Closed-Form BER Expression for Fourier and Wavelet Transform-Based Pulse-Shaped Data in Downlink NOM

Closed-Form BER Expression for Fourier and Wavelet Transform-Based Pulse-Shaped Data in Downlink NOMA

Abstract: Non-orthogonal multiple access (NOMA) technique is a strong candidate for 5G cellular networks that enables greater multiuser capacity and user fairness through the multiplexing in the power domain. The user data is pulse shaped using orthogonal frequency division multiplexing (OFDM) technique based on Fast Fourier Transform (FFT) for conventional NOMA. We propose a Discrete Wavelet Transform based pulse shaping technique for NOMA. We present a closed form expression of bit error rate (BER) for FFT-NOMA as well as Wavelet based NOMA (WNOMA) systems. Theoretical and simulation BER results show that WNOMA outperforms FFT-NOMA in additive white Gaussian noise.

Existing system: Bit error rate (BER) performance compared to FFTNOMA, due to spectrally confined side lobes in Wavelet transform that counter inter-carrier interference, as well as inter-symbol interference. Moreover, the additional bandwidth occupied by the redundant CP in FFT-NOMA is conserved in WNOMA, owing to absence of cyclic prefix (CP) that gives spectral efficiency compared to FFT-NOMA. For

uplink NOMA, a closed form expression for BER is derived in that is based on a simple baseband modulation technique. A few works refer to DWT based NOMA technique; however none of the works present a closed form BER expression.

Proposed system: The Fifth Generation (5G) wireless and cellular networks promise to connect millions of users through multiple devices and non-orthogonal multiple access (NOMA) technique is proposed as a solution to enhance multiuser capacity.

NOMA ensures transmission of superimposed multiple user signals through variable power allocation. NOMA is included in the third-generation partnership project (3-GPP) in LTE-A, wherein it is referred to as multiuser superposition transmission (MUST) and in the latest television standard ATSC-3, as layered division multiplexing (LDM). In downlink NOMA, Fourier transform based orthogonal multiplexing FFT-OFDM is applied to the superimposed user data, as a pulse-shaping technique. However, pulse-shaping based on Wavelet transform based OFDM (WOFDM) is also considered in a few works.

Advantages: The novelty of the proposed work in this article pertains to the derivation of analytical form of BER for near and far users, in case of FFT-NOMA as well as WNOMA. While deriving the BER, we consider the effect of channel noise through discrete Fourier Transform (DFT) and DWT filter banks for FFT-NOMA and WNOMA respectively.

The closed form expression utilizes the Euclidean distance approach proposed. The theoretical and simulations results exhibit improved BER performance of WNOMA over FFT-NOMA. Disadvantages: Bit error rate (BER) performance compared to FFTNOMA, due to spectrally confined side lobes in Wavelet transform that counter inter-carrier interference, as well as inter-symbol interference. Moreover, the additional bandwidth occupied by the redundant CP in FFT-NOMA is conserved in WNOMA, owing to absence of cyclic prefix (CP) that gives spectral efficiency compared to FFT-NOMA.

For uplink NOMA, a closed form expression for BER is derived in that is based on a simple baseband modulation technique. A few works refer to DWT based NOMA technique; however none of the works present a closed form BER expression.

Modules: Multiuser superposition transmission: The Fifth Generation (5G) wireless and cellular networks promise to connect millions of users through multiple devices and non-orthogonal multiple access (NOMA) technique is proposed as a solution to enhance multiuser capacity.

NOMA ensures transmission of superimposed multiple user signals through variable power allocation. NOMA is included in the third-generation partnership project (3-GPP) in LTE-A, wherein it is referred to as multiuser superposition transmission (MUST) and in the latest television standard ATSC-3, as layered division multiplexing (LDM). In downlink NOMA, Fourier transform based orthogonal multiplexing FFT-OFDM is applied to the superimposed user data, as a pulse-shaping technique. However, pulse-shaping based on Wavelet transform based OFDM WOFDM) is also considered in a few works.

Cyclic prefix: Bit error rate (BER) performance compared to FFTNOMA, due to spectrally confined side lobes in Wavelet transform that counter inter-carrier interference, as well as inter-symbol interference. Moreover, the additional bandwidth occupied by the redundant CP in FFT-NOMA is conserved in WNOMA, owing to absence of cyclic prefix (CP) that gives spectral efficiency compared to FFT-NOMA. For uplink NOMA, a closed formex pression for BER is derived in that is based on a simple baseband modulation technique. A few works refer to DWT based NOMA technique; however none of the works present a closed form BER expression. The novelty of the proposed work in this article pertains to the derivation of analytical form of BER for near and far users, in case of FFT-NOMA as well as WNOMA. While deriving the BER, we consider the effect of channel noise through discrete Fourier Transform (DFT) and DWT filter banks for FFT-NOMA and WNOMA respectively. The closed form expression utilizes the Euclidean distance approach

proposed . The theoretical and simulations results exhibit improved BER performance of WNOMA over FFT-NOMA. Additive white Gaussian noise: Where Pi is power allocated to ith user. Before transmission, the data stream is pulse shaped by either taking Inverse FFT or cyclic prefixing for OFDM symbols’ transmission, or by taking inverse DWT for WOFDM symbols. The pulse-shaped data is transmitted over the channel having additive white Gaussian noise (AWGN) w (t). In case of OFDM based pulse-shaped data, the initially added CP is removed from received signal y(t), and then the data is subjected to FFT, equalized in case of non-ideal channel and de-mapped from QPSK symbol constellation to bit form.

However, for the WOFDM pulse-shaped data, the received signal is transformed using DWT, equalized in case of non-ideal channel and de-mapped to bits after QPSK demodulation. For the near user, the far user’s signal is subtracted from the composite signal after SIC, while for the far user, the near user’s low power signal is processed as noise.

Closed Form Expressions for Ber of Downlink Fft-Noma and Wnoma Techniques : For the closed-form expression of BER for QPSK modulated and pulse-shaped data using FFT-NOMA and WNOMA, we have considered the overall noise present in the received signal after passing through the AWGN channel and corresponding filter banks for FFTNOMA and WNOMA and denoted as NFFT and NDWT respectively. In case of OFDM, the channel effect is considered as flat fading for each sub-carrier. For DWT, the denoising of received signal occurs as the high frequency components are discarded during multi resolution analysis.

Perfect reconstruction and alias cancellation allows improved signal recovery and reduced effect of channel noise compared to FFT. This in turn enhances received signal-to-noise ratio (SNR) in WNOMA, thereby reducing the BER.