<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-07-08</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000926282</issuerCik>
        <issuerName>ADTRAN INC</issuerName>
        <issuerTradingSymbol>ADTN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001327057</rptOwnerCik>
            <rptOwnerName>McCray Gregory James</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ADTRAN</rptOwnerStreet1>
            <rptOwnerStreet2>901 EXPLORER BLVD.</rptOwnerStreet2>
            <rptOwnerCity>HUNTSVILLE</rptOwnerCity>
            <rptOwnerState>AL</rptOwnerState>
            <rptOwnerZipCode>35806</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-07-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>21641.798</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Includes 3,943 shares of time-based restricted stock under a restricted stock award (an &quot;RSA&quot;) and 35.53 shares of restricted stock acquired in connection with such RSA pursuant to a dividend reinvestment feature of the applicable equity plan.</footnote>
        <footnote id="F2">Pursuant to that certain Business Combination Agreement, dated August 30, 2021, by and among the Issuer, ADVA Optical Networking SE, Acorn HoldCo, Inc. (now named ADTRAN Holdings, Inc. (&quot;Holdings&quot;)), and Acorn MergeCo, Inc., the Issuer became a wholly owned subsidiary of Holdings on July 8, 2022 (the &quot;Effective Time&quot;). At the Effective Time, each share of the Issuer's common stock converted, on a one-for-one basis, into a share of common stock of Holdings.</footnote>
    </footnotes>

    <remarks>The reporting person's status as a director of the Issuer terminated as of the Effective Time.</remarks>

    <ownerSignature>
        <signatureName>/s/ Michael Foliano, by power of attorney</signatureName>
        <signatureDate>2022-07-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
