In general, the unipolar ACO-OFDM signal is generated by clipping the bipolar OFDM signal at zero, represented as in [14]
![](data:image/png;base64,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)
The clipping distortion that is resulted from clipping operation falls only on the even subcarriers, without affecting the data on the odd subcarriers. The ACO-OFDM signal in terms of data and clipping distortion is represented as
$${x}_{ACO,n}=\frac{1}{2}\left({x}_{n}+\left|{x}_{n}\right|\right)$$
2
$${x}_{ACO,n}={x}_{D,n}+{x}_{C,n}$$
3
where \({x}_{C,n}=\frac{1}{2}\left|{x}_{n}\right|\) (\(\left|.\right|\) denotes the absolute operator) is the clipping distortion falling on the even subcarriers, that does not affect the modulated data \({x}_{D,n}={\frac{1}{2}x}_{n}\) present on the odd subcarriers as shown in [9, 14].
Multiple layers of ACO-OFDM represented by Equation (3), are then combined and expressed in [12] as
$${x}_{LACO}\left(n\right)=\sum _{l=1}^{L}{x}_{ACO}^{l}\left(n\right)$$
4
$${x}_{ACO}^{l}={{x}^{l}}_{D,n}+{{x}^{l}}_{C,n}$$
5
where ‘l’ represents the layers, \({{x}^{l}}_{D,n}\) and \({{x}^{l}}_{C,n}\)represents the data and the clipping distortion of ‘l’ layers.
2.1 LACO-OFDM with TDDR
The TDDR was applied to each layer of LACO-OFDM in [12], represented as
\({x}_{LACO-TDDR}\left(n\right)\) =\(\left(1-\alpha \right)\text{*}{{x}^{l}}_{D}\left(n\right)+\alpha \text{*}\left(sign\right({{x}^{l}}_{D}\left(n\right)){\text{*}{x}^{l}}_{C}\)(n) (6)
where ‘\(\alpha\)’ is the combination factor that defines the relation between modulated data \({x}_{D,n}\) and the non-linear processing of \(sign\left({x}_{D,n}\right)\text{*}{|x}_{D,n}|\).
2.2 LACO-OFDM with TDDC
Similar to ACO-TDDR, the principle of operation remains the same in ACO-TDDC, represented as
\({x}_{LACO-TDDC}\left(n\right)=\left(1-\alpha \right)\text{*}{{x}^{l}}_{D}\left(n\right)+\alpha \text{*}\left(sign\right({{x}^{l}}_{D}\left(n\right)\left)\text{*}{{x}^{l}}_{D}\left(n\right)\right)\) (7) \(\)