In the previous post, an implementation demo of the Screen-OFDM system was shown. The detailed generation of Screen-OFDM (2-dimensional OFDM) is described in this post.

**Index Terms**: Optical Camera Communication, OCC, OFDM, optical OFDM, 1D-OFDM, 2D-OFDM, OFDM-OCC, Screen OFDM.

## Benefit of OFDM

**1) General Benefits**

The concept of OFDM has reached sufficient maturity for standardization and employment in the 1990s. Recall that the OFDM system has various advantages compared to conventional single-carrier baseband modulation systems, e.g., OOK.

- OFDM, with its multicarrier modulation (MCM), splits the high bit-rate stream (in the space-time domain) into many lower bit-rate streams, i.e., each data stream is sent using an independent carrier (that is orthogonal to the other streams. This attractive feature (potentially) releases the critical need for a classic channel equalizer for a properly designed system.
- Another significant advantage of MCM is its good Inter-Symbol Interference mitigation property. The interference may come between pixels in the space-time domain or between subcarriers in the frequency-time domain for the intended screen-camera system. The channel needs to be comprehensively analyzed and modeled for clear verification, and the proper design and manipulation of OFDM need to be discussed to leverage the key resources of the system.

**2) Applying for Screen OCC**

The application of a multicarrier modulation technique to the Screen OCC system results in numerous benefits, as summarized below.

- MCM using 2D-DFT for the screen-camera system performs as well as typical 1D DFT-OFDM modulation. In the screen-camera system, the troubling of complex forms of noise (blurred image, irregular attenuation functions, and interference conditions) seems to be unmitigated in the space-time domain. The transformation of data from the space-time domain into the space-time-frequency domain brings us resolvable functions. Such the frequency-domain attenuation function H shows clearly its characteristics. Thus the dedicated allocation of orthogonal carriers can mitigate the inter-carrier interference, and the ambient light which is problematic in the single-carrier modulation can be efficiently removed in the frequency domain by ignoring the DC-component. Efficient solutions for OFDM make the system work without an expensive equalizer. These advantages make MCM (using 2D-DFT) functional as the screen-camera OCW.
- A massive MIMO Tx can be divided into smaller codes for higher link quality. In order to accomplish this approach, additional designs and the proper use of OFDM are needed. Unfortunately, even this promising approach has its drawbacks, as the bandwidth efficiency is reduced due to the required use of a cyclic prefix. There is a trade-off in selecting the size of OFDM symbols within the Tx: bigger sizes bring better bandwidth efficiency, while the smaller sizes encounter lower attenuation in the frequency domain. The sizes can be selected experimentally to compensate for the imperfect sub-bands condition.

## 2D-OFDM Orthogonality

We can show that 2D-DFT has orthogonality, just like 1D-DFT:

The orthogonality between the 2D subcarriers is shown as follows

Undeniably, one of the significant properties of 2D-DFT is its separability. This property implies that the 2D-DFT of an image can be computed by first computing the 1D-DFT along each row of the image and then computing the 1D-DFT along each column of the intermediate result. This process can also be reversed: columns first, rows later. Since the orthogonality between the 1D-DFT subcarriers is well-known, the orthogonality inherits its property for 2D-DFT.

It is known that the sinc-function represents the impulse response h(t) of the IFFT (see the left of the following figure). Similarly, a 2D-version of the sinc-function (the right figure) represents the impulse response of the 2D-IFFT. The 2D-IDFT of a 2D-rectangular wave may be quite different from the sinc-function.

1D version of a sinc-function 2D version of a sinc-function

## OFDM Choices

A historical implementation of OFDM was with the banks of sinusoidal. The DFT replacement has been used since the 1970s, and the maturity of DFT-OFDM was realized in the 1990s. Recently, filter-bank multicarrier has attracted researchers into OFDM.

For an OWC system, particularly for Screen OCC, the non-negative waveform required to drive light sources leads to the development of different mapping techniques prior to the IDFT. Such Asymmetrically Clipped Optical OFDM(ACO-OFDM) and DC-biased Optical OFDM (DCO-OFDM) are well-developed techniques for LiFi OFDM systems. In comparison, DWT has a variant that produces the required unipolar waveform for light sources. Table 1 briefly compares the given techniques.

Wavelet OFDM has only been standardized recently by the IEEE Standard Association (i.e., the IEEE 1901 forPower Line Network), although it provides more attractive features than FFT-OFDM (e.g., no redundancy, higher spectral separation, and reduced subchannel-interference). The theoretical performance of Wavelet OFDM was analyzed, and it was shown that Wavelet OFDM outperformed windowed OFDM, even with the use of less active subcarriers (sub-bands). A proper version of Wavelength OFDM theoretically showed better spectral efficiency, suppression of side-lobes, and significantly better BER. However, in practice, the typical DWT is a quadrature-mirror-filter-based, multi-scale bandwidth separation, leading to the development of the Wavelet Packet transform, i.e., a generalized version of DWT for the optical OFDM system. Last but not least, an abundance of wavelet packet applications to OWC systems have been introduced, demonstrating smaller PAPR and better robustness in dealing with channel imperfection.

## Conclusion

There are several ways to generate 2D-OFDM for our Screen-Camera OCC.

A mature screen-camera system employing 2D-OFDM has been proposed in the IEEE Access paper (available online). In that paper, the results of the theoretical analysis and implementation have been addressed in detail. Numerical results demonstrated that the implementation of the Screen OFDM system was more reliable compared to the implementation of the A-QL code even though ScreenOFDM carries over ten times more data than A-QL, under the sample testing conditions. Please refer to the paper for more technical details.