDM technology boasts advantages such as high spectral efficiency and strong resistance to multipath fading, and is widely used in mobile communications, digital video broadcasting, and downlink signals for the Starlink low-Earth orbit constellation. Within the OFDM framework, by designing a special reference signal structure, it can be used for both channel estimation in communications and acquisition and tracking of navigation signals.

[0110] Figure 2 The signal processing flow of an OFDM system is demonstrated. The transmitter modulates the input bitstream and converts the serial data into parallel data. Then, the inverse fast Fourier transform (IFFT) is used on these parallel data. The data is modulated and then converted back into a serial time-domain signal. Meanwhile, reference data Used to modulate the reference signal This is how it was obtained. Further with signals The signals are added together to obtain a composite signal, and a cyclic prefix (CP) is added before it. Finally, the signal is transmitted to the receiver via a wireless channel.

[0111] In the receiver, the synchronization module utilizes a reference signal. Estimated propagation time delay The synchronization signal is provided to the navigation service, and the sampling timing and carrier frequency deviation are adjusted to obtain a synchronization signal. Then, the cyclic prefix (CP) is removed from the synchronization signal, and the signal after serial-to-parallel conversion undergoes Fast Fourier Transform (FFT) and channel estimation and equalization to obtain parallel data. Finally, the balanced data The received bit stream is obtained after parallel-to-serial conversion and demodulation, thereby providing communication services.

[0112] Performance Analysis

[0113] To illustrate the superiority of the integrated communication and navigation receiver synchronization module implementation method proposed in this invention, its performance in communication and navigation is compared with that of traditional methods.

[0114] The simulation experiment targets OFDM-type integrated communication and navigation signals broadcast by low-Earth orbit satellites. The synchronization method proposed in this invention (referred to as OFDM DLL) and a traditional method (referred to as OFDM SYNC) are used to process these signals, and their communication and navigation performance is compared. OFDM SYNC is based on OFDM signals, and its synchronization is achieved through a two-dimensional search of time delay and frequency offset. In contrast, OFDM DLL uses a delay-locked loop for synchronization.

[0115] The simulation parameters are shown in Table 1. The OFDM signal parameters directly adopt a typical 5G NR configuration.

[0116] Table 1 Key simulation parameters of the OFDM system

[0117]

[0118] (1) Communication performance

[0119] The bit error rate (BER) is used to evaluate the communication performance of different schemes, and the results are plotted on... Figure 3 From. Figure 3 The following conclusions can be drawn: the BER curve of OFDM DLL is below that of OFDM SYNC. Specifically, when the transmit power is 60 dBm, the BER of OFDM DLL is reduced by 0.17% compared to OFDM SYNC.

[0120] (ii) Navigation performance

[0121] Time delay estimation error Used to characterize navigation performance, it can be based on the estimated time delay. and actual time delay It is deduced that:

[0122] (11)

[0123] Figure 4 Comparing the estimation errors of the two schemes over time reveals that the time delay estimation error of the 2D search exhibits a periodic sawtooth wave pattern. This is because the minimum resolution of the 2D search is limited to a single sampling interval, while the time delay varies linearly with time, resulting in low navigation accuracy. The proposed scheme (OFDM DLL) has a significantly lower estimation error than OFDM SYNC because the delay-locked loop provides a high-precision time delay estimate.

[0124] In addition, using estimation error The standard deviation (STD) is used to characterize the navigation performance of the proposed OFDM DLL, such as... Figure 5 As shown, ranging accuracy increases with the increase of LEO satellite transmission power.

[0125] In summary, the comparative results show that the proposed ICAN receiver synchronization scheme improves communication and navigation performance, and the delay-locked loop (DLL) is crucial for providing high-precision navigation tracking.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A signal processing method for the synchronization module of an integrated communication and navigation receiver, characterized in that, Includes the following processes: The received signal is mixed with a local carrier and then filtered to obtain an intermediate frequency signal; The intermediate frequency signal is multiplied by the locally replicated reference signal, and then coherently integrated to obtain the integral results on the in-phase and quadrature components. The autocorrelation function values ​​of the three branches were calculated using the integration results; The time delay is calculated based on the autocorrelation function value; The time delay is filtered and calculated to obtain an estimated time delay value; the estimated time delay value is then passed to the time synchronization module and the reference signal generation module. Meanwhile, the frequency offset value is calculated based on the integration result. After filtering, the frequency offset value is used to obtain the frequency offset estimate, which is then transmitted to the frequency synchronization module and the carrier generation module. The reference signal time offset corresponding to the instantaneous branch is The reference signal time offset ratio corresponding to the leading branch The time offset of the reference signal corresponding to the delay branch is less than 1 correlator spacing. One larger correlation spacing; The autocorrelation function values ​​of the three branches are calculated using the integration results, i.e., the autocorrelation function values ​​of the branches. The expression is: ； in, This indicates the time delay between the received signal and the locally copied signal. This represents the autocorrelation function of the reference signal on the in-phase and quadrature components. Indicates the frequency offset between the received signal and the local carrier. This indicates the phase offset between the received signal and the local carrier. It is the integration period. This represents the sinc function. This represents the integral result over the in-phase components; This represents the integral result over orthogonal components; Similarly, the autocorrelation function value of the leading branch is obtained. Autocorrelation function values ​​of delay branches ; The time delay is calculated based on the autocorrelation function value, expressed as follows: ； The process of obtaining the estimated time delay by filtering the time delay is as follows: First, obtain the filtered time delay. Calculate using the following formula: ； in, and These are the filtering time delay and the measurement time delay in the previous integration cycle, respectively. This represents the natural frequency that determines output accuracy and dynamic response performance; Finally, the filtered delay Delay estimate in the previous integration period Calculate the estimated time delay. : ； The process of measuring the frequency offset value based on the integration result is as follows: The integral value is first calculated from the integral results on the in-phase and quadrature components. : ； The phase change between adjacent integration cycles is obtained by multiplying the integral value from the previous integration cycle with the integral value corresponding to the current integration cycle. The expression is as follows: ； in, express The conjugate of complex numbers, The modulus of a complex number Indicates the integration period Phase changes in the middle; The frequency offset value is calculated based on this phase change. : ； The range of frequency measurement is , It is the integration period; The frequency offset value is filtered to obtain the frequency offset estimate. .

2. The signal processing method according to claim 1, characterized in that, The received signal is mixed with a local carrier and then filtered to obtain an intermediate frequency signal, expressed as: ； in, t Indicates time, The real part of the complex number is represented by j, and the imaginary unit is represented by j. It is the frequency of the local carrier. and These represent the in-phase and quadrature components of the intermediate frequency signal, respectively.

3. The signal processing method according to claim 1, characterized in that, The integral results over the in-phase and quadrature components are specifically expressed as follows: 。 4. The signal processing method according to claim 1, characterized in that, Based on the noise bandwidth of the DLL The calculation shows that: 。 5. A synchronization module for an integrated communication and navigation receiver that implements the signal processing method according to any one of claims 1-4, characterized in that, The synchronization module has two signal paths: one for synchronously receiving signals for communication services; the other is a navigation tracking loop for estimating the time and frequency offsets of the received signals and estimating the time delay for navigation services. The navigation tracking loop includes a delay-locked loop that acts as a code tracking loop and a frequency-locked loop; The delayed-locked loop consists of three branches: an immediate branch, a leading branch, and a delayed branch; The signal path for synchronously received signals includes a time synchronization module and a frequency synchronization module; Each of the three branches is connected to a reference signal generation module and a carrier generation module.

6. The synchronization module of the integrated communication and navigation receiver according to claim 5, characterized in that, The outputs of the three branches are connected to a time delay discriminator, and the outputs of the time delay discriminator are connected to a DLL filter; the output of the instant branch is connected to an FLL filter. The DLL filter connects to the time synchronization module and the reference signal generation module; The FLL filter connects the frequency synchronization module and the carrier generation module.

7. A receiver integrating communication and navigation, comprising the synchronization module of claim 5 or 6.

Images