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Structure-Based Low Complexity MMSE Channel Estimator for OFDM Wireless Systems

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Abstract

Wireless communication systems utilizing orthogonal frequency division multiplexing (OFDM) transmissions are capable of delivering high data rates over multipath frequency selective channels. This paper deals with joint estimation/interpolation of wireless channel using pilot symbols transmitted concurrently with the data. We propose a low complexity, spectrally efficient minimum mean square error channel estimator which exploits the correlation structure of channel frequency response for reducing the complexity. Specifically, it is shown that if pilots are inserted appropriately across OFDM subcarriers, the proposed algorithm requires no matrix inversion, thereby significantly relieving the computational burden without deteriorating the performance. Moreover, the knowledge of channel correlation is also not required for the proposed estimator. Simulation results validate that the proposed technique outperforms existing low-complexity variants in terms of mean square error and computational complexity.

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Notes

  1. The treatment is similar for MIMO systems by assuming orthogonal training mechanism where only one antenna is active at a given pilot symbol.

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Authors and Affiliations

  1. Electrical Engineering Department, COMSATS Institute of Information Technology, Abbottabad, Pakistan

    Alam Zaib & Shahid Khattak

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  1. Alam Zaib
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  2. Shahid Khattak
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Correspondence to Alam Zaib.

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Appendix 1: MSE of Proposed Estimator

Appendix 1: MSE of Proposed Estimator

The MSE of proposed estimator given in (26) can be derived as follows.

$${\mathrm{MSE}} = \frac{1}{N}\mathbb {E}\left\{ \left\| \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}\right\| ^2\right\}$$
(28)

Using the expression (25) for the proposed estimator in (28) we get

$${\mathrm{MSE}} = \frac{1}{N}\mathbb {E}\left\{ \left\| \frac{1}{q}\sum _{i=1}^q\left( \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(i)}\right) \right\| ^2\right\}$$
(29)
$$= \frac{1}{Nq^2}\mathbb {E}\left\{ \sum _{i=1}^q\left( \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(i)}\right) \sum _{j=1}^q\left( \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(j)}\right) ^{\mathrm{H}}\right\}$$
(30)
$$= \frac{1}{Nq^2}\mathbb {E}\left\{ \sum _{i=1}^q\left\| \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(i)}\right\| ^2+\sum _{i\ne j}^q\left( \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(i)}\right) \left( \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(j)}\right) ^{\mathrm{H}}\right\}$$
(31)
$$= \frac{1}{Nq^2}\sum _{i=1}^q\mathbb {E}\left\{ \left\| \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(i)}\right\| ^2\right\}$$
(32)
$$= \frac{1}{q^2}\sum _{i=1}^q\mathrm{MSE}^{(i)}$$
(33)

where in arriving at (32) we used the fact that \(\mathbb {E}\left\{ \left( \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(i)}\right) \left( \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(j)}\right) ^{\mathrm{H}}\right\} =0\) due to orthogonality of errors corresponding to individual estimates and \(\mathrm{MSE}^{(i)}\triangleq (1/N)\mathbb {E}\left\{ \left\| \varvec{\mathcal {H}}- \widehat{\varvec{\mathcal {H}}}^{(i)}\right\| ^2\right\}\) represents the MSE corresponding to the estimate \(\widehat{\varvec{\mathcal {H}}}^{(i)}\). Now using the result from (24) with K replaced by \(|{\mathcal {P}}^i|=K/q\) we can write

$${\mathrm{MSE}}^{(i)} = 1 - \frac{K}{qL(1+\beta /\rho )}$$
(34)

Finally, using (34) in (33) we get the desired result which completes the proof.

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Zaib, A., Khattak, S. Structure-Based Low Complexity MMSE Channel Estimator for OFDM Wireless Systems. Wireless Pers Commun 97, 5657–5674 (2017). https://doi.org/10.1007/s11277-017-4800-4

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