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Plasmonic phased array feeder enabling ultra-fast beam steering at millimeter waves

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Abstract

In this paper, we demonstrate an integrated microwave photonics phased array antenna feeder at 60 GHz with a record-low footprint. Our design is based on ultra-compact plasmonic phase modulators (active area <2.5µm2) that not only provide small size but also ultra-fast tuning speed. In our design, the integrated circuit footprint is in fact only limited by the contact pads of the electrodes and by the optical feeding waveguides. Using the high speed of the plasmonic modulators, we demonstrate beam steering with less than 1 ns reconfiguration time, i.e. the beam direction is reconfigured in-between 1 GBd transmitted symbols.

© 2016 Optical Society of America

Corrections

15 December 2016: Corrections were made to the author listing and abstract.

1. Introduction

Steerable phased array antennas (PAA) are a key technology for next generation radio access network (5G-RAN) [1], satellite payloads [2], and novel sensing applications [3]. But in order to cope with the requirements of novel network architectures [4, 5] or millimeter wave (mmW) systems [6–8], PAAs need to be integratable on a single platform with least possible footprint, offering ultra-fast reconfigurability, and featuring broadband characteristics [9, 10].

Many mmW concept demonstrations have already been performed with discrete components [10–13]. However, these experiments will only reveal their full potential and become economically attractive once fully integrated [14]. Over the past few years, this challenge has been addressed in many publications within the context of integrated microwave photonics (IMWP). To this point, remarkable results have been achieved with integration platforms that include [14]: indium phosphide [15, 16], Silica glass planar lightwave circuits (PLCs) [17], silicon photonics [18], and silicon nitride [19]. Yet, with these platforms mmW PAAs have typically provided footprints of a few cm2 [19], slow reconfigurability based on thermal [20] or wavelength tuning [16], and bandwidth limitations of a few tens of GHz [21]. Among the fastest beam steering demonstrations, concepts relying on fiber-based Lithium Niobate (LiNbO3) modulators offer reconfiguration time in the order of ns [10, 22]. Interesting work has also been made using advanced simulations [23, 24].

In this paper we demonstrate for the first time a mmW multi-GBd beam steering system based on integrated plasmonic technology that offers (1) ultra-fast capability with >1ps tuning speeds and (2) an ultra-compact size, with modulator area of only a few μm2. This technology enables the creation of completely integrated array feeders, capable of steering mmW arrays of hundreds of antenna elements at ultra-high speed on an extremely reduced footprint, opening the path towards a fully-monolithic realization and therefore a reduction of unit costs.

2. Context of application

A possible utilization of photonics in next generation 5G wireless communication systems is depicted in Fig. 1. In this example, microwave photonics is used to increase the capacity of the mobile cells without impacting the complexity of the user equipment [10]. The signals for multiple users are generated in the basement of the building using digital signal processing (DSP) and high-end electronic front-ends, see Fig. 1(a). This base band unit (BBU) then sends the mmW signal over fibers to the remote radio head (RRH) of the access network. In this scenario, the users are time division multiplexed (TDM) in the DSP of the BBU. In the RRH, see Fig. 1(b), the optical signal enters a phased array feeder (PAF) which generates multiple copies with phase offsets that will allow to steer the beam in a particular direction. Steering is done in such a way that the beam is sent towards one user position via a steering control signal sent in parallel to the data signal in the optical fiber. In the scenario from Fig. 1, the PAA in the RRH is used to realize a time-to-space mapping of the TDM symbol by switching the beam direction in a symbol-by-symbol fashion, i.e. switching the beam direction between each transmitted symbols [10]. This is actually an example where high-speed beam steering might enable high speed data distribution without increasing the complexity in the user electronics [10], Fig. 1(d). However, this concept, or any other MWP solutions, requires integration on a reliable, cost effective, and compact platform [1, 14].

 figure: Fig. 1

Fig. 1 Symbol-by-symbol beam steering scenario. (a) The baseband unit (BBU) in the basement of the building sends time division multiplexed (TDM) data to multiple users via (b) a remote radio head (RRH). The RRH uses a steering control signal from the BBU to steer the single TDM symbols in different directions, acting as a spatial de-multiplexer. (c) Here, the RRH comprises of a plasmonic phased array feeder (PAF). (d) Since the user only receives a tributary of the TDM signal, the user equipment can be based on slow and low cost electronics.

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Our proposal relies on the integration of a phased array feeder (PAF) based on plasmonic phase modulators [25–28] to build the PAA in the RRH. This solution enables integration of array feeders on very small footprints. Figure 1(c) shows a 4 × 1 phased array feeder with an active area of the plasmonic phase modulators of only 2.5 μm2. The utilization of phase shifters instead of true-time delays in the array feeder is justified by [29]. It has been demonstrated that for applications with limited fractional bandwidth (<15%), phase shifters perform as good as more advanced true-time delays while lowering the system complexity.

3. Plasmonic phased array feeder

The key element of our ultra-fast steering demonstration is a plasmonic phased array feeder (plasmonic PAF), Fig. 2(a). It is composed of an array [28] of 4 plasmonic phase modulators (PPMs) [30], Fig. 2(b). Plasmonic modulators are based on the generation and control of surface plasmon polaritons (SPPs) [31], which are electromagnetic surface waves created at a dielectric-metal interface. Recent reviews on plasmonic modulators for applications in optical communications are given in [26, 28]. In our demonstration, PPMs are employed to electrically control the phase of the microwave photonic signal radiated by the antennas of a linear antenna array, Fig. 2(c). As plasmonic modulators offer highest speed modulation on a µm2-scale footprint [26, 28], PPMs give access to ultra-fast beam steering capabilities in combination with an ultra-compact size (short structures of tens of µm length). This will enable highest integration densities on a small footprint.

 figure: Fig. 2

Fig. 2 (a) Colorized SEM image of a the plasmonic phased array feeder (PAF). The plasmonic phase modulators (PPM) used in the PAF are composed of a 25 μm-long and 100 nm-wide metal-insulator-metal (MIM) slot waveguides. The slot is filled with a second-order nonlinear material to allow for phase modulation based on the Pockels effect. (b) Microscope image of a low footprint PPM used in the PAF.

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Each PPM consists of a 25 μm-long plasmonic metal-insulator-metal (MIM) slot waveguide created by 100 nm separated gold (Au) electrodes, see Fig. 2(b). An organic nonlinear optical (NLO) material with a large electro-optic coefficient [32, 33] is deposited in the slots by spin-coating to enable phase modulation based on the linear electro-optic effect (Pockels effect). The voltage applied to the electrodes induces a refractive index change in the material in the slot, and thus, the phase of the optical signal is shifted proportional to the applied voltage. The Au electrodes are fabricated on an SOI wafer by e-beam evaporation and a lift-off process. The silicon access waveguides are fabricated via e-beam lithography and dry etching. An advantage of PPMs compared to other integrated photonic phase modulators is that the modulation of the phase does not impact the amplitude of the signal, i.e. there is no associated amplitude modulation. The propagation losses per unit length in the PPMs amount to approximately ~0.5 dB/µm. This is a high value compared to other technologies. Nonetheless, these losses are mitigated by the much shorter device lengths [25] that can be achieved with plasmonic-organic-hybrid modulators. Recent progresses in organic electro-optic materials [34] even promises more efficient devices.

Four PPMs are arranged in parallel and electrically connected in series to allow for push-pull operation [28]. The required footprint per phase modulators is a few μm2, as can be seen in Fig. 2(b). The size of the chip layout is limited only by the standard electrical test probes that are available, in ground-signal-ground configuration with a 100 μm pitch.

The operation principle of the plasmonic PAF is illustrated with the help of Fig. 2. An optical reference laser (narrow-linewidth) at frequency νR enters the chip via a silicon grating coupler, Fig. 2(d). A 1 × 4 splitter is used to distribute the optical reference laser to the 4 PPMs. The silicon feeding waveguides are tapered down to excite surface plasmon polaritons (SPP) in the plasmonic slot waveguide [35]. The phases of the SPPs are shifted proportionally to the voltages applied to the modulator electrodes, see Fig. 2(e). After the PPMs, the light is converted back to the photonic domain and guided in silicon waveguides. Each phase-shifted copies of the reference laser are then combined with the optical carrier in 2 × 1 MMI couplers. The optical carrier is at a frequency νC = νR + 60 GHz and carry the modulated data signal. The optical carrier is depicted in Fig. 2(f) and the combined output spectra with the optical signal in phasor representation are shown in Fig. 2(g). The radio-over-fiber (RoF) signals exit the chip by means of silicon grating couplers. Each Radio-over-Fiber (RoF) output signal is then fed into a photodetector, where mmW signals are generated. The signal generation is based on photonic beating [36], i.e. a copy of the data will be generated at the frequency difference between the two lasers (60 GHz). Changing the relative phase shift induced by the PPMs changes the phase of the generated mmW signal, thus allowing to control the beam propagation direction of the antenna array.

The beam steering angle depends on the relative phase difference between neighboring PPMs. More specifically, in order to steer the main lobe of radiation to the angular direction ψ0, the electrical phase at the n-th antenna element is given by Eq. (1) [37].

an=n2πfRFc0dcosψ0

where fRF is the central mmW frequency, c0 is the speed of light in air, and d is the antenna spacing of the array.

High-speed electro-optic tests were conducted on the PPMs. The broadband modulation capability of the PPMs employed is shown in Fig. 3. The device was driven by a −3 dBm sinusoidal RF signal with frequency swept from 10 GHz up to 70 GHz. The results measured with an optical spectrum analyzer show that the PPMs offer a flat frequency response up to frequencies of at least 70 GHz, limited by the measurement equipment. Only ± 1.5 dB modulation ripples can be seen in the frequency response. By analyzing the ratio between the optical carrier and the modulation sidebands, the Vπ, RF/2, as needed in push-pull operation, can be estimated to be in the order of 8.5 V ± 2 V across the complete 10-70 GHz band.

 figure: Fig. 3

Fig. 3 Measured optical transmission spectrum for −3 dBm RF modulation of the PPM used in the system experiments, from 10 GHz to 70 GHz. The higher sidebands at large frequencies are related to variations in the impedance matching between the pico-probe and the device through the measurement bandwidth.

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4. Experimental setup

For the experimental demonstration, we use the phased array feeder (PAF) described in the previous section to build a 2x1 antenna RRH. A 4x1 array would have been fully supported by the plasmonic PAF but the available RF equipment allowed us simultaneous operation of only two antennas. The experimental setup is detailed in Fig. 4. The experimental setup comprises of three parts. (a) The BBU with the signal generation, (b) the RRH with the plasmonic feeder, and (c) the user equipment (UE) with bandwidth tunable receivers (digital filtering).

 figure: Fig. 4

Fig. 4 Experimental setup. (a) In the BBU, data from AWG are encoded by means of an IQ modulator onto a carrier laser (at frequency νC). After optical amplification, the carrier laser is transmitted to the RRH. A second reference laser (at frequency νR) having a frequency difference corresponding to the desired millimeter wave frequency (60 GHz) is fed to the RRH as well. (b) In the RRH the two lasers are combined within the plasmonic PAF chip and mapped onto photodiodes, where they are converted to millimeter wave (mmW) signals. (c) To emulate a 0.7 and 1.4 GHz bandwidth UE (at a carrier of 60 GHz) we use a high-bandwidth DSO. For this, we receive the signal with 60 GHz high-gain antenna and down-convert the signal to an intermediate frequency (IF) of 11 GHz. The DSO is then used to perform the recording. The IF signals are then analyzed with a vector software analyzer (VSA) performing: the down-conversion to IQ baseband signals, low pass filtering to emulate a 0.7 and 1.4 GHz bandwidth UE, and digital signal processing (DSP) with standard recovery algorithm (timing, carrier, equalization). (d) The plot shows time traces right after the ADC (without DSP) for a “low” steering speed of 8 MHz, i.e. frames of 62 symbols are steered towards user 1 or 2 alternatively.

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The signals are generated in the BBU, see Fig. 4(a). An arbitrary wave form generator (AWG) is used to generate a pseudorandom binary sequence (PRBS) of length 211-1 with 1 and 2 GBd and various modulation formats (BPSK, QPSK). The data are then encoded onto a narrow linewidth laser (< 100 kHz linewidth at a frequency νC) by means of an IQ modulator. The optical signal is then amplified (EDFA) and filtered with an optical band-pass filter (0.6 nm). The power level of the carrier at the output of the BBU is −2 dBm. In parallel, a second, narrow linewidth reference laser with a frequency (νR) offset against the carrier laser of fRF=60 GHz, is part of the BBU. The reference laser has a power of 16 dBm. The power of the reference laser is much higher in order to compensate for the excess losses in the integrated plasmonic feeder in the RRH.

The RRH is realized as a phased array antenna (PAA) comprising of a plasmonic PAF and a millimeter wave front end, Fig. 4(b). In the plasmonic PAF, the reference laser is first split onto 4 arms. The arms are then phase modulated to induce the progressive phase delay needed for beam steering. Finally, the phase shifted copies of the reference laser are combined with the data signal in a coupler stage within the PAF. The two outputs of the plasmonic PAF form the two RoF signals entering the mmW front end. The mmW front ends consist of a low noise EDFA to boost the signal, an optical delay line (DL) to compensate the fixed fiber length difference, an optical filter to remove the out-of-band noise of the EDFA, a variable optical attenuator (VOA), a 70 GHz photodiode performing the optical to mmW conversion, an amplifier to boost the mmW signal, and finally a horn antenna (20 dBi). The antenna spacing is ~2 cm. The two users are spatially separated by 30° (~angle between maximum and null of the array pattern) and placed at a distance of 3 m from the PAA.

Ideally for our demonstration, the UEs at the receiver side, see Fig. 4(c), should be built with commercial components fulfilling mobile communication standards (such as 802.11ad). As depicted in Fig. 1(d), commercial UEs should include: a 60 GHz antenna, a mixer with fLO at 60 GHz directly providing IQ baseband signals, a low pass filter (LPF), and the digital signal processing (DSP) stage. However, we have not used such UEs because we need the flexibility of a research setup to switch the bandwidth of the LPF from 0.7 to 1.4 GHz in order to demonstrate the advantage of symbol-by-symbol steering. Our bandwidth tunable UEs are therefore implemented as following: First, the 60 GHz mmW data signals are received by Huber&Suhner Sencity Matrix antennas and amplified by V-band amplifiers. An intermediate frequency (IF) conversion stage is then used to shift the signals down to 11 GHz. This stage is implemented in order to enable direct recording with our digital sampling oscilloscope (DSO) having a limited measurement bandwidth. The IF signals are, after recording with the DSO, processed with a commercial vector software analyzer (VSA) for both users in parallel. In the VSA, the signals are first down-converted numerically into IQ baseband signals. The IQ baseband signals are then filtered using tunable digital filters with bandwidth BWRxDSP. In our symbol-by-symbol demonstration in the next section, the bandwidth of this digital filter is switched from 1.4 GHz to 0.7 GHz in order to emulate UEs with lower processing bandwidth. Finally, a digital signal processing (DSP) chain applies the different recovery algorithms (timing, carrier, equalization) as needed for demodulation.

Figure 5 depicts the experimental setup used in our laboratory. The pictures detail the mmW paths after the RRH with the transmitting PAA, see inset (a), the 3m channel (main picture), and the two users. See inset (b) for close up on the receiver chain of user 2.

 figure: Fig. 5

Fig. 5 Picture of the experiment setup. The PAA, zoom in inset (a), is built with two photodiodes (70 GHz), two amplifiers (28 dB gain), and two horn antennas (directivity of 20 dBi) and antenna spacing of 2 cm. The two users are 3m apart from the transmitter PAA and separated by 30°. In the inset (b), the mmW components used for user 2 are detailed the antenna, an amplifier (20 dB gain), and an RF mixer (LO at 49 GHz). The signals of the two users at an intermediate frequency of 11 GHz are directly recorded with a DSO.

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Before testing ultra-fast steering, we performed “low speed” characterization of the setup, i.e. instead of steering symbol-by-symbol, we steered the beam frame-by-frame. The result for a switching rate of 8 MHz between the two users is depicted in Fig. 4(d). At 8 MHz, the beam is steered every 62.5 ns corresponding to frames containing 62 symbols (at a symbol rate of 1 GBd). In Fig. 4(d), the received signals are depicted without any DSP processing (right after the ADCs). Time traces for user 1 and 2 are plotted in black and red, respectively. The result shows that the frames are indeed transmitted either towards user 1 or towards user 2. The reception was limited by the amplifiers noise with a worth case extinction ratio of 3 −5 dB. Measurements at various switching rates have shown that the extinction ratio does not depend on the switching speed but is rather related to the quality of the mmW components.

For ultra-fast beam steering, synchronization between the transmitted data sequence and the steering control signal was needed. For instance, for symbol-by-symbol beam steering one needs to steer the beam in between symbol transitions and not during a symbol transmission and thus requires time synchronization with about 10% of the symbol duration. To calibrate the length of the mobile backhauling fibers, we used an auto-correlation based method. This worked as follow: the same PRBS pattern is sent on both channels (data and control sequence). The data are then modulated via the IQ modulator in the BBU while the phase shifter of the PAA will be modulated in the RRH. The physical distance difference between the two modulators (~80 m of fiber) leads to a superposition of the PRBS sequences on the output signals. By performing an auto-correlation of the signal in the receiver, the absolute delay difference between the two modulators can be derived from the correlation peaks.

5. Ultra-fast beam steering results

After the aforementioned low-speed testing we moved on to ultra-fast symbol-by-symbol measurements. Here, the phased array antenna is reconfigured between each symbol transmission in order to steer every symbol in a different direction. This way the user will only receive one tributary out of a larger number of data and therefore operate at lower symbol rates [10]. This symbol-by-symbol steering experiment has been performed with a mmW signal at a frequency of fr=60 GHz. In opposite to Fig. 4(d), the results plotted in this section leverage the full DSP chain of the UEs, explaining the better signal qualities.

In a first step, we performed measurements with user equipment (UE) having a processing bandwidth corresponding to the full transmitted symbol rate, i.e. the digital filter bandwidth BWRxDSP in Fig. 4(c) is set to ~1.4 GHz for a transmitted signal of 1 GBd (with roll-off factor of 0.35). Figure 6 shows the received eye and constellation diagrams for the two users after the symbol-by-symbol transmission. It can be seen that there is always a null between symbols as each user receives only every second symbol. As a matter of fact, the transmitted 1 GBd (period of 1 ns) QPSK sequence is converted into two 50% return-to-zero bit streams (period of 2 ns) at the receivers by ultra-fast symbol-by-symbol steering. The resulting EVMs are 24.4% and 25.1% for user 1 and 2, respectively. We thereby verify beam switching times smaller than 1 ns, i.e. smaller than the symbol duration.

 figure: Fig. 6

Fig. 6 Received signals for 1GBd transmitted QPSK signal received as two independent 0.5GBd bit streams in full bandwidth receivers (1.4 GHz).

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In a second step, we reduced the UEs BW by a factor two in order to demonstrate the key advantage of symbol-by-symbol steering. The UEs DSP bandwidth is now sets to 0.7 GHz by adapting the resampling in our commercial vector signal analyzer. The results plotted in Fig. 7 show that the signals can still be detected with a good EVM (24.4% for user 1 and 25.1% for user 2). In fact, the EVM penalty is only ~4% when reducing the UEs BW by a factor two. In this scenario, the bandwidth can be reduced from 1.4 GHz to 0.7 GHz. The receiver bandwidth matches the received symbol rate times the roll-off factor of 0.35 for both cases.

 figure: Fig. 7

Fig. 7 Received signals for receivers with only half the bandwidth of the transmitter (~700 MHz), compared to Fig. 6 the quality degradation is low.

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Finally, the symbol-by-symbol steering results for various modulation formats and symbol rates are summarized in Fig. 8. We show experimental results for 1 GBd BSPK and 1 and 2 GBd QPSK. In a commercial system one could optimize the various EVM values by using a larger array, optimizing the RXs filter shapes (rectangular in this case), and by optimizing the shape of the control signal. These results shows that reducing the bandwidth of the receivers works for advanced modulation formats at different symbols rates. As we are switching the beam between two users, the bandwidth can be reduced by a factor two. It is worth noting that the symbol rate of the demonstration is not limited by the PPMs bandwidth but rather by the limited SNR of the full millimeter wave setup. The performances of the receivers were limited by the standard pulse shaping used in this experiment. In order to improves the results, a possible path is to develop custom types of “matched filters” specially designed for symbol-by-symbol steering.

 figure: Fig. 8

Fig. 8 EVM Results for BPSK at 1GBd, QPSK at 1 and 2 GBd (symbol rate of the transmitted signal). For simplicity, the corresponding bitrate per user is used on the x-axis of the plot.

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6. Conclusion

In this paper, we demonstrated an integrated phased array feeder for millimeter wave communication based on ultra-compact plasmonic phase modulators. The paper shows how the plasmonic platform can empower the development of future beam steering schemes by offering (1) ultra-compact size of the active area and thus large integration density and (2) ultra-fast beam steering with reconfiguration times of less than 1 ns. The wireless experiment has been performed at carrier frequency of 60 GHz and shown beam steering with beam steering reconfiguration in less than 1 ns. In other words, we were able to adjust the beam direction in between 1 GBd symbols. This method called symbol-by-symbol steering provides the advantage of shifting the complexity of the electronics away from the user equipment. The demonstration shows how the plasmonic platform may pave the way for complex system-on-chip schemes while providing larger bandwidth and smaller footprint compared to other platforms.

Funding

The EU project PLASILOR (670478), the National Science Foundation (DMR-1303080) and the Air Force Office of Scientific Research (FA9550-15-1-0319) are acknowledged for partial funding of this project.

Acknowledgments

We acknowledge Florence Babando for the artwork of Fig. 1.

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Figures (8)

Fig. 1
Fig. 1 Symbol-by-symbol beam steering scenario. (a) The baseband unit (BBU) in the basement of the building sends time division multiplexed (TDM) data to multiple users via (b) a remote radio head (RRH). The RRH uses a steering control signal from the BBU to steer the single TDM symbols in different directions, acting as a spatial de-multiplexer. (c) Here, the RRH comprises of a plasmonic phased array feeder (PAF). (d) Since the user only receives a tributary of the TDM signal, the user equipment can be based on slow and low cost electronics.
Fig. 2
Fig. 2 (a) Colorized SEM image of a the plasmonic phased array feeder (PAF). The plasmonic phase modulators (PPM) used in the PAF are composed of a 25 μm-long and 100 nm-wide metal-insulator-metal (MIM) slot waveguides. The slot is filled with a second-order nonlinear material to allow for phase modulation based on the Pockels effect. (b) Microscope image of a low footprint PPM used in the PAF.
Fig. 3
Fig. 3 Measured optical transmission spectrum for −3 dBm RF modulation of the PPM used in the system experiments, from 10 GHz to 70 GHz. The higher sidebands at large frequencies are related to variations in the impedance matching between the pico-probe and the device through the measurement bandwidth.
Fig. 4
Fig. 4 Experimental setup. (a) In the BBU, data from AWG are encoded by means of an IQ modulator onto a carrier laser (at frequency νC). After optical amplification, the carrier laser is transmitted to the RRH. A second reference laser (at frequency νR) having a frequency difference corresponding to the desired millimeter wave frequency (60 GHz) is fed to the RRH as well. (b) In the RRH the two lasers are combined within the plasmonic PAF chip and mapped onto photodiodes, where they are converted to millimeter wave (mmW) signals. (c) To emulate a 0.7 and 1.4 GHz bandwidth UE (at a carrier of 60 GHz) we use a high-bandwidth DSO. For this, we receive the signal with 60 GHz high-gain antenna and down-convert the signal to an intermediate frequency (IF) of 11 GHz. The DSO is then used to perform the recording. The IF signals are then analyzed with a vector software analyzer (VSA) performing: the down-conversion to IQ baseband signals, low pass filtering to emulate a 0.7 and 1.4 GHz bandwidth UE, and digital signal processing (DSP) with standard recovery algorithm (timing, carrier, equalization). (d) The plot shows time traces right after the ADC (without DSP) for a “low” steering speed of 8 MHz, i.e. frames of 62 symbols are steered towards user 1 or 2 alternatively.
Fig. 5
Fig. 5 Picture of the experiment setup. The PAA, zoom in inset (a), is built with two photodiodes (70 GHz), two amplifiers (28 dB gain), and two horn antennas (directivity of 20 dBi) and antenna spacing of 2 cm. The two users are 3m apart from the transmitter PAA and separated by 30°. In the inset (b), the mmW components used for user 2 are detailed the antenna, an amplifier (20 dB gain), and an RF mixer (LO at 49 GHz). The signals of the two users at an intermediate frequency of 11 GHz are directly recorded with a DSO.
Fig. 6
Fig. 6 Received signals for 1GBd transmitted QPSK signal received as two independent 0.5GBd bit streams in full bandwidth receivers (1.4 GHz).
Fig. 7
Fig. 7 Received signals for receivers with only half the bandwidth of the transmitter (~700 MHz), compared to Fig. 6 the quality degradation is low.
Fig. 8
Fig. 8 EVM Results for BPSK at 1GBd, QPSK at 1 and 2 GBd (symbol rate of the transmitted signal). For simplicity, the corresponding bitrate per user is used on the x-axis of the plot.

Equations (1)

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a n = n 2 π f R F c 0 d cos ψ 0
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