# Performance Analysis of a 3D Wireless Massively Parallel Computer
## 1 Introduction
### Wireless Technologies  
A wireless communication technology for the ABC's should meet some criteria over size, energy consumption and transfer rate, among others. A review of three wire-free data transfer methods is given in previous papers [4; 5; 7]. In capacitive coupling, data is transferred using the electrical charges on a capacitor's plates. The power consumption is less than 1 pJ/b (see Figure 1a). It occupies small area per channel. Data rates are usually very high ([PERSON] et al. 's [8]). It is possible to use grids of channels in parallel: 260 Gb/s using 144 channels [9] and 32 Gb/s using 128 channels [10]. Capacitive coupling rarely supports distances over 10 \(\upmu\)m. It is highly sensitive to misalignment of facing pads of capacitors. In inductive coupling, data are stored inside a coil to be transferred to a coupled coil. Data rates are in a range of gigabits per second (e.g., 1.1 Gb/s by [PERSON] et al. [11] and 8 Gb/s by [PERSON] et al. [12]). It is possible to use grids of channels in parallel (1024 parallel links with 8 Tb/s by [PERSON] et al. [12]). It is very space-efficient with very low power consumption (see Figure 1b). The links are up to a few hundred micrometres. Lower link distances, less than 10 cm, links with lower data rates (e.g., [PERSON] et al. [13]) are proposed for a wearable body area network. On-chip mm wave RFs have historically suffered from their size, the power they consume, the high volume of noise added to the signal, packet collision and signal interference intensified by their long range; however, energy consumption has fallen recently (see Figure 1c). The most popular frequency bands are 60 GHz and 120 GHz [14, 15]. A THz band is feasible [16, 17]. The occupied area per radio module differs (e.g., from 0.05 mm\({}^{2}\) in [PERSON] et al. [18] to 56 mm\({}^{2}\) in [PERSON] et al. [19]). Mm-wave RF is a well understood and robustly researched technology. Figure 1 collates data from a number of studies in the three aforementioned technologies. Figure 1a plots capacitive coupling technologies [8, 10, 20, 21, 22, 23], Figure 1b summaries inductive coupling [24, 25, 26, 27, 28, 13, 24, 28] and Figure 1c belongs to mm-wave on-chip radios [29, 30, 31, 32, 33, 34, 35, 36, 37]. Figure 1 shows that the energy consumption in all three categories have dropped over the last 15 years. It should be noted that values in this figure are normalised and therefore cannot be 100% accurate, but the general trend of reduction in energy can be seen. Sources of this inaccuracy include differences in design, link length and bit error rate in different works. Three categories of wireless technologies are compared against three main criteria: data rate, energy consumption and communication distance. Figure 2 shows that only a few on-chip radio devices can satisfy all the criteria. 1 Gb/s is selected for the lower limit for data rate criterion. It is hard to identify a lower limit for energy consumption. An approximated 10 pJ/b energy consumption is used as a lower limit (see [7]). The on-chip radio devices that satisfy these criteria are listed in Table 1.  
Figure 1: Normalised energy needed to send a bit over (**a**) 1 \(\upmu\)m using capacitive coupling; (**b**) 1 \(\upmu\)m using Inductive coupling; (**c**) 1 mm using radio waves. Figure 2: Data rate, distance and power consumption criteria applied to reviewed wireless technologies; (**a**) Data rate vs. distance; (**b**) data rate vs. power consumption; (**c**) power consumption vs. distance. Shadowed areas cover the technologies that satisfy the criteria. It should be noted that the results in Figure 1c do not match the distance, and data rate criteria; therefore, Figure 1c and Table 1 do not share the same results. Table 1 shows that the best energy consumption per bit per mm has been around 0.0005 pJ/bit/mm in recent years, which is approximately 0.05 pJ/bit for a 1 cm distance (based on the rule of inverse square). This means the overall power consumption is in the range of 1 mW for a 20 Gb/s transceiver.