The results discussed in this section refer to a scenario where a number of users are randomly distributed in an area of 1km^{2}. The scenario uses an average urban population density of 1,350 habitants and 570 dwellings per km^{2} (we take the city of Dublin, Ireland, as a reference); we analyse an MD-MIMO system with 20 active users and 64 RRHs. We have also simulated a city centre scenario with a density 4 times higher, scaling proportionally the number of active users and antennas. Since however the results were similar to those of the first scenario (Fig. 1), they are not reported in this paper. We assume the maximum spectrum bandwidth available is 50 MHz and the number of PONs (we assume a 64-way split) is enough to cover all dwellings and RRHs. We used exhaustive search in Matlab to solve the optimization problems previously described; the number of antennas used in each PON (m_{i}) is determined by distributing uniformly the overall optimal number of antennas among the PONs.

The results presented in Fig. 1 show the optimal number of antennas and spectrum resources used for **cost ratios** of **wireless spectrum to PON capacity (R _{wb}**) and

**PON capacity to antenna site**(R

_{bm}) varying over several orders of magnitude. We have also attempted to estimate a potential reference value for R

_{Wb}and R

_{bm}, taking into consideration estimated costs for spectrum, antennas and PON channels. The cost of the spectrum (at 1.8GHz) was approximated to 0.1138 GBP per MHz per habitant for a 20-year lease, following data in [9]. The cost of antenna site leasing was chosen to be $1900 per month, according to [10]. The cost for leasing one of the eight NG-PON2 wavelengths was calculated at $1,510 per year, by carrying out a discounted cash flow model over costs reported in [11] (we considered 1% OPEX on passive and 4% on active infrastructure, a return on investment of 5% and a Weighted Average Cost Of Capital of 10%). All costs were brought back to a similar currency and normalized to one-year period; since we only consider cost ratios, we assume that similar ratios might still be valid when the lease time operates over much shorter time scales for highly dynamic resource allocation. The approximate reference value for R

_{bm}is thus calculated at 0.066 (although, due to high variability of antenna site costs, we highlight in the plots a two order of magnitude shaded area from 0.006 to 0.6), while the approximate value for R

_{Wb}is of 0.0065.

The plots are organized as follows: the first three in the upper line, (al), (b1) and (c1) report the optimal number of antennas from, respectively, the fronthaul overlay model, the fronthaul shared wavelength model, and the split-PHY shared wavelength model. In the lower line, (a2), (b2) and (c2) report the associated optimal spectrum bandwidth. Plots (b3) and (c3) in the last column report instead the wireless data rate, across all users, for the wavelength sharing model with, respectively, fronthaul (b3) and split-PHY (c3). The plots show that the higher R_{wb}, the higher is the sensitivity of the optimal number of antennas to R_{bm}: indeed low cost in optical transport facilitates the use of more antennas as c_{b}decreases over C_{W}. From plot (al) we can see that for the fronthaul overlay model the reference value (between red and green curves) has low sensitivity to changes in the R_{bm}ratio, meaning that the optimal strategy is to use the lowest numbers of antennas necessary for MD-MIMO. This is due to the high cost of optical transport with respect to spectrum, and only when this ratio changes considerably (i.e., by 100 times-blue curve) the system becomes sensitive to R_{bm} and the optimal strategy quite variable with it. When fronthaul is considered (b1), the situation does not change considerably within the reference shaded zone although the strategy becomes more sensitive to changes in R_{bm} and R_{wb}. The sensitivity becomes instead more pronounced for the wavelength sharing over split-PRY case (cl), as the red and green curves (i.e., around the reference value) become steeper for values near the shaded area. In this scenario in fact the split-PRY drastically reduces the C-RAN bit rate, which, combined to the ability to share PON wavelengths between multiple RRHs signals, lowers considerably the cost of optical transport. Thus for split-PRY the optimal MD-MIMO strategy is visibly dependent on the cost ratios, making resource allocation optimisation a necessity in dynamic markets where costs change with demand, or across different countries and geotypes.

Looking at the bandwidth plots in the lower line (a2), (b2) and (c2), we can see that while the spectrum used tends to decrease as more antennas are used, the relation is not strictly inversely proportional, because the model objective is the minimisation of the cost per bit. Moreover, the optimal bandwidth is less sensitive to R_{bm}for the fronthaul overlay model, as the high optical transport cost makes it difficult to use more antennas. For split-PRY, the lower cost of optical transport allows instead the use of more antennas even when more spectrum is utilized, leading to an increase in the overall capacity (as visible in plot (c3)). Finally, the last column plots (b3) and (c3) show the overall MD-MIMO system rate (according to Shannon capacity) for fronthaul and split-PRY over shared wavelength models: the lower cost of split-PRY transport enables higher wireless data rates compared to fronthaul.

I. Macaluso, B. Cornaglia and M. Ruffini, “Antenna, spectrum and capacity trade-off for cloud-RAN Massive distributed MIMO over next generation PONs,” *2017 Optical Fiber Communications Conference and Exhibition (OFC)*, Los Angeles, CA, 2017, pp. 1-3.

keywords: {5G mobile communication;antennas;MIMO communication;next generation networks;passive optical networks;radio access networks;resource allocation;cost-optimal antenna;spectrum resource allocation;capacity trade-off;cloud-RAN massive distributed MIMO;next generation PON;mobile 5G MD-MIMO;passive optical networks;wavelength overlay;shared wavelength approaches;split-PHY;mobile capacity;fronthaul;radio access network;massive distributed multiple input multiple output system;Antennas;Passive optical networks;Bandwidth;Mobile communication;Wireless communication;Mobile computing;Dynamic scheduling},

URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7936823&isnumber=7936771