A Hybrid Scheme for Low PAPR in Filter Bank Multi Carrier Modulation

Abstract

The demand for more bandwidth is increasing day by day due to explosive growth in data generated on account of services enabled on mobile phone, laptops and IOT devices. In the near future Internet for everything (IoE) technology where social media, processes, big data etc. will require internet connectivity all the times. Filter bank multicarrier with offset quadrature amplitude modulation system (FBMC/OQAM) is one of the promising techniques for next generation wireless communication system (5G). In FBMC-OQAM orthogonality condition is relaxed to obtain, better bandwidth utilization. This FBMC-OQAM is a multi-carrier transmission scheme where sub-carriers are independent to each other in time domain. The composite signal has large variation in amplitude, thus lead to peak to average power variation problem. This paper presents a FBMC scheme based on DFT spread and identically time shifted multicarriers (ITSM) conditions. In the chosen scheme DFT and IDFT is performed once and system behave as a nearly single carrier. This paper also deals with, PAPR reduction scheme. The chosen scheme is based on clipping and non-liner companding scheme, and obtained results are compared with recently proposed method.

Appendix

The impulse response of the pulse shaping prototype filter is denoted by h(t), and K represents the overlapping factor of the pulse.

Using the polyphase decomposition theory, we have

$$ H(z) = \sum\limits_{i = 0}^{KN - 1} {h(i)} z^{ - i} $$

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The above filter can be de-composed into N elementary filters,

$$ H(z) = \sum\limits_{n = 0}^{N - 1} {\sum\limits_{k = 0}^{K - 1} {h\left[ {kN + n} \right]} } z^{ - (kN + n)} $$

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$$ H(z) = \sum\limits_{n = 0}^{N - 1} {\left[ {\sum\limits_{k = 0}^{K - 1} {h\left[ {kN + n} \right]z^{ - kN} } } \right]} z^{ - n} $$

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The term $\left[ {\sum\nolimits_{k = 0}^{K - 1} {h\left[ {kN + n} \right]z^{ - kN} } } \right]$ is known as polyphase component of H(z), once prototype filter is designed then using frequency shifting filter bank can be designed (Fig. 14).

Fig. 14

Implementation of polyphase networks

The transfer function of the mth filter can be written as

$$ P_{m} (Z) = H\left( {Ze^{{ - 2\pi j\frac{m}{N}}} } \right) = \sum\limits_{n^{\prime} = 0}^{N - 1} {\left[ {\sum\limits_{k = 0}^{K - 1} {h\left[ {kN + n} \right]z^{ - kN} } } \right]} e^{{ - 2\pi j\frac{m}{N}}} z^{ - n^{\prime}} $$

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$$ \left[ \begin{gathered} P_{0} (Z) \hfill \\ P_{1} (Z) \hfill \\ \vdots \hfill \\ P_{N - 1} (Z) \hfill \\ \end{gathered} \right] = \left[ {\begin{array}{*{20}l} 1 \hfill & 1 \hfill & \ldots \hfill & 1 \hfill \\ 1 \hfill & {W^{ - 1} } \hfill & \ldots \hfill & {W^{ - (N - 1)} } \hfill \\ 1 \hfill & \ldots \hfill & \ldots \hfill & \ldots \hfill \\ 1 \hfill & {W^{ - (N - 1)} } \hfill & \ldots \hfill & {W^{{ - (N - 1)^{2} }} } \hfill \\ \end{array} } \right]\left[ \begin{gathered} H_{0} (Z^{N} ) \hfill \\ Z^{ - 1} H_{1} (Z^{N} ) \hfill \\ \vdots \hfill \\ Z^{ - (M - 1)} H_{N - 1} (Z^{N} ) \hfill \\ \end{gathered} \right] $$

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where $W = e^{ - j2\pi /N}$. Thus it performs the frequency de-composition of input signal. In poly phase networks first input data is divided into blocks of size B_W, and each carrier is passed through the filter h(t) and multiply by a phase factor. This process is repeated for each sub-carrier in all the block. Due to the various phases applied complete structure is known as poly phase network.