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This study presents an optimisation-based audio watermarking scheme using group-amplitude quantisation. To enhance the robustness, the watermark is embedded in the lowest-frequency coefficients in discrete wavelet transform (DWT). The performance of this watermarking scheme is analysed in terms of audio quality (signal-to-noise ratio (SNR)) and robustness (bit error ratio (BER)). As there is a tradeoff relationship between the audio quality and robustness, this study presents an optimisation-based group-amplitude quantisation scheme for audio watermarking. First, SNR is rewritten as a watermarking cost function in matrix form. Then an equation connecting the watermarking cost function and the group-amplitude quantisation equation is proposed. Second, the Lagrange principle is used to derive the optimisation solution. The optimal results are then applied to embed the watermark. Finally, the performance of the proposed scheme is tested. Experimental results show that the hidden data are robust against most common attacks, such as re-sampling, MP3 compression, low-pass filtering and amplitude scaling.