This paper investigates power allocation for D2D communications in a Heterogeneous Network (HetNet) which includes a macro cell and pico cells, whereas femto cells are distributed inside. The objective is to minimize the total power consumption of D2D transmitter while satisfying a set of Quality of Service in D2D receivers and cellular users communication interference. To this end, we first obtain expression for the formula of signal to interference plus noise ratio (SINR) and spectral

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... cy of each D2D receiver. Then, an optimization problem is formulated to minimize the total transmit power of D2D transmitters subject to QoS constraints. It is shown that this optimization problem is linear programming and it can be solved in polynomial time with standard tools. In addition, the maximization value of D2D pair transmission rates are determined with fixed cellular users parameters.