InFocus: A spatial coding technique to mitigate misfocus in near field LoS beamforming

TL;DR

The misfocus effect is investigated and InFocus, a low complexity technique to construct beams that are well suited for massive wideband phased arrays is proposed, which mitigates beam misfocus and beam squint when applied to near-field and far-field systems.

Abstract

Phased arrays, commonly used in IEEE 802.11ad and 5G radios, are capable of focusing radio frequency signals in a specific direction or a spatial region. Beamforming achieves such directional or spatial concentration of signals and enables phased array-based radios to achieve high data rates. Designing beams for millimeter wave and terahertz communication using massive phased arrays, however, is challenging due to hardware constraints and the wide bandwidth in these systems. For example, beams which are optimal at the center frequency may perform poor in wideband communication systems where the radio frequencies differ substantially from the center frequency. The poor performance in such systems is due to differences in the optimal beamformers corresponding to distinct radio frequencies within the wide bandwidth. Such a mismatch leads to a misfocus effect in near field systems and the beam squint effect in far field systems. In this paper, we investigate the misfocus effect and propose InFocus, a low complexity technique to construct beams that are well suited for massive wideband phased arrays. The beams are constructed using a carefully designed frequency modulated waveform in the spatial dimension. For the special case of beamforming along the boresight of an array, this waveform is analogous to the frequency modulated continuous wave (FMCW) chirp signal in radar. InFocus mitigates beam misfocus and beam squint when applied to near field and far field systems. Simulation results indicate that InFocus enables massive wideband phased array-based radios to achieve higher data rates than comparable beamforming solutions.

Figures (14)

• Figure 1: The figure shows an LoS communication system with a 2D-circular planar array of radius $R$ at the TX and a single antenna RX. We assume that the TX and the RX lie on the $xy$ and $xz$ planes. The line joining the center of the TX and the RX is of length $\ell$. This line makes an angle $\gamma$ with the boresight direction, i.e., the $z-$axis.
• Figure 2: We consider a boresight scenario with a half-wavelength spaced array at the TX. Here, $f_{\mathrm{c}}= 300\, \mathrm{GHz}$, $R=10\, \mathrm{cm}$, $\Delta= \lambda_{\mathrm{c}}/2$ and $\ell=15 \, \mathrm{cm}$. The phase profile in standard beamforming is shown in Fig. \ref{['fig:phi_std']}. When this profile is applied at the TX, the RF signals are spatially concentrated around the RX at $15\, \mathrm{cm}$ as shown in Fig. \ref{['fig:Power_z']}.
• Figure 3: For the system in Fig. \ref{['fig:boresightpic']}, we observe from Fig. \ref{['fig:freq_resp_std']} that the equivalent SISO channel with the standard beam has a low gain for $|f-f_{\mathrm{c}}|>10\, \mathrm{GHz}$. Here, $f_{\mathrm{c}}=300\, \mathrm{GHz}$, $\Delta=0.5\,\mathrm{mm}$, $R=10\,\mathrm{cm}$ and $\ell=15\, \mathrm{cm}$. Fig \ref{['fig:misfocus_surf']} shows that the focus point changes with the frequency of operation when the TX applies $\phi_{\mathrm{std}}(x,y)$ to its array.
• Figure 4: The instantaneous frequency of a chirp over $s\in [s_1,s_2]$ varies linearly with $s$ as shown in Fig. \ref{['fig:chirpfreq']}. Here, the start and end frequencies are $\omega_{s_1}$ and $\omega_{s_2}$. In Fig. \ref{['fig:chirpsig']}, we show the real and imaginary components of the chirp signal. The frequency spectrum of this chirp is concentrated within $[\omega_{s_1}, \omega_{s_2}]$ and is approximately flat in this band.
• Figure 5: The chirp-based phase profile constructed with InFocus for $B=40\, \mathrm{GHz}$ is shown in Fig. \ref{['fig:psi_des']}. Here, we consider a boresight scenario with $f_{\mathrm{c}}= 300\, \mathrm{GHz}$, $\ell=15\, \mathrm{cm}$ and $R= 10 \, \mathrm{cm}$. For $\Delta=0.5\, \mathrm{mm}$, the proposed phase profile applied at the TX is shown in Fig. \ref{['fig:combined_phase_boresight']}. The equivalent SISO channel response with the proposed method is large and approximately flat over the desired bandwidth, i.e., $[280\, \mathrm{GHz}, 320\, \mathrm{GHz}]$, when compared to standard beamforming.