Introduction Phase Coded SF

11 Figure shows the signal re‐construction process with a record of intra‐pulses N = . The received echo for each of the intra‐pulses can be formulated as, ∙ ∙ ∏ ∙ ∙ a b Figure : SF c ‐LFM Pulse Reconstruction Algorithm N = : a Collected ntra‐Pulses Echoes, b Signal Reconstruction Algorithm All of the collected echo intra‐pulses will reside at the origin of the time‐frequency plot, as shown in the left diagram of Figure . n the signal re‐construction process, the echo pulses will be re‐arranged into their respective frequency bands and time slots. Mathematically, this is by adding a time shift of, , and a frequency shift of, into each echo intra‐pulse. Then, Equation becomes, ∙ ∙ ∏ ∙ ∙ ∙ where, . . Solving Equation , then, down‐converting them to baseband, and finally, removing the additional phase added during the waveform generation, this finally gives, ∙ ∏ ∙ From Equation , it is shown that the phase for each collected intra‐pulse echo should be shifted with a time shift, , and a phase shift with ∅ , where ∅ can be quantified as, ∅ 12

3. FPGA‐based Baseband Waveform Synthesizer

An FPGA‐based baseband waveform synthesizer was built Chua and Koo, . n the hardware, it uses Altera Cyclone V chips as its programmable core with on‐board dual‐channel, ‐bits, MSPS DAC. Figure shows the custom made FPGA waveform synthesizer board and Table lists the main features of the board. n order to generate the required baseband LFM signals for up‐conversion, the board is configured with a real‐ time re‐configurable radar waveform synthesizer as shown in work by Chua et. al. Chua et. al., . Figure depicts the block diagram of the implemented synthesizer. a b Figure : SF c ‐LFM Pulse Reconstruction Algorithm N = : a Collected ntra‐Pulses Echoes, b Signal Reconstruction Algorithm Figure : Block Diagram of the Phase Coded SF c ‐LFM Waveform Synthesizer Table : Main Features of Custom Designed Altera Cyclone FPGA Board Module Specifications FPGA  Altera EP CE E C N  , LEs  Kbits total memory  8x 8‐bit multipliers  General Purpose PLLs  user Os DAC  Analog Device AD DAC  Channel MSPS  ‐bits resolution 13

4. Experimental Setup

An in‐lab proof‐of‐concept experimental setup was constructed to verify the waveform synthesis technique. Figure illustrates the simplified block diagram of the entire setup. Figure : An llustration of Proof‐of‐Concept Experimental Setup n the transmitter, the baseband intra‐pulses are up‐converted to its respective carrier using an off‐the‐shelf microwave quadrature modulator. An RF signal generator generates the required stepped carrier signal for the up‐conversion. n order to ensure coherency in the transmitted intra‐pulses, the selected signal generator has low phase noise ‐ dBcz kz offset to minimize the phase difference between the intra‐ pulses. The up‐converted intra‐pulses are fed into a calibrated microwave delay line for single point target echo emulation. The intra‐pulse echoes were then down‐converted using an off‐the‐shelf microwave demodulator and finally these echoes were recorded using an embedded controller with high‐speed digitizer. Table : SF c ‐LFM Waveform Parameters Parameters Value Number of intra‐pulses, N 8 ntra‐pulses bandwidth, BW Mz Pulse Repetition Frequency, PRF kz Pulse Width, T p µs Carrier Frequency, f c Mz  st carrier frequency, f 1 8 Mz  nd carrier frequency, f 2 8 Mz  rd carrier frequency, f 3 Mz  th carrier frequency, f 4 Mz  th carrier frequency, f 5 Mz  th carrier frequency, f 6 Mz  th carrier frequency, f 7 Mz  8 th carrier frequency, f 8 Mz Effective Bandwidth, B eff Mz Effective Pulse Width, T eff µs 14 Table summarizes the SF c ‐LFM signal parameters N = 8 . The intra pulses are up‐converted to different carrier frequency, f 1 – f 8 , as depicted in Equation . Based on Equation and Equation , for the generated SF c ‐LFM signal, the effective bandwidth, B eff , is Mz, and the effective pulse width, T eff , is 8 µs.

5. Results and Findings

The spectrum of SF c ‐LFM waveform in carrier band are recorded using a spectrum analyzer. Figure shows the recorded frequency spectrum of each of the transmitted intra‐pulses and the DSP combined spectrum of the resultant signal. Figure : Frequency Spectrum of SF c ‐LFM N = 8, B = Mz : DSP Combined Spectrum Black colour , ndividual ntra‐Pulse Spectrum Other colours A phase decoding process or intra‐pulses decryption is required to remove the phase code added during the baseband waveform generation. Figure 8 illustrates that, without the phase decoding process, the re‐constructed pulses will not be able to compress into its equivalent impulse response. a b c Figure 8: Match Filter Output of SF c ‐LFM Received Signal; a N = , b N = , c N = 8. 1 Figure – Figure show the recorded intra‐pulses, the re‐constructed pulse and the Auto‐Correlation Function ACF a.k.a match filter output of the reconstructed pulse. Meanwhile, the measured Peak Side‐Lobe Ratio PSLR and the mpulse Response Width RW improvement factor obtained for SF c ‐LFM waveforms are tabulated in Table . a b Figure : SF c ‐LFM for N = , t d = ns; a Top – ntra‐Pulses, Middle – Reference Signal, Bottom – Reconstructed Pulse; b ACF of the Reconstructed Pulse a b Figure : SF c ‐LFM for N = , t d = ns; a Top – ntra‐Pulses, Middle – Reference Signal, Bottom – Reconstructed Pulse; b ACF of the Reconstructed Pulse a b Figure : SF c ‐LFM for N = 8, t d = ns; a Top – ntra‐Pulses, Middle – Reference Signal, Bottom – Reconstructed Pulse; b ACF of the Reconstructed Pulse a b Figure : SF c ‐LFM for N = , t d = ns; a Top – ntra‐Pulses, Middle – Reference Signal, Bottom – Reconstructed Pulse; b ACF of the Reconstructed Pulse