# A Practical Resource Management Scheme for Cellular Underlaid D2D Networks
## 4 Proposed Resource Management for Cellular Underlaid D2D Networks  
The optimization in Equation (5) requires tremendous complexity because it is not a convex problem but a combinatorial problem. In addition, a central node such as a cellular BS should  
Figure 1: An underlaid device-to-device (D2D) communication network. have perfect information of entire channels to solve the problem and have full control of D2D communications, which inevitably causes excessive signalling overhead for the feedback of channel state information (CSI). In particular, both the complexity and signalling overhead exponentially increase as the number of D2D pairs \(N\) increases. In this paper, we thus propose a fully distributed resource management scheme for cellular underlaid D2D communication networks. The proposed scheme does not require any signalling overhead for CSI and can be operated in a fully distributed manner with a simple signalling broadcast by the BS. Figure 2 shows the flow diagram for our proposed scheme. 1. Every D2D transmitter transmits reference symbols to enable D2D receivers and BS to estimate channel gains. We assume that each D2D transmitter is assigned orthogonal radio resource for the reference symbols. Figure 2: Flow diagram of the proposed scheme for cellular underlaid D2D communication networks. Each D2D receiver only estimates the channel gain received from its associated transmitter, while the BS estimates all channel gains received from all \(N\) D2D transmitters. * The BS sorts \(N\) measured channel gains in an ascending order. The D2D transmitter with the \(i\)-th largest channel gain is indexed by \(\hat{i}\). Then, the sorted set of D2D transmitters can be denoted by \(\{\hat{1},\cdots,\hat{i},\cdots,\hat{N}\}\) and \(|g_{\hat{1}\hat{1}}|^{2}\leq\cdots\leq|g_{\hat{N}\hat{1}}|^{2}\cdots\leq|g_{ \hat{N}\hat{1}}|^{2}\) is satisfied. The BS determines an eligible set \(\mathcal{E}\), defined by \[\mathcal{E}=\{\hat{1},\hat{2},\cdots,\hat{i}^{*}\}\,\] (6) where \(\hat{i}^{*}\) can be obtained by \[\hat{i}^{*}=\max\left\{\hat{i}\ \middle|\ \sum_{k=1}^{\hat{i}}|g_{\hat{k}\hat{1}}|^{2} \leq I_{\text{th}}\right\}.\] (7) Even if all D2D transmitters in the eligible set transmit data simultaneously, the interference constraint imposed by BS is satisfied. Thus, no matter which combination of D2D transmitters in the eligible set transmit data, the interference constraint will be satisfied. The BS broadcasts a bitmap message with \(N\) bits to notify which D2D transmitters are included in the eligible set \(\mathcal{E}\). * If each D2D transmitter \(\hat{i}\) is included in the eligible set, then it waits for a response packet, which will be transmitted from a D2D receiver in Step 5. Otherwise, it terminates this algorithm. If each D2D receiver \(\hat{i}\) is included in the eligible set, then it starts a timer. Otherwise, it terminates this algorithm. The value of timer is determined by \(\frac{\mathcal{C}}{|g_{\hat{i}\hat{i}}|^{2}}\), where \(C\) is a constant to be determined by a controller and \(|g_{\hat{i}\hat{i}}|^{2}\) was measured in Step 2. * A D2D receiver whose timer expires first, denoted by \(\hat{t}\), transmits a response packet towards its associated transmitter \(\hat{t}\). Note that the timer of the D2D receiver that has the largest channel gain will expire first and thus a D2D pair with the best channel condition can be selected satisfying the interference constraint. * All D2D transmitters can receive the response packet transmitted by the receiver \(\hat{t}\) in Step 5. The D2D transmitter \(\hat{t}\) can transmit its data, but each D2D transmitter \(\hat{i}\) included in \(\mathcal{E}\setminus\{\hat{t}\}\) checks the following condition: \[\frac{|g_{\hat{i}\hat{i}}|^{2}}{|g_{\hat{i}\hat{i}}|^{2}}\geq\eta,\ \ \hat{i}\in\mathcal{E}\setminus\{\hat{t}\},\] (8) where \(|g_{\hat{i}\hat{i}}|^{2}\) can be obtained by measuring the response packet transmitted by receiver \(\hat{t}\), and \(\eta\) is a threshold value required in the proposed scheme.