Integrated Sensing For Future Wireless Networks – Aryan Kaushik (1)

From the performance analysis in Section 7.2.1.1, we can see that the AF in (7.11) depends on both the transmitted frequency ωm and the phase θm in each sub-pulse m. Let us first con- sider the AF for M = 8, ¯M = 8, and ˆM = 4 with frequency sequence 2π[7,0,2,2,6,1,1,2] and phase sequence π[1,0,2,1,3,2,2,1]/2.

This is one random choice of phase and frequency sequences. Sub- plots (a)–(d) in Fig. 7.4 present the three-dimensional surface plot, the contour plot, the zero-Doppler cut, and the zero-delay cut, respectively. The AF has a maximum value of 1 as the energy of the signal is normalized. In addition, the maximum of the AF occurs at τ = ω = 0 as with any waveform.

From (7.14), it can be seen that the zero-delay cut is invariant to the transmitted frequencies or phases. There- fore, irrespective of the transmitted data, the zero-delay cut and the Doppler resolution will remain the same. On the other hand, as evident from (7.12), the zero-Doppler cut depends heavily on the transmit- ted frequencies and phases between sub-pulses. As such, the mainlobe width in the zero-Doppler cut depends on the data transmitted in each sub-pulse, thus affecting the delay resolution, which we will discuss in more detail in Example 7.2.

Example 7.2. Given that the zero-Doppler cut illustrates the impact of communication data on the mainlobe width of the AF, in this example, we focus on the behavior of the zero-Doppler cut with re- spect data modulation. In Fig. 7.5, we plot zero-Doppler cuts of four frequency and phase sequences for M = 8, ¯M = 8, and ˆM = 4. To draw some interesting insights, we consider the frequency sequences 2π[1,1,1,1,1,1,1,1], 2π[1,1,0,1,1,1,1,1], 2π[1,1,1,1,1,1,1,1], and 2π[0,1,4,6,5,3,7,2] with the phase sequences π[2,2,2,2,2,2,2,2]/2, π[2,2,2,2,2,2,2,2]/2, π[2,0,0,0,2,2,2,2]/2, π[2,0,3,3,0,1,0,2]/2.

We also note that the resolution or minimal separable distance in delay and Doppler is proportional to the mainlobe width, which is usually measured at the −3 dB point, of the AF [18, Chapter 1]. Therefore, we can observe that the transmitted data has a significant effect on the mainlobe width thus, affecting the delay resolution.

More specifically, sequence 1 has the largest mainlobe width measured at the −3 dB point, resulting in the worst delay resolution. On the other hand, sequence 4 has the thinnest mainlobe width measured at the −3 dB point, resulting in the best delay resolution. This can be explained by the randomization among sub-pulses which improves the radar sensing performance by reducing the interference compared to the non-randomized version [21]. As such, the worst radar sensing performance would be achieved when the same frequency and phase are repeated in all M sub-pulses as given by sequence 1.

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ISBN: 978-0-443-22143-9 For information on all Academic Press publications visit our website at https://www.elsevier.com/books-and-journals Publisher: Mara Conner Acquisitions Editor: Tim Pitts Editorial Project Manager: Sumit Yadav Production Project Manager: Anitha Sivaraj Cover Designer: Miles Hitchen Typeset by VTeX Contents Contributors ……………………………………………………………………………………………….. xv About the editor …………………………………………………………………………………………… xix Acknowledgments ………………………………………………………………………………………… xxi CHAPTER 1 Introduction to integrated sensing and communications for the next generation of wireless connectivity …………………………………. 1 Soumya Prakash Dash, Aryan Kaushik, and Ana Garcia Armada 1.1 Introduction……………………………………………………………………………..

1 1.2 A historical overview on ISAC ………………………………………………………. 2 1.2.1 Initial development of radars …………………………………………………. 3 1.2.2 Mutual inspiration between radar and communication ……………………. 3 1.2.3 Radar and communication development in parallel…………………………

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