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Visible Light Communication (VLC) is a data communication technology that modulates the intensity of the light to transmit the information mostly by means of Light Emitting Diodes (LEDs). The data rate is mainly throttled by the limited bandwidth of the LEDs. To combat, Multi-carrier Code Division Multiple Access (MC-CDMA) is a favorable technique for achieving higher data rates along with reduced Inter-Symbol Interference (ISI) and easy access to multi-users at the cost of slightly reduced compromised spectral efficiency and Multiple Access Interference (MAI). In this article, a multi-user VLC system is designed using a Discrete Wavelet Transform (DWT) that eradicates the use of cyclic prefix due to the good orthogonality and time-frequency localization properties of wavelets. Moreover, the design also comprises suitable signature codes, which are generated by employing double orthogonality depending upon Walsh codes and Wavelet Packets. The proposed multi-user system is simulated in MATLAB software and its overall performance is assessed using line-of-sight (LoS) and non-line-of-sight (NLoS) configurations. Furthermore, two sub-optimum multi-users detection schemes such as zero forcing (ZF) and minimum-mean-square-error (MMSE) are also used at the receiver. The simulated results illustrate that the doubly orthogonal signature waveform-based DWT-MC-CDMA with MMSE detection scheme outperforms the Walsh code-based multi-user system.