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The 5G cellular network employs non-orthogonal multiple access (NOMA) to enhance network connectivity and capacity, and device-to-device (D2D) communications to improve spectrum efficiency. However, the underlay D2D communications may destroy the execution condition for the successive interference cancellation (SIC) decoding of NOMA cellular networks by introducing the extra interference, which degrades the cellular transmission reliability. Thus, we develop the interlay mode as a special D2D mode for NOMA system, which enables the power domain multiplexing of the D2D pair and cellular users to eliminate the strong interference between them by the SIC decoding. When D2D pair conducts the selection between the interlay mode and underlay mode, the SIC decoding constraint should be satisfied at both D2D receiver and NOMA base station. In order to maximize the system sum rate while …