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In this paper, a robust watermarking algorithm using balanced multiwavelet transform is proposed. The latter transform achieves simultaneous orthogonality and symmetry without requiring any input prefiltering. Therefore, considerable reduction in computational complexity is possible, making this transform a good candidate for real-time watermarking implementations such as audio broadcast monitoring and DVD video watermarking. The embedding scheme is image adaptive using a modified version of a well-established perceptual model. Therefore, the strength of the embedded watermark is controlled according to the local properties of the host image. This has been achieved by the proposed perceptual model, which is only dependent on the image activity and is not dependent on the multifilter sets used, unlike those developed for scalar wavelets. This adaptivity is a key factor for achieving the imperceptibility requirement often encountered in watermarking applications. In addition, the watermark embedding scheme is based on the principles of spread-spectrum communications to achieve higher watermark robustness. The optimal bounds for the embedding capacity are derived using a statistical model for balanced multiwavelet coefficients of the host image. The statistical model is based on a generalized Gaussian distribution. Limits of data hiding capacity clearly show that balanced multiwavelets provide higher watermarking rates. This increase could also be exploited as a side channel for embedding watermark synchronization recovery data. Finally, the analytical expressions are contrasted with experimental results where the robustness of the proposed watermarking system is evaluated against standard watermarking attacks.

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In this paper, we derive the bit error rate (BER) and pairwise error probability (PEP) for massive multipleinput multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems for different M -ary modulations based upon the approximate noise distribution after channel equalization. The PEP is used to obtain the upper-bounds for convolutionally coded and turbo coded massive MIMO-OFDM systems for different code generators and receive antennas. In addition, complexity analysis of the log-likelihood ratio (LLR) values is performed using the approximate noise probability density function (PDF). The derived LLR computations can be timeconsuming when the number of receive antennas is very large in massive MIMO-OFDM systems. Thus, a reduced complexity approximation is introduced using Newton's interpolation with different polynomial orders and the results are compared with the exact simulations. The Neumann large matrix approximation is used to design the receiver for a zero-forcing equalizer (ZFE) by reducing the number of operations required in calculating the channel matrix inverse. Simulations are used to demonstrate that the results obtained using the derived equations match closely the Monte-Carlo simulations.