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Unmanned aerial vehicle (UAV) communications over cellular networks are currently gaining increased interest because it can enable real-time control of UAVs and wide-area coverage. We discuss various challenges for future UAV cellular networks, where cellular networks with down-tilted antennas optimized for terrestrial users can extend terrestrial cellular services to aerial users. To overcome challenges such as large channel variation and UAV power consumption in UAV cellular networks, we propose a technique of preamble design for these networks using scalable sequences. Specifically, three types of scalable sequences are proposed for efficient use of battery power in UAVs, namely, maximum-length scalable sequence, Zadoff-Chu scalable sequence, and linear frequency modulated (LFM) scalable sequence. The properties of these scalable sequences are analyzed and compared through simulations in different channel environments.