Beyond Scaling Laws: On the Rate Performance of Dense Device-to-Device Wireless Networks

Abstract

We consider a device-to-device wireless network where n users are densely deployed in a squared planar region and communicate with each other without the help of a wired infrastructure. For this network, we examine the three-phase hierarchical cooperation scheme originally proposed by Ozgur, Leveque, and Tse, and the two-phase improved hierarchical cooperation scheme successively proposed by Ozgur and Leveque based on the concept of network multiple access. Exploiting recent results on the optimality of treating interference as noise in Gaussian interference channels, we optimize the achievable average per-link rate and not just its scaling law (as a function of n). In addition, we provide further improvements on both the previously proposed hierarchical cooperation schemes by a more efficient use of time-division multiple access and spatial reuse. Because of our explicit achievable rate expressions, we are able to compare the hierarchical cooperation scheme with multihop routing (i.e., decode-and-forward relaying), where the latter can be regarded as the current practice of device-to-device infrastructureless wireless networks. Our results show that the improved and optimized hierarchical cooperation schemes yield very significant rate gains over multihop routing in realistic conditions of channel propagation exponents, signal-to-noise ratio, and number of users. This sheds light on the long-standing question about the real advantage of hierarchical cooperation scheme over multihop routing beyond the well-known scaling laws analysis. In contrast, we also show that our rate optimization is nontrivial, since when hierarchical cooperation is applied with off-the-shelf choice of the system parameters, no significant rate gain with respect to multihop routing is achieved. We also show that for large pathloss exponent (e.g., α = 7), the sum rate is a nearly linear function of the number of users n in the range of networks of practical size (e.g., n ≤ 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> ). This also sheds light on a long-standing dispute on the effective achievability of linear sum rate scaling with hierarchical cooperation. Finally, we notice that the achievable sum rate for large α is much larger than for small α (e.g., α = 4). This suggests that the hierarchical cooperation scheme may be a very effective approach for networks operating at millimeter-waves, where the pathloss exponent is generally large.