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Cyclic interleaving scheme for an IFDMA system

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Abstract

In this paper, a new interleaving scheme for an interleaved frequency division multiple access (IFDMA) system is proposed. The proposed scheme combines the advantages of code division multiple access (CDMA) with maximal length sequence (m-sequence) and orthogonal frequency division multiple access (OFDMA). Multiaccess interference (MAI) among users is eliminated by employing orthogonal carriers, and the intersymbol interference (ISI) due to multipath channels is minimized by using cyclic interleaving. Diversity gain is achieved in the proposed method with maximal ratio combining (MRC) in the case of a Rayleigh environment. Compared to complex multiuser (MU) detection, the detection process in the proposed method is relatively simple. Multipath orthogonality is achieved in the proposed method, avoiding the need for channel equalization. The proposed method is compared with the conventional interleaving employing well-known minimum mean square error frequency domain equalization (MMSE-FDE). The Monte Carlo simulation results prove the superiority of the proposed interleaving over conventional interleaving with MMSE-FDE, showing that the present scheme is suitable for both uplink and downlink mobile radio transmissions.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments that greatly improved the quality of this paper.

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Correspondence to S. Lenty Stuwart.

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This work was supported by the SERB Early Career Research Award with file number ECR/2017/001188, Department of Science and Technology, Government of India.

Appendix

Appendix

1.1 A.1 Proof 1

Without loss of generality, the closed-form expression is deduced from the complex expression.

$$ c_{(N^{2}q+Q(Ql)_{\text{mod}N}+Qm)\text{mod} N}= c_{(l+Qm)\text{mod} N} $$
(A.1)

The term (Ql)modN on the left-hand side of Eq. A.1 can be simplified as follows:

$$ \begin{array}{@{}rcl@{}} (Ql)_{\text{mod}N}&=&(Nl-l)_{\text{mod}N} \\ &=&(N(l+1-1)-l)_{\text{mod}N} \\ &=&((l-1)N+N-l)_{\text{mod}N} \\ &=&N-l \end{array} $$
(A.2)

where Q = N − 1 and Nl < N. Further simplification of Eq. A.1 after substituting the result obtained from Eq. A.2 on the left-hand side of Eq. A.1 is given by the following:

$$ \begin{array}{@{}rcl@{}} c_{(N^{2}q+Q(Ql)_{\text{mod}N}+Qm)\text{mod} N}&=&c_{(N^{2}q+(N-1)(N-l)+Qm)\text{mod} N}\\ &=&c_{(N^{2}q+N^{2}-Nl-N+l+Qm)\text{mod} N}\\ &=&c_{(l+Qm)\text{mod} N} \end{array} $$

1.2 A.2 Proof 2

This proof also deals with simplification of the expression.

$$ d^{(i)}_{(N^{2}q+Q)\text{mod}Q}= d^{(i)}_{q} $$
(A.3)

The expression on the left side of Eq. A.3 is reduced as follows:

$$ \begin{array}{@{}rcl@{}} d^{(i)}_{(N^{2}q+Q)\text{mod}Q}&=&d^{(i)}_{((Q-1)^{2}q+Q)\text{mod}Q}\\ &=&d^{(i)}_{(qQ^{2}-2Qq+q+Q)\text{mod}Q}\\ &=&d^{(i)}_{q} \end{array} $$

1.3 A.3 Proof 3

The unit value for the exponential term corresponding to the g th path of the desired user in Eq. 13 is proven as follows:

$$ e^{j[-(B-g)_{\text{mod}(VQ)}\varphi(i)+(B)_{\textrm {mod}(VQ)}\varphi(i)-g\varphi(i)]}=1 $$
(A.4)

The term − (Bg)mod(VQ)φ(i) + (B)mod(VQ)φ(i) − gφ(i) on the left-hand side of Eq. A.4 can be rewritten as follows: − (Bg)mod(VQ)φ(i) + (B)mod(VQ)φ(i) − (g)mod(VQ)φ(i), since g < VQ. The property of congruence modulo [25] yields the following relation:

$$ (B-g)_{\text{mod}(VQ)}\varphi(i)=(B)_{\textrm {mod}(VQ)}\varphi(i)-(g)_{\textrm {mod}(VQ)}\varphi(i) $$
(A.5)

Replacing (A.5) into (A.4) proves the result.

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Kumar, J.A., Stuwart, S.L. Cyclic interleaving scheme for an IFDMA system. Ann. Telecommun. 75, 241–252 (2020). https://doi.org/10.1007/s12243-020-00748-5

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