Light-emitting diode (LED)-based communications, such as visible light communications (VLC) and infrared (IR) communications, are candidate techniques to provide short-range and high-speed data transmission. In this paper, M-ary pulse amplitude modulation (M-PAM), used as a high bandwidth efficiency scheme, is compared with an optimized DC-biased optical orthogonal frequency division multiplexing (DCO-OFDM) scheme. Considering the bandwidth limit and constrained peak transmitted power characteristics of LEDs, a bit loading algorithm with an optimized modulation index is used for the DCO-OFDM. To reduce the inter-symbol interference caused by LEDs, a waveform design algorithm with a minimum mean squared error (MMSE) equalizer is applied to the M-PAM system. From numerical results, M-PAM with the optimized signal processing can provide a substantially higher data rate than the optimally designed DCO-OFDM for the same performance.