Optimum Modulation Orders for 1-bit Compressively Sampled Signals in Multicarrier Transmission

In compressed sensing (CS), quantization is essential for efficient discretization in real systems, but its large bit depth increases hardware complexity and energy consumption. To overcome these issues, 1-bit CS is regarded as a new data acquisition technique. In this paper, we discover that there exist optimum modulation orders for orthogonal multicarrier transmission of 1-bit CS signals over wireless channels. In specific, we develop an upper bound on the reconstruction errors when modulated 1-bit CS signals are transmitted in multicarrier communications with a fixed number of subcarriers. In the upper bound, a tradeoff between the bit error probability and the quantization error is found over the orders of quadrature-amplitude modulation (QAM), which leads to the existence of an optimum modulation order minimizing the reconstruction errors. Simulation results demonstrate that the reconstruction performance of 1-bit CS is bounded by the theoretical upper bound, and subsequently confirm the existence of optimum modulation orders.