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Joint radar-communication designs are exploited in applications where radar and communications systems share the same frequency band or when both radar sensing and information communication functions are required in the same system. Finding a waveform that is suitable for both radar and communication is challenging due to the difference between radar and communication operations. In this paper, we propose a new method of designing dual-functional waveforms for both radar and communication using signals from multiplexed communications users. Specifically, signals from different communications users multiplexed in the time, code or frequency domains across different data bits are linearly combined to generate an overall radar waveform. Three typical radar waveforms are considered. The coefficients of the linear combination are optimized to minimize the mean squared error with or without a constraint on the signal-to-noise ratio (SNR) for the communications signals. Numerical results show that the optimization without SNR constraint can almost perfectly approximate the radar waveform in all the cases considered, giving good dual-functional waveforms for both radar and communication. Also, among different multiplexing techniques, time division multiple access is the best option to approximate the radar waveform, followed by code division multiple access and orthogonal frequency division multiple access. [ABSTRACT FROM AUTHOR]