## Final Report Summary - BSA-D2D (Base Station (BS) Aided D2D (Device to Device) communication in cellular networks)

Recent studies predict that the traffic to mobile devices will increase by two orders of magnitude in the next few years. In particular, it is widely recognised that multimedia download generated by the widespread success of Internet-capable smartphones and other portable devices (e.g. the iPhone and the iPad) strains wireless networks to a degree where service quality for all users is significantly impacted. For example, in the US the AT&T wireless network has been crippled by the iPhone-generated traffic at the point that even making plane phone calls has become very difficult in very dense areas such as Manhattan or downtown San Francisco. Wireless operators around the world are seriously worried about the investments in cellular infrastructure, deployment of base stations towers and re-planning of the cellular coverage that the advent of these new devices will require in order to achieve an acceptable quality of service.

We argue that the cellular architecture is intrinsically limited by some bottlenecks. These limitations are fundamental, since they follow from the limits indicated by Shannon information theory. A conventional cellular architecture is based on the uplink (user devices to base station) and downlink (base station to user devices). The information theoretic models underlying uplink and downlink are the multiple access channel (MAC) and the broadcast channel (BC). It is well-known that in the most idealised situation, even neglecting inter-cell interference (ICI), the capacity (in bit/s/Hz) of MAC and BC scales as O(M log SNR), where M is the number of antennas at the base station (BS) and SNR is the operating (average) SNR, and where we assume that in each cell there are K = M user devices with an arbitrary number of antennas. For a conventional architecture treating ICI as an additional source of noise, SNR must be replaced with SINR, the signal to interference plus noise ratio. In this case, even though (hypothetically) each transmitter increases its transmit power without bounds, the system saturates to a finite capacity per cell, since the SINR is upper bounded by some constant even in the very large transmit power regime.

Multiple input multiple output (MIMO) can be used at the network level and BSs can be coordinated in order to act as a joint distributed multi-antenna transmitter / receiver. This approach, however, yields still interference-limited capacity since the number of channel coefficients that can be reliably estimated by transmitters and receivers is fundamentally bounded by the time-frequency coherence of the channel. Therefore, estimating higher and higher dimensional 'network MIMO' channels costs proportionally more and more signal space dimensions and eventually the interference reduction versus dimensionality cost tradeoff limits the overall capacity improvement that can be achieved with such MIMO cooperative solutions.

Finally, moving away from cellular in favour of a completely ad-hoc infrastructure-less wireless network architecture is also not a good idea. Wireless ad-hoc networks have been sharply characterised in recent years in terms of the scalability of their throughput capacity with respect to the number of nodes. It is well-known that 'extended' networks, i.e. planar networks physical diameter grows as O(vn), where n is the number of user devices (nodes), yields a throughput per connection that vanishes as O(1/vn). This result holds under very general conditions and it is essentially tight. This grim result indicates that covering a large geographical area with a wireless ad-hoc network is highly inefficient as capacity does not scale with the size of the network. Intuitively, this is due to the fact that the average distance between source and destination nodes is O(vn) (the diameter of the network) and, under the most common pathloss laws found in practice, the most efficient strategy consists of multi-hop routing. It takes O(vn) hops for a packet to reach its destination on average, and O(vn) simultaneous routes can be created in the network, while the number of source-destination active links is clearly O(n).

From the above short survey of the main capacity scaling laws of cellular and wireless ad-hoc networks, it clearly appears that if we wish to address a two orders of magnitude traffic increase as predicted in, we have to consider a novel and different network architecture. Some very promising solutions have been developed in the UE BSA-D2D/ OTP 34663, during the stay of Dr Caire in 2011 - 2012 at CNRS/L2S.

We argue that the cellular architecture is intrinsically limited by some bottlenecks. These limitations are fundamental, since they follow from the limits indicated by Shannon information theory. A conventional cellular architecture is based on the uplink (user devices to base station) and downlink (base station to user devices). The information theoretic models underlying uplink and downlink are the multiple access channel (MAC) and the broadcast channel (BC). It is well-known that in the most idealised situation, even neglecting inter-cell interference (ICI), the capacity (in bit/s/Hz) of MAC and BC scales as O(M log SNR), where M is the number of antennas at the base station (BS) and SNR is the operating (average) SNR, and where we assume that in each cell there are K = M user devices with an arbitrary number of antennas. For a conventional architecture treating ICI as an additional source of noise, SNR must be replaced with SINR, the signal to interference plus noise ratio. In this case, even though (hypothetically) each transmitter increases its transmit power without bounds, the system saturates to a finite capacity per cell, since the SINR is upper bounded by some constant even in the very large transmit power regime.

Multiple input multiple output (MIMO) can be used at the network level and BSs can be coordinated in order to act as a joint distributed multi-antenna transmitter / receiver. This approach, however, yields still interference-limited capacity since the number of channel coefficients that can be reliably estimated by transmitters and receivers is fundamentally bounded by the time-frequency coherence of the channel. Therefore, estimating higher and higher dimensional 'network MIMO' channels costs proportionally more and more signal space dimensions and eventually the interference reduction versus dimensionality cost tradeoff limits the overall capacity improvement that can be achieved with such MIMO cooperative solutions.

Finally, moving away from cellular in favour of a completely ad-hoc infrastructure-less wireless network architecture is also not a good idea. Wireless ad-hoc networks have been sharply characterised in recent years in terms of the scalability of their throughput capacity with respect to the number of nodes. It is well-known that 'extended' networks, i.e. planar networks physical diameter grows as O(vn), where n is the number of user devices (nodes), yields a throughput per connection that vanishes as O(1/vn). This result holds under very general conditions and it is essentially tight. This grim result indicates that covering a large geographical area with a wireless ad-hoc network is highly inefficient as capacity does not scale with the size of the network. Intuitively, this is due to the fact that the average distance between source and destination nodes is O(vn) (the diameter of the network) and, under the most common pathloss laws found in practice, the most efficient strategy consists of multi-hop routing. It takes O(vn) hops for a packet to reach its destination on average, and O(vn) simultaneous routes can be created in the network, while the number of source-destination active links is clearly O(n).

From the above short survey of the main capacity scaling laws of cellular and wireless ad-hoc networks, it clearly appears that if we wish to address a two orders of magnitude traffic increase as predicted in, we have to consider a novel and different network architecture. Some very promising solutions have been developed in the UE BSA-D2D/ OTP 34663, during the stay of Dr Caire in 2011 - 2012 at CNRS/L2S.