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A non-iterative resource allocation strategy for device-to-device communications in underlaying cellular networks

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Abstract

We develop a joint spectrum sharing and power control strategy to increase the admissible number of device-to-device (D2D) links in an underlaying cellular network while guaranteeing the quality-of-service (QoS) of both D2D links and cellular users (CUs). The proposed spectrum sharing algorithm, termed as interference-filling (IF), examines whether the SINR requirements of all the existing CUs and D2D users can be met if a new D2D pair is admitted. In the sequel, two power control schemes are proposed to check the resultant interference level and increase the transmit power of the admitted D2D pairs group-by-group to further improve the system throughput. IF algorithm is based on the ordering statistics of the interference amounts from D2D transmitters to CUs, thus neither grid searching nor iteration is needed. Furthermore, the two proposed power control schemes are in closed-forms. These two favorable properties make the proposed strategy cost-effective and computationally efficient. Numerical results show the effect of the proposed IF and power control schemes in term of admissible D2D pairs and system sum rate.

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Notes

  1. Here we say D2D m underlay CU n, if they share the same spectrum.

  2. Since channel assignment has not been applied to D2D pairs, we can assume that D2D link gains from \(D_{n,t}\) to \(D_{m,r}\) are invariant with respect to (w.r.t.) the cellular channel n.

  3. For notational simplicity even with ambiguity, herein we reuse \(I^c_n\) and \(I^d_m\) as the normalized interference amount of \(U_n\) and \(D_{m,r}\), respectively.

  4. Due to the huge and unaffordable simulation time, exhaustive search method is only included in the case of tens of D2D pairs.

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Correspondence to Yao-Jen Liang.

Appendix

Appendix

Proof of Proposition 1

After IF applied, each interference pool of \(D_m\), \(\forall D_m \in {\mathcal {G}}_n\) should not be overflowed, that is

$$\begin{aligned}&\frac{I^d_m}{I^d_{m,max}} \mathop {=}\limits ^{(3)(5)}\frac{\sum _{D_i\in {\mathcal {G}}_ni\ne m}P^d_i|g_{m,i}|^2+P^c_n|h_{m,n}|^2}{\frac{P^d_m|g_{m,m}|^2}{\eta ^d_m}-\sigma ^2} \le 1 \end{aligned}$$
(37)
$$\begin{aligned} \mathop {\Rightarrow }\limits ^{(a)}&\frac{\sum _{i\ne m}P^d_i|g_{m,i}|^2+P^c_n|h_{m,n}|^2}{P^d_m|g_{m,m}|^2} \le \frac{1}{\eta ^d_m}\end{aligned}$$
(38)
$$\begin{aligned} \mathop {\Rightarrow }\limits ^{(b)}&\sum _{i\ne m}\frac{|g_{m,i}|^2}{|g_{m,m}|^2} + \frac{P^c_n}{P^d_m}\frac{|h_{m,n}|^2}{|g_{m,m}|^2} \le \frac{1}{\eta ^d_m}. \end{aligned}$$
(39)

In above approximations, (a) assumes that SINR requirement of \(D_{m,r}\), \(\eta ^d_m \gg 1\); while (b) comes from equal power allocation among D2D pairs, i.e., \(P^d_i = P^d_m, \,\forall i\ne m\). Since the second term in the left hand side of (39) is nonnegative and \(\eta ^d_m \gg 1\), we have

$$\begin{aligned} |g_{m,i}|^2 \ll |g_{m,m}|^2< 1,\,\forall i\ne m. \end{aligned}$$
(40)

Let \({\mathcal {G}}_n=\{D_1,D_{2'},\ldots ,D_{m'}\}\) and \(D_1\) be the selected D2D to increase its transmit power by a factor of \(b>1\), without loss of generality. Further set the sum rate of \({\mathcal {G}}_n\) after increasing \(D_1\)’s transmit power be \(r'_n\). From (11),

$$\begin{aligned} \frac{r'_n}{W_n}&= \log _2\left( 1+\frac{bP^d_1|g_{1,1}|^2}{\sum _{D_i\in {\mathcal {G}}_n, i\ne 1}P_i^d|g_{1,i}|^2+P_n^c|h_{1,n}|^2+\sigma ^2}\right) \nonumber \\&\quad + \sum _{j=2',3',\ldots ,m'}\log _2\left( 1+\frac{P^d_j|g_{j,j}|^2}{(b-1)P_1^d|g_{j,1}|^2+ \sum _{D_i\in {\mathcal {G}}_n, i\ne j}P_i^d|g_{j,i}|^2+P_n^c|h_{j,n}|^2+\sigma ^2}\right) \nonumber \\&= \log _2\left( \frac{N^d_1 + bP^d_1|g_{1,1}|^2}{N^d_1}\right) + \sum _{j=2',3',\ldots ,m'}\log _2\left( \frac{N^d_j+(b-1)P^d_1|g_{j,1}|^2+P^d_j|g_{j,j}|^2}{N^d_j+(b-1)P^d_1|g_{j,1}|^2}\right) , \end{aligned}$$
(41)

where

$$\begin{aligned} N^d_j = \sum _{D_i\in {\mathcal {G}}_n, i\ne j}P_i^d|g_{j,i}|^2+P_n^c|h_{j,n}|^2+\sigma ^2. \end{aligned}$$
(42)

Similarly,

$$\begin{aligned} \frac{r_n}{W_n} = \sum _{j=1,2',\ldots ,m'}\log _2\left( \frac{N^d_j + P^d_j|g_{j,j}|^2}{N^d_j}\right) , \end{aligned}$$
(43)

then

$$\begin{aligned} \frac{r'_n-r_n}{W_n} =&\log _2[\frac{N^d_1 + bP^d_1|g_{1,1}|^2}{N^d_1 + P^d_1|g_{1,1}|^2}\nonumber \\&\times \prod _{j=2',3',\ldots ,m'}\frac{N^d_j+(b-1)P^d_1|g_{j,1}|^2+P^d_j|g_{j,j}|^2}{N^d_j+P^d_j|g_{j,j}|^2}\frac{N^d_j}{N^d_j+(b-1)P^d_1|g_{j,1}|^2}]. \end{aligned}$$
(44)

By using the fact that \((b-1)P^d_1|g_{j,1}|^2 \rightarrow 0\), since \(|g_{j,1}|^2 \ll 1\) in (40), we acquire

$$\begin{aligned} \frac{r'_n-r_n}{W_n} \cong \log _2\left( \frac{N^d_1 + bP^d_1|g_{1,1}|^2}{N^d_1 + P^d_1|g_{1,1}|^2}\right) > 0. \end{aligned}$$
(45)

Proposition 1 is thus proved. \(\square \)

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Liang, YJ., Lin, YS. A non-iterative resource allocation strategy for device-to-device communications in underlaying cellular networks. Wireless Netw 23, 2485–2497 (2017). https://doi.org/10.1007/s11276-016-1302-3

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