Efficient Noise Variance Estimation under Pilot Contamination for Large-Scale MIMO Systems

Jorge Iscar Vergara, Ismail Guvenc, Sener Dikmese, Nadisanka Rupasinghe

    Research output: Contribution to journalArticleScientificpeer-review

    5 Citations (Scopus)


    Massive multiple-input multiple-output (MIMO) is expected to be one of the enabling technologies for fifth generation (5G) cellular networks. One of the major challenges in massive MIMO systems is the accurate joint estimation of the channel and noise variance, which significantly affects the performance of wireless communications in practical scenarios. In this paper, we first derive a novel maximum likelihood (ML) estimator for the noise variance at the receiver of massive MIMO systems considering practical impairments such as pilot contamination. Then, this estimate is used to compute the minimum mean square error (MMSE) estimate of the channel. In order to measure the performance of the proposed noise variance estimator, we derive the corresponding Cramer-Rao lower bound (CRLB). Simulation results show that the estimator is efficient in certain scenarios, outperforming existing approaches in the literature. Furthermore, we develop the estimator and CRLB for equal and different noise variance at the receive antennas. Although the proposed estimator is valid for all antenna array sizes, its use is particularly effective for massive MIMO systems.

    Original languageEnglish
    Pages (from-to)2982-2996
    JournalIEEE Transactions on Vehicular Technology
    Issue number4
    Early online date24 Oct 2017
    Publication statusPublished - 2018
    Publication typeA1 Journal article-refereed


    • 5G
    • Channel estimation
    • Contamination
    • Covariance matrices
    • CRLB
    • massive MIMO
    • maximum likelihood
    • Maximum likelihood estimation
    • method of moments
    • MIMO
    • MMSE channel estimation
    • noise variance estimation
    • Partial transmit sequences
    • pilot contamination

    Publication forum classification

    • Publication forum level 2

    ASJC Scopus subject areas

    • Automotive Engineering
    • Aerospace Engineering
    • Applied Mathematics
    • Electrical and Electronic Engineering


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