<PAGE>

                                                                     EXHIBIT 4.3
 
                             OMNIPOINT CORPORATION
                          CERTIFICATE OF DESIGNATION

                               establishing the

            Voting Powers, Designations, Preferences, Limitations,
                     Restrictions, and Relative Rights of

                   7% CUMULATIVE CONVERTIBLE PREFERRED STOCK

                     ------------------------------------

                        Pursuant to Section 151 of the
               General Corporation Law of the State of Delaware

                     ------------------------------------


     OMNIPOINT CORPORATION, a corporation organized and existing under the
General Corporation Law of the State of Delaware (the "Issuer"), does hereby
certify that pursuant to authority conferred upon the Board of Directors of the
Issuer by its Amended and Restated Certificate of Incorporation and pursuant to
the provisions of Section 151 of the General Corporation Law of the State of
Delaware, the following resolution establishing the Issuer's 7% Cumulative
Convertible Preferred Stock was duly adopted by the Board of Directors, on
April 30, 1998, which resolution remains in full force and effect.  Certain
capitalized terms used herein are defined in Article 11.

          RESOLVED, that pursuant to the authority expressly granted to and
          vested in the Board of Directors of the Corporation by the provisions
          of Section Fourth (B) of the Amended and Restated Certificate of
          Incorporation, as amended from time to time (the "Certificate of
          Incorporation"), and pursuant to Section 151(g) of the General 
          Corporation Laws of the State of Delaware, there be from the 5,000,000
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          shares of Preferred Stock, $0.01 par value, of the Corporation,
          authorized to be issued pursuant to the Certificate of Incorporation,
          a series of Preferred Stock, consisting of 325,000 shares of 7%
          Cumulative Convertible Preferred Stock (referred to herein as the
          "Preferred Stock"), having the number of shares and, to the extent
          that the designations, powers, preferences and relative and other
          special rights and the qualifications, limitations and restrictions of
          such Preferred Stock are not stated and expressed in the Certificate
          of Incorporation, the powers, preferences and relative and other
          special rights and the qualifications, limitations and restrictions
          thereof, as follows:


1.   Designation and Number of Shares

          1.1  The series will be known as the 7% Cumulative Convertible
Preferred Stock.

          1.2  The Preferred Stock will be a series consisting of 325,000 shares
of the authorized but unissued preferred stock of the Issuer.

2.   Dividends

          2.1  Holders of Preferred Stock will be entitled to receive, when, as
and if declared by the Board of Directors, out of funds legally available
therefor, dividends on each outstanding share of Preferred Stock, payable
quarterly in arrears at a rate per annum equal to 7% of the liquidation
preference per share.

          (a) All dividends will be cumulative, whether or not earned or
declared, on a quarterly basis on February 1, May 1, August 1, and November 1 of
each year (each such date being referred to herein as a "Dividend Payment
Date"), commencing August 1, 2001, unless the Issuer elects the early
termination of the Deposit Account, pursuant to the terms of the Deposit Account
Agreement, in which case payment of dividends will commence on the Dividend
Payment Date immediately following the date of such early termination.
Dividends will accumulate on a day to day basis from May 2, 2001 unless the
Issuer elects early termination of the Deposit Account, in which case dividends
will accumulate from the day after the Dividend Payment Date immediately
preceding the date of such early termination.  Each distribution in the form of
a dividend shall be payable in arrears to Holders of record as they appear on
the stock books of the Issuer on each record date as established 

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by the Board of Directors of the Issuer (the "Dividend Payment Record Date") not
more than 60 nor less than ten days preceding a Dividend Payment Date.

               (i) Dividends payable on the Preferred Stock for each full
     dividend period will be computed by dividing the annual dividend rate by
     four.  Dividends payable on the Preferred Stock for any period less than a
     full dividend period will be computed on the basis of a 360-day year
     consisting of twelve 30-day months.

               (ii) The Preferred Stock will not be entitled to any dividend
     whether payable in cash, property or securities, in excess of the full
     cumulative dividends.

               (iii)  No interest, or sum of money in lieu of interest, will be
     payable in respect of any accumulated and unpaid dividends which may be in
     arrears.

          (b) Dividends, to the extent declared by the Issuer's Board of
Directors may, at the option of the Issuer, be paid in cash, by delivery of
fully paid and nonassessable shares of Common Stock, or a combination thereof.
If the Issuer elects to pay dividends in shares of Common Stock, the number of
shares of Common Stock to be distributed will be calculated by dividing such
payment by 95% of the Market Value as of the Dividend Payment Record Date.

          2.2  (a)  No dividends or other distributions (other than a dividend
or distribution in Junior Securities) may be declared, made or paid or funds set
apart for payment on the Common Stock, Junior Securities or Parity Securities,
and no Common Stock, Junior Securities or any Parity Securities, including the
Preferred Stock, may be repurchased, exchanged, redeemed or otherwise acquired
for any consideration (or any money paid to or made available for a sinking fund
for the redemption of any shares of any such stock) by the Issuer (except by
conversion into or exchange for Junior Securities), nor may funds be set apart
for payment with respect thereto, unless full cumulative dividends shall have
been or contemporaneously are paid or declared and a sum sufficient for the
payment thereof is set apart for such payment on all outstanding shares of
Preferred Stock for all Dividend Payment Dates on or prior to such declaration,
payment, redemption, purchase, exchange or acquisition.

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<PAGE>
 
          (b) Notwithstanding the provisions of Section 2.2(a), whether or not
full cumulative dividends have been or will be paid in cash on the shares of the
Preferred Stock, the Issuer shall be entitled to declare and pay cash dividends
on Parity Securities and Junior Securities to the extent that

               (1) the funds for such cash dividend payments are derived,
     directly or indirectly, from the proceeds of an offering of Parity
     Securities or Junior Securities with respect to which such cash dividends
     are to be paid (or a concurrent offering of related securities), and

               (2) provided that in connection with such offering it is
     disclosed to the purchasers of such Parity Securities or Junior Securities,
     as the case may be, in an offering memorandum, prospectus, or similar
     communication, that a portion of the proceeds thereof may be used for the
     payment of cash dividends on such securities.

Notwithstanding the provisions of Section 2.2(a), whether or not full cumulative
dividends have been or will be paid in cash on the shares of the Preferred
Stock, the Issuer may repurchase, redeem or otherwise retire or set aside funds
for those purposes with respect to any Parity Securities or Junior Securities in
exchange for or out of the net proceeds of the substantially concurrent sale
(other than to a Subsidiary of the Issuer) of other Parity Securities or Junior
Securities, as the case may be, of the Issuer.

          (c) Notwithstanding the foregoing, if full dividends have not been
declared and paid or set apart on the Preferred Stock and any other Parity
Securities, dividends may be declared and paid on the Preferred Stock and such
other Parity Securities so long as the dividends are declared and paid pro rata
so that the amounts of dividends declared per share on the Preferred Stock and
such other Parity Securities will in all cases bear to each other the same ratio
that accrued and unpaid dividends per share on the shares of the Preferred Stock
and such other Parity Securities bear to each other; provided, that if such
dividends are paid in cash on the other Parity Securities, dividends will also
be paid in cash on the Preferred Stock.

          (d) (i) The Holders of shares of the Preferred Stock at the close of
business on a Dividend Payment Record Date will be entitled to receive the
dividend payment on those shares (except that Holders of shares called for
redemption 

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<PAGE>
 
on a Redemption Date between the Dividend Payment Record Date and the Dividend
Payment Date will be entitled to receive such dividend on such redemption date
as indicated in Section 5.1 hereof) on the corresponding Dividend Payment Date
notwithstanding the subsequent conversion thereof or the Issuer's default in
payment of the dividend due on that Dividend Payment Date.

          (ii) Except as provided in clause (i) of this Section 2.2(d) and in
Section 4.2, the Issuer shall make no payment or allowance for unpaid dividends,
whether or not in arrears, on converted shares or for dividends on the shares of
Common Stock issued upon conversion.

3.   Ranking

          3.1  The Preferred Stock will, with respect to dividend distributions
and distributions upon the liquidation, winding up or dissolution of the Issuer,
rank:

          (a) senior to all classes of Common Stock and to each series of
preferred stock existing on the date of this Certificate of Designation and each
other class of Capital Stock or series of preferred stock issued by the Issuer,
which is established after the date of this Certificate of Designation, the
terms of which do not expressly provide that such class or series will rank
senior to or on a parity with the Preferred Stock as to dividend distributions
and distributions upon the liquidation, winding up or dissolution of the Issuer
(collectively, with the Common Stock, referred to as the "Junior Securities");

          (b) subject to certain conditions, on a parity with any class of
Capital Stock or series of preferred stock issued by the Issuer, which is
established after the date of this Certificate of Designation by the Board of
Directors, the terms of which expressly provide that such class or series will
rank on a parity with the Preferred Stock as to dividend distributions and
distributions upon the liquidation, winding up or dissolution of the Issuer
(collectively referred to as "Parity Securities"); and

          (c) subject to certain conditions, junior to each class of Capital
Stock or series of preferred stock issued by the Issuer, which is established
after the date of this Certificate of Designation by the Board of Directors, the
terms of which expressly provide that such class or series will rank senior to
the Preferred Stock as to dividend distributions and distributions upon
liquidation, winding-up or dissolution of the Issuer (collectively referred to
as "Senior Securities").

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          3.2  Except as otherwise provided herein (including, without 
limitation, Section 8.3 hereof), the Issuer is entitled to amend its Certificate
of Incorporation to authorize one or more additional series of preferred stock,
file certificates of designation, and issue without restriction from time to
time, any series of Junior Securities, Parity Securities, or Senior Securities.

4.   Conversion

          4.1  (a)  Each Holder of Preferred Stock shall have the right, at its
option, at any time and from time to time to convert, subject to the terms and
provisions of this Article 4, any or all of such Holder's shares of Preferred
Stock.  In such case, the shares of Preferred Stock shall be converted into such
whole number of fully paid and nonassessable shares of Common Stock as is equal,
subject to Section 4.6, to:

          the product of the number of shares of Preferred Stock being so
     converted multiplied by

          the quotient of (i) the Liquidation Preference divided by (ii) the
     Conversion Price then in effect,

except that with respect to any share which shall be called for redemption such
right shall terminate at the close of business on the Redemption Date unless the
Issuer shall default in making the payment due upon redemption thereof.

          (b) The conversion right of a Holder of Preferred Stock shall be
exercised by the Holder by the surrender of the certificate representing shares
to be converted to the Issuer or to the Transfer Agent accompanied by the
Conversion Notice.

               (i) Immediately prior to the close of business on the Conversion
     Date, each converting Holder of Preferred Stock shall be deemed to be the
     Holder of record of Common Stock issuable upon conversion of such Holder's
     Preferred Stock notwithstanding that the share register of the Issuer shall
     then be closed or that certificates representing such Common Stock shall
     not then be actually delivered to such person.

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<PAGE>
 
               (ii) Upon notice from the Issuer, each Holder of Preferred Stock
     so converted shall promptly surrender to the Issuer or the Transfer Agent
     certificates representing the shares so converted (if not previously
     delivered), duly endorsed in blank or accompanied by proper instruments of
     transfer.

               (iii)  On any Conversion Date, all rights with respect to the
     shares of Preferred Stock so converted, including the rights, if any, to
     receive notices, will terminate, except the rights of Holders thereof to:
     (1) receive certificates for the number of shares of Common Stock into
     which such shares of Preferred Stock have been converted; (2) receive the
     payment in cash or shares of Common Stock of any accumulated and unpaid
     dividends accrued thereon pursuant to Section 4.2 hereof; and (3) exercise
     the rights to which they are entitled as Holders of Common Stock.

          (c) If the Conversion Date shall not be a Business Day, then such
conversion right shall be deemed exercised on the next Business Day.

          4.2  When shares of Preferred Stock are converted pursuant to this
Section 4, unless converted between a Dividend Payment Record Date and a 
Dividend Payment Date, all accumulated and unpaid dividends (whether or not in
arrears or currently payable) on the Preferred Stock so converted to (and not
including) the Conversion Date shall immediately be due and payable, at the
Issuer's option:

               (a)  in cash;

          (b) in the whole number of fully paid and nonassessable shares of
Common Stock equal to the quotient of (i) the amount of accumulated and unpaid
dividends payable to the Holders of Preferred Stock hereunder, divided by (ii)
95% of the Market Value for the period ending on the Conversion Date; or

               (c)  a combination thereof.

          4.3  The Conversion Price shall be subject to adjustment if any
Conversion Price Adjustment Event described in Section 4.3(a) occurs.  The
adjustment will be accomplished from time to time as described in Section
4.3(b).

               (a) In case the Issuer shall at any time or from time to time:

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<PAGE>
 
               (i) make a redemption payment or pay a dividend (or other
     distribution) payable in shares of Common Stock to all Holders of any class
     of Capital Stock of the Issuer (other than the issuance of shares of Common
     Stock in connection with the payment in redemption for, of dividends on, or
     the conversion of the Preferred Stock);

               (ii) make any issuance to all Holders of shares of Common Stock
     of rights, options or warrants entitling them to subscribe for or purchase
     shares of Common Stock or securities convertible into or exchangeable for
     shares of Common Stock at less than Market Value as of the date of
     conversion or exchange; provided, however, that no adjustment shall be made
     with respect to such a distribution to the extent the Holder of shares of
     Preferred Stock would be entitled to receive such rights, options or
     warrants upon conversion at any time of shares of Preferred Stock into
     Common Stock, and provided further, that if such rights, options or
     warrants are only exercisable upon the occurrence of certain triggering
     events, then the Conversion Price will not be adjusted until such
     triggering events occur;

               (iii)  any subdivision, combination or reclassification of any
     class of Common Stock;

               (iv) any distribution consisting exclusively of cash (excluding
     any cash distribution upon a merger or consolidation to which Section 4.5
     applies) to all Holders of shares of any class of Common Stock (which
     distribution is not also being made to the holders of the Preferred Stock
     based on the number of shares of Common Stock into which the Preferred
     Stock is then convertible) in an aggregate amount that, combined together
     with (1) all other such all-cash distributions made within the then-
     preceding 12-months in respect of which no adjustment has been made and (2)
     any cash and the fair market value of other consideration paid or payable
     in respect of any tender offer by the Issuer or any of its Subsidiaries for
     shares of any class of Common Stock concluded within the then-preceding 12-
     months in respect of which no adjustment has been made, exceeds 

                                       8
<PAGE>
 
     15% of the Issuer's Market Capitalization on the record date of such
     distribution;

               (v) the completion of a tender or exchange offer made by the
     Issuer or any of its Subsidiaries for shares of any class of Common Stock
     that involves an aggregate consideration that, together with (1) any cash
     and other consideration payable in a tender or exchange offer by the Issuer
     or any of its Subsidiaries for shares of any class of Common Stock expiring
     within the then-preceding 12-months in respect of which no adjustment has
     been made and (2) the aggregate amount of any such all-cash distributions
     referred to in (iv) above to all Holders of shares of any class of Common
     Stock within the then-preceding 12-months in respect of which no adjustment
     has been made, exceeds 15% of the Issuer's Market Capitalization just prior
     to the expiration of such tender offer; or

               (vi) a distribution to all Holders of any class of Common Stock
     (which distribution is not also being made to the holders of the Preferred
     Stock based on the number of shares of Common Stock into which the
     Preferred Stock is then convertible unless the Common Stock does not share
     pro rata in such distribution) consisting of evidences of indebtedness,
     shares of Capital Stock other than Common Stock of the Issuer or assets
     (including securities, but excluding those dividends, rights, options,
     warrants and distributions referred to above).

          (b) If any Conversion Price Adjustment Event occurs, the Issuer will
calculate the adjustment to the Conversion Price as follows for each specific
event.  In the following descriptions, the variables have the following
definitions:

C    equals the total number of shares of Preferred Stock outstanding at the
     time of the Conversion Price Adjustment Event;

U    equals the number of shares of Common Stock underlying rights, options, or
     warrants issued entitling the holders to subscribe for or purchase shares
     of Common Stock or securities convertible into or exchangeable for shares
     of Common Stock issued in the Conversion Price Adjustment Event;

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X    equals the total number of shares of Common Stock outstanding immediately
     prior to the Conversion Price Adjustment Event (not including unexercised
     options, warrants, or rights);

Y    equals the total number of shares of Common Stock outstanding immediately
     after the Conversion Price Adjustment Event (not including unexercised
     options, warrants, or rights);

Z    equals the total number of shares of Common Stock outstanding at the time
     of the Conversion Price Adjustment Event;

Cash equals any distribution consisting exclusively of cash (excluding any cash
     distributed upon a merger or consolidation to which Section 4.5 applies) to
     all Holders of shares of any class of Common Stock in an aggregate amount
     that, combined together with (1) all other such all-cash distributions made
     within the then-preceding 12-months in respect of which no adjustment has
     been made and (2) any cash and the fair market value of other consideration
     paid or payable in respect of any tender offer by the Issuer or any of its
     Subsidiaries for shares of any class of Common Stock concluded within the
     then-preceding 12 months in respect of which no adjustment has been made
     pursuant to Section 4.3(a)(iv);

ExP  equals the exercise or other consideration to be paid by the Holder upon
     the exercise of or conversion of "U";

MC   equals Market Capitalization;

MV   equals Market Value per share of the Common Stock as of the date of
     conversion or exchange of "U";

#Sh  equals the number of shares in the class of Common Stock receiving the
     distribution contemplated in Section 4.3(a)(vi) or subject to the tender
     offer contemplated in Section 4.3(a)(v);

TOff equals the aggregate consideration that, together with (1) any cash and
     other consideration payable in a tender or exchange offer by the Issuer or
     any of its Subsidiaries for shares of any class of Common Stock expiring
     within the then-preceding 12-months in respect of which no adjustment has
     been made and (2) the aggregate amount of any such all-cash distributions
     referred to in 

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       Section 4.3(a)(iv) to all Holders of shares of any class of Common Stock
       within the then-preceding 12-months in respect of which no adjustment has
       been made;

TOff/S equals the tender offer price, per share;

TPur   equals the number of shares purchased in the tender offer;

Value  equals the aggregate fair market value of the distribution described in
       Section 4.3(a)(vi), as determined in good faith by the Board of Directors
       of the Issuer;

CP     equals the Conversion Price immediately prior to the Conversion Price
       Adjustment Event;

ACP    equals the Conversion Price immediately after the Conversion Price 
       Adjustment Event;

               (i) In the case of an event described in Sections 4.3(a)(i) or
     4.3(a)(iii), the Conversion Price in effect immediately before such event
     shall be adjusted pursuant to the following formula: X/Y multiplied by
     CP=ACP./1/

               (ii) In the case of an event described in section 4.3(a)(ii), the
     Conversion Price in effect immediately before such event shall be adjusted
     pursuant to the following formula:  X/(X+U ((MV-ExP)/MV)) multiplied by
     CP=ACP./2/  If any options, warrants, convertible securities, or other
     rights of the nature described in Section 4.3(a)(ii) ("Rights") expire
     without exercise or conversion, the Conversion Price will be readjusted
     to the Conversion Price which 
-----------------------

/1/  For example, where X=12 million shares, and 500,000 shares are being issued
     in the Conversion Price Adjustment Event (Y=12,500,000), and CP is $32.00,
     the Adjusted Conversion Price (ACP) is $30.72.

/2/  For example, where X=12 million shares, and U=500,000 shares, MV is $40,
     ExP is $35, and CP is $32.00, the Adjusted Conversion Price (ACP) is
     $31.83.  If ExP is $0, the Adjusted Conversion Price (ACP) is $30.72.

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     would otherwise be in effect had the adjustment made upon the issuance of
     such Rights had been made on the basis of delivery of only the number of
     shares of Common Stock actually delivered upon the exercise or conversion
     of such Rights.

               (iii)  In the case of an event described in Section 4.3(a)(iv),
     the Conversion Price in effect immediately before such event shall be
     adjusted pursuant to the following formula:  CP-((Cash-15% MC)/C)=ACP./3/

     There will be no adjustment to the Conversion Price pursuant to Section
     4.3(a)(iv) if (Cash-15% MC) is less than or equal to zero.

               (iv) In the case of an event described in Section 4.3(a)(v), and
     if the tender offer price or exchange offer price per share is greater than
     Market Value, the Conversion Price in effect immediately before such event
     shall be adjusted pursuant to the follow  ing formula:  CP-((TPur
     multiplied by (TOff/S-MV))/(#Sh-TPur))=ACP./4/

     There will be no adjustment to the Conversion Price pursuant to Clause
     4.3(a)(v) if TOff/S is less than or equal to Market Value or if TPur
     multiplied by TOff/S is less than 15% of MC.

               (v) In the case of an event described in Section 4.3(a)(vi), the
     Conversion Price in effect immediately before such 


--------------------

/3/  For example, where Cash distributed equals $20,000,000, Market
     Capitalization equals $100,000,000 (15% MC=$15,000,000), CP equals $32.00
     and there are 2,000,000 shares of Preferred Stock outstanding (C), the
     Adjusted Conversion Price (ACP) is $29.50.

/4/  For example, where TOff/S is $45.00 at a time when MV is $35, CP equals
     $32.00, 1,000,000 shares were purchased in the tender offer (TPur), and
     there were 12,000,000 shares of the class outstanding (#SH), the Adjusted
     Conversion Price (ACP) is $31.09.

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     event shall be adjusted pursuant to the following formula: CP-
     (Value/#Sh)=ACP./5/

An adjustment made pursuant to this Section 4.3 shall become effective
retroactively: (x) in the case of a Conversion Price Adjustment Event described
in Section 4.3(a)(i), (ii), (iv), or (vi), immediately following the close of
business on the record date for the determination of Holders of Common Stock
entitled to participate in such event; or (y) in the case of a Conversion Price
Adjustment Event described in Section 4.3(a)(ii), the close of business on the
day upon which such corporate action becomes effective; or (z) in the case of a
Conversion Price Adjustment Event described in Section 4.3(a)(v), the close of
business on the day of the completion of such tender offer or exchange offer.

          (c) Notwithstanding anything herein to the contrary, no adjustment
under this Section 4.3 need be made to the Conversion Price unless such
adjustment would require an increase or decrease of at least 1% of the
Conversion Price then in effect.  Any lesser adjustment shall be carried forward
and shall be made at the time, if ever, of and together with the next subsequent
adjustment, which, together with any adjustment or adjustments so carried
forward, shall amount to an increase or decrease of at least 1% of such
Conversion Price.

          (d) Notwithstanding anything to the contrary contained in this
Certificate of Designation, no Conversion Price adjustment will be made as a
result of the issuance of Common Stock on conversion of the Preferred Stock.

          (e) Each event requiring adjustment to the Conversion Price shall
require only a single adjustment even though more than one of the adjustment
clauses set forth in Section 4.3(a), Section 4.4 or Section 4.5, may be
applicable to such Conversion Price Adjustment Event.

          (f) If the Issuer shall take a record of the Holders of any class of
its Capital Stock for the purpose of entitling them to receive a dividend or
other distribution which would otherwise constitute a Conversion Price
Adjustment Event, and shall thereafter and before the distribution to
stockholders thereof legally abandon its plan to pay or deliver such dividend or
distribution, then thereafter no 

------------------------

/5/  For example, where CP is $32.00, Value equals $1,500,000, and there were
     12,000,000 shares of the class outstanding (#SH), ACP is $31.88.

                                       13
<PAGE>
 
adjustment in the Conversion Price then in effect shall be required by reason of
the taking of such record.

          (g) Upon any increase or decrease in the Conversion Price, then, and
in each such case, the Issuer promptly shall deliver to each registered Holder
of Preferred Stock a certificate signed by an authorized officer of the Issuer,
setting forth in reasonable detail the event requiring the adjustment and the
method by which such adjustment was calculated and specifying the increased or
decreased Conversion Price then in effect following such adjustment.

          (h) The Issuer reserves the right to make such reductions in the
Conversion Price in addition to those required in the foregoing provisions as it
considers to be advisable  in order that any event treated for Federal income
tax purposes as a dividend of stock or stock rights will not be taxable to the
recipients. In the event the Issuer elects to make such a reduction in the
Conversion Price, the Issuer will comply with the requirements of Rule 14e-1
under the 1934 Act, and any other securities laws and regulations thereunder if
and to the extent that such laws and regulations are applicable in connection
with the reduction of the Conversion Price.

          4.4  In the event the Issuer distributes rights or warrants (other
than those referred to in Section 4.3(a)(ii)) pro rata to all Holders of shares
of any class of Common Stock, so long as any such rights or warrants have not
expired or been redeemed by the Issuer, the Holders of any Preferred Stock
surrendered for conversion will, in the discretion of the Issuer and subject to
the last paragraph of this Section 4.4, be entitled to receive upon such
conversion, in addition to the shares of Common Stock then issuable upon such
conversion (the "Conversion Shares"), a number of rights or warrants to be
determined as follows:

          (a) if such conversion occurs on or prior to the date for the
distribution to Holders of rights or warrants of separate certificates
evidencing such rights or warrants (the "Distribution Date"), the same number of
rights or warrants to which a Holder of a number of shares of Common Stock
equal to the number of Conversion Shares is entitled at the time of such
conversion in accordance with the terms and provisions applicable to the rights
or warrants, and

          (b) if such conversion occurs after such Distribution Date, the same
number of rights or warrants to which a Holder of the number of shares of Common
Stock of the Issuer into which such Preferred Stock was convertible 

                                       14
<PAGE>
 
immediately prior to such Distribution Date would have been entitled on such
Distribution Date in accordance with the terms and provisions of and applicable
to the rights or warrants.

          In the event the Holders of the Preferred Stock are not entitled to
receive such rights or warrants pursuant to Section 4.4(a) or 4.4(b), the
Conversion Price will be subject to adjustment upon any declaration or
distribution of such rights or warrants pursuant to Section 4.3, above.

          4.5  (a)  In case of:

               (i) any capital reorganization or reclassification or other
     change of outstanding shares of Common Stock (other than a change in par
     value, or from par value to no par value, or from no par value to par
     value), or

               (ii) any consolidation or merger of the Issuer with or into
     another Person (other than a consolidation or merger in which the Issuer is
     the resulting or surviving Person and which does not result in any
     reclassification or change of outstanding Common Stock), or

               (iii)  any sale, transfer or other conveyance to another Person
     of all or substantially all of the assets of the Issuer computed on a
     consolidated basis (other than the sale, transfer, assignment or
     distribution of shares of Capital Stock or assets to a Subsidiary)

(any of the events described in Section 4.5(a) being referred to in this Section
4.5 as a "Transaction"), then the adjustment described in Section 4.5(b) will be
made.

          (b) Each share of Preferred Stock then outstanding shall, without the
consent of any Holder of Preferred Stock, become convertible only into the kind
and amount of shares of stock or other securities (of the Issuer or another
issuer) or property or cash receivable upon such Transaction by a Holder of the
number of shares of Common Stock into which such share of Preferred Stock could
have been converted immediately prior to such Transaction after giving effect to
any adjustment event.

                                       15
<PAGE>
 
          (c) The provisions of this Section 4.5 and any equivalent thereof in
any such certificate similarly shall apply to successive Transactions. The
provisions of this Section 4.5 shall be the sole right of Holders of Preferred
Stock in connection with any Transaction and such Holders shall have no separate
vote thereon.

          4.6  In the case of any distribution by the Issuer to its stockholders
of substantially all of its assets, each Holder of Preferred Stock will
participate pro rata in such distribution based on the number of shares of
Common Stock into which such Holders' shares of Preferred Stock would have been
convertible immediately prior to such distribution, unless the amount of such
distribution would result in a payment less than the Liquidation Preference, in
which case the Liquidation Preference shall be paid.

          4.7  If, as a result of any Conversion Price Adjustment Event, a
Holder of the Preferred Stock becomes entitled to receive upon conversion shares
of two or more classes of Capital Stock, the Issuer shall determine the
reasonable allocation of the adjusted Conversion Price between the classes of
Capital Stock. After such allocation, the Conversion Price of each class of
Capital Stock shall thereafter be subject to adjustment on terms applicable to
the Preferred Stock in this Article 4.

          4.8  The Issuer shall at all times reserve and keep available for
issuance upon the conversion of the Preferred Stock, such number of its
authorized but unissued shares of Common Stock as will from time to time be
sufficient to permit the conversion of all outstanding shares of Preferred
Stock, and shall take all action required to increase the authorized number of
shares of Common Stock if at any time there shall be insufficient authorized
unissued  shares of Common Stock to permit such reservation or to permit the
conversion of all outstanding shares of Preferred Stock.

          4.9  The issuance or delivery of certificates for Common Stock upon
the conversion of shares of Preferred Stock shall be made without charge to the
converting Holder of shares of Preferred Stock for such certificates or for any
tax in respect of the issuance or delivery of such certificates or the
securities represented thereby, and such certificates shall be issued or
delivered in the respective names of, or in such names as may be directed by,
the Holders of the shares of Preferred Stock converted; provided, however, that
the Issuer shall not be required to pay any tax which may be payable in respect
of any transfer involved in the issuance and delivery 

                                       16
<PAGE>
 
of any such certificate in a name other than that of the Holder of the shares of
Preferred Stock converted, and the Issuer shall not be required to issue or
deliver such certificate unless or until the Person or Persons requesting the
issuance or delivery thereof shall have paid to the Issuer the amount of such
tax or shall have established to the reasonable satisfaction of the Issuer that
such tax has been paid.

5.   Optional Redemption of Preferred Stock

          5.1  (a)  Shares of the Preferred Stock will not be redeemable prior
to May 1, 2001.

          (b) On or after May 1, 2001, the Preferred Stock may be redeemed, in
whole or in part, at the option of the Issuer, in cash, by delivery of fully
paid and nonassessable shares of Common Stock or a combination thereof, upon
Redemption Notice given not less than 20 days' notice nor more than 60 days'
prior to the Redemption Date, during the 12-month periods commencing on May 1 of
the years indicated below, at the following Redemption Prices per share, plus in
each case all accumulated and unpaid dividends to the Redemption Date:
<TABLE>
<CAPTION>
 
                                                          Redemption
                                                          ----------
Year                                                    Price Per Share
----                                                    ---------------
<S>                                                     <C> 
2001...................................................    $52.00
2002...................................................    $51.50
2003...................................................    $51.00
2004...................................................    $50.50
2005 and thereafter....................................    $50.00
</TABLE>

          (c) In the event that fewer than all the outstanding shares of the
Preferred Stock are to be redeemed, the shares to be redeemed will be determined
pro rata or by lot.

          (d) If the Issuer elects to pay the Redemption Price in shares of
Common Stock, the number of shares of Common Stock to be distributed will be
calculated by dividing the aggregate Redemption Price payable to any Holder by
95% of the Market Value as of the Redemption Notice Date.

          (e) From and after the applicable Redemption Date (unless the Issuer
shall be in default of payment of the Redemption Price), dividends on the shares
of the Preferred Stock to be redeemed on such Redemption Date shall cease to

                                       17
<PAGE>
 
accumulate, such shares shall no longer be deemed to be outstanding, and all
rights of the Holders thereof as stockholders of the Issuer (except the right to
receive the Redemption Price) will cease.

          5.2 If any dividends on the Preferred Stock are in arrears, no shares
of the Preferred Stock will be redeemed unless all outstanding shares of the
Preferred Stock are simultaneously redeemed.

          5.3 In the event the Issuer shall elect to redeem shares of the
Preferred Stock pursuant to Section 5.1 hereof, the Issuer must provide the
Holders with the Redemption Notice as described in Section 5.1(b), and

          (a) (i)  On or before any Redemption Date, each Holder of shares of
Preferred Stock to be redeemed shall surrender the certificate or certificates
representing such shares of Preferred Stock (properly endorsed or assigned, or
transferred, if the Issuer shall so require and the Redemption Notice shall so
state) to the Issuer or the Redemption Agent (if appointed) in the manner and at
the place designated in the Redemption Notice.

               (ii) On the first Business Day following the Redemption Date,
     the Issuer or the Redemption Agent, as applicable, shall pay or deliver to
     the Holder whose name appears on such certificate or certificates as the
     owner thereof, the full Redemption Price due such Holder in cash, in fully
     paid and nonassessable shares of Common Stock or in a combination thereof.

               (iii) The shares represented by each certificate to be
     surrendered shall be automatically (and without any further action of the
     Issuer or the Holder) canceled as of the Redemption Date whether or not
     certificates for such shares are returned to the Issuer and returned to
     authorized but unissued shares of preferred stock of no series.

               (iv) If fewer than all the shares represented by any such
     certificate are to be redeemed, a new certificate shall be issued
     representing the unredeemed shares, without cost to the Holder, together
     with the amount of cash, if any, in lieu of fractional shares.

          (b) If  a Redemption Notice shall have been given as provided in
Section 5.1, dividends on the shares of Preferred Stock so called for redemption

                                       18
<PAGE>
 
shall cease to accrue, such shares shall no longer be deemed to be outstanding,
and all rights of the Holders thereof as stockholders of the Issuer with respect
to shares so called for redemption (except for the right to receive from the
Issuer the Redemption Price) shall cease (including any right to receive any
dividends otherwise payable on any Dividend Payment Date that would have
occurred after the Redemption Date) either (i) from and after the Redemption
Date (unless the Issuer shall default in the payment of the Redemption Price, in
which case such rights shall not terminate at the Redemption Date) or (ii) if
the Issuer shall so elect and state in the Redemption Notice, from and after the
time and date (which date shall be the Redemption Date or an earlier date not
less than 20 days after the date of mailing of the Redemption Notice) on which
the Issuer shall irrevocably deposit in trust for the Holders of the shares to
be redeemed with a designated Redemption Agent as paying agent sufficient to pay
at the office of such paying agent, on the Redemption Date, the Redemption
Price.  Any money or shares of Common Stock so deposited with such Redemption
Agent which shall not be required for such redemption shall be returned to the
Issuer forthwith.  Subject to applicable escheat laws, any moneys or shares of
Common Stock so set aside by the Issuer and unclaimed at the end of one year
from the Redemption Date shall revert to the general funds of the Issuer, after
which reversion the Holders of such shares so called for redemption shall look
only to the general funds of the Issuer for the payment of the Redemption Price
without interest. Any interest accrued on funds held by the Redemption Agent
shall be paid to the Issuer from time to time.

          (c) In the event that fewer than all the outstanding shares of the
Preferred Stock are to be redeemed, the shares to be redeemed shall be
determined pro rata or by lot, as determined by the Issuer, except that the
Issuer may redeem such shares held by any Holder of fewer than 100 shares (or
shares held by Holders who would hold fewer than 100 shares as a result of such
redemption), as may be determined by the Issuer.

6.   Change of Control

          6.1 (a)  In the event of a Change of Control, Holders shall, if the
Market Value at such time is less than the Conversion Price, have a one time
option (the "Change of Control Option"), upon not less than 30 days' notice nor
more than 60 days' notice, to convert all of their outstanding shares of
Preferred Stock into shares of Common Stock at an adjusted Conversion Price
equal to the greater of:

                                       19
<PAGE>
 
               (i) the Market Value on the date on which the Change of Control
     event occurred and

               (ii) $17.18.

          (b) In lieu of issuing the shares of Common Stock issuable upon
conversion in the event of a Change of Control, the Issuer may, at its option,
make a cash payment equal to the Market Value of such Common Stock otherwise
issuable.

          6.2 In the event of a Change of Control, notice of such Change of
Control shall be given, within five Business Days of the Change of Control Date,
by the Issuer by first-class mail to each record Holder of shares of Preferred
Stock, at such Holder's address as the same appears on the books of the Issuer.
Each such notice shall state:  (i) that a Change of Control has occurred; (ii)
the last day on which the Change of Control Option may be exercised (the
"Expiration Date"); (iii) the name and address of the paying agent; and (iv) the
procedures that Holders must follow to exercise the Change of Control Option.

          6.3 On or before the Expiration Date, each Holder of shares of
Preferred Stock wishing to exercise the Change of Control Option shall surrender
the certificate or certificates representing the shares of Preferred Stock to be
converted, in the manner and at the place designated in the notice described in
Section 6.2, and on such date the cash or shares of Common Stock due to such
Holder shall be delivered to the person whose name appears on such certificate
or certificates as the owner thereof and each surrendered certificate shall be
returned to authorized but unissued shares. Upon surrender (in accordance with
the notice described in Section 6.2 of the certificate or certificates
representing any shares to be so converted (properly endorsed or assigned for
transfer, if the Issuer shall so require and the notice shall so state), such
shares shall be converted by the Issuer at the Conversion Price as adjusted.

          6.4 The rights of Holders of Preferred Stock pursuant to this Article
6 are in addition to, and not in lieu of, the rights of holders of Preferred
Stock provided for in Article 4 hereof.

          6.5 The foregoing provisions are not waivable by the Issuer.

                                       20
<PAGE>
 
7.   Liquidation Preference

          7.1 Upon any voluntary or involuntary liquidation, dissolution or
winding up of the Issuer, Holders of the Preferred Stock will be entitled to be
paid, out of assets of the Issuer available for distribution the Liquidation
Preference per share plus an amount in cash equal to all accumulated and unpaid
dividends thereon to the date fixed for liquidation, dissolution or winding up
(including an amount equal to a prorated dividend for the period from the last
dividend payment date to the date fixed for liquidation, dissolution or winding
up), before any distribution is made on any Junior Securities, including,
without limitation, the Common Stock.

          7.2 If, upon any voluntary of involuntary liquidation, dissolution or
winding-up of the Issuer, the amounts payable with respect to the Preferred
Stock and all other Parity Securities are not paid in full, the Holders of the
Preferred Stock and the Parity Securities will share equally and ratably in any
distribution of assets of the Issuer in proportion to the full Liquidation
Preference and accumulated and unpaid dividends to which each is entitled.

          7.3 After payment of the full amount of the Liquidation Preference and
accumulated and unpaid dividends to which they are entitled, the Holders of
shares of the Preferred Stock will have no right or claim to any of the
remaining assets of the Issuer.

          7.4 Neither the sale, conveyance, exchange or transfer (for cash,
shares of stock, securities or other consideration) of all or substantially all
of the property or business of the Issuer (other than in connection with the
winding up of its business), nor the merger or consolidation of the Issuer with
or into any other corporation, will be deemed to be a dissolution, liquidation,
or winding up, voluntary or involuntary, of the Issuer.

8.   Voting Rights

          8.1 Holders of the Preferred Stock have no voting rights with respect
to general corporate matters except as provided by law or as set forth herein.

          8.2 (a) If dividends payable on the Preferred Stock are in arrears and
unpaid for six consecutive quarterly periods, the Holders of the Preferred Stock
voting separately as a class with the shares of any other preferred stock or
preference securities having similar voting rights (the "Voting Rights Class")
will be entitled at the next regular or special meeting of stockholders of the
Issuer to elect two directors of the Issuer to fill newly created directorships.

                                       21
<PAGE>
 
          (b) Such voting rights may be exercised at a special meeting of the
holders of the shares of the Voting Rights Class, called as hereinafter
provided, or at any annual meeting of stockholders held for the purpose of
electing directors, and thereafter at each such annual meeting until such time
as all dividends in arrears on the shares of Preferred Stock shall have been
paid in full, at which time or times such voting rights and the term of the
directors elected pursuant to Section 8.2(a) shall terminate.

          (c) At any time when such voting rights shall have vested in holders
of shares of the Voting Rights Class described in Section 8.2(a), a proper
officer of the Issuer may call, and, upon the written request of the record
holders of shares representing twenty-five percent (25%) of the voting power of
the shares then outstanding of the Voting Rights Class, addressed to the
Secretary of the Issuer, shall call a special meeting of the holders of shares
of the Voting Rights Class.  Such meeting shall be held at the earliest
practicable date upon the notice required for annual meetings of stockholders at
the place for holding annual meetings of stockholders of the Issuer, or, if
none, at a place designated by the Board of Directors.  Not withstanding the
provisions of this Section 8.2(c), no such special meeting shall be called
during a period within the 60 days immediately preceding the date fixed for the
next annual meeting of stockholders, in which such case the election of
directors pursuant to Section 8.2(a) shall be held at such annual meeting of
stockholders.

          (d) At any meeting held for the purpose of electing directors at which
the holders of the Voting Rights Class shall have the right to elect directors
as provided herein, the presence in person or by proxy of the holders of shares
representing more than fifty percent (50%) in voting power of the then 
outstanding shares of the Voting Rights Class shall be required and shall be
sufficient to constitute a quorum of such class for the election of directors by
such class.

          (e) Any director elected pursuant to the voting rights created under
this Section 8.2 shall hold office until the next annual meeting of stockholders
(unless such term has previously terminated pursuant to Section 8.2(b)) and any
vacancy in respect of any such director shall be filled only by vote of the
remaining director so elected by holders of the Voting Rights Class, or if there
be no such remaining director, by the holders of shares of the Voting Rights
Class at a special meeting called in accordance with the procedures set forth in
this Section 8.2, or, if no such special meeting is called, at the next annual
meeting of stockholders.  Upon any 

                                       22
<PAGE>
 
termination of such voting rights, the term of office of all directors elected
pursuant to this Section 8 shall terminate.

          8.3 The affirmative vote or consent of the Holders of at least 66-2/3%
of the outstanding Preferred Stock will be required for:

          (a) the issuance of any class of Senior Securities (or security
convertible into Senior Securities or evidencing a right to purchase any shares
or any class or series of Senior Securities), and

          (b) amendments to the Issuer's Certificate of Incorporation that would
affect adversely the rights of Holders of the Preferred Stock, including,
without limitation,

               (i) any increase in the authorized number of shares of Preferred
     Stock beyond 10,000,000 shares and

               (ii) the issuance of any shares of Preferred Stock in excess of
     the number of shares of such stock authorized in this Certificate of
     Designation as of the date of the original issuance of the Preferred
     Stock.

              (c) In all such cases each share of Preferred Stock shall be
entitled to one vote.

          8.4 Except as set forth in this Certificate of Designation, the
creation, authorization or issuance of any shares of Junior Securities or Parity
Securities or an increase or decrease in the amount of authorized Capital Stock
of any class, including any preferred stock, shall not require the consent of
the Holders of the Preferred Stock and shall not be deemed to affect adversely
the rights, preferences, privileges or voting rights of Holders of shares of the
Preferred Stock.


9.   Amendment, Supplement and Waiver

          9.1 Without the consent of any Holder of the Preferred Stock, the
Issuer may amend or supplement this Certificate of Designation to cure any
ambiguity, defect or inconsistency, to provide for uncertificated Preferred
Stock in addition to or in place of certificated Preferred Stock, to provide for
the assumption of the 

                                       23
<PAGE>
 
Issuer's obligations to Holders of the Preferred Stock in the case of a merger
or consolidation, to make any change that would provide any additional rights or
benefits to the Holders of the Preferred Stock or that does not adversely affect
the legal rights under this Certificate of Designation of any such Holder.

10.  Certain Definitions

     Set forth below are certain defined terms used in this Certificate of
Designation.

          10.1   "Affiliate" of any specified Person means any other Person
directly or indirectly controlling or controlled by or under direct or indirect
common control with such specified Person.  For purposes of this definition,
"control" (including, with correlative meanings, the terms "controlling,"
"controlled by" and "under common control with"), as used with respect to any
person, shall mean the possession, directly or indirectly, of the power to
direct or cause the direction of the management or policies of such person,
whether through the ownership of voting securities, by agreement of or
otherwise.

          10.2   "Business Day" means any day other than a Legal Holiday.

          10.3   "Capital Stock" means any and all shares, interests,
participations, rights or other equivalents (however designated) of corporate
stock or partnership or membership interests, whether common or preferred.

          10.4   "Change of Control" means:  (a) the sale, lease, transfer,
convey ance or other disposition of all or substantially all of the assets of
the Issuer to any "person" or "group" (within the meaning of Sections 13(d)(3)
and 14(d)(2) of the Exchange Act or any successor provision to either of the
foregoing, including any group acting for the purpose of acquiring, holding or
disposing of securities within the meaning of Rule 13d-5(b)(1) under the
Exchange Act) other than Existing Shareholders (except in connection with a
liquidation or dissolution of the Issuer that does not constitute a Change of
Control under clause (b) below), (b) the approval by the requisite shareholders
of the Issuer of a plan of liquidation or statutory dissolution (which shall not
be construed to include a plan or merger or consolidation) of the Issuer, unless
Existing Shareholders "beneficially own" (as defined in Rule 13d-3 under the
Exchange Act) at least the same percentage of voting power after the
consummation of such plan as before or otherwise retain the right or ability, by
voting power, to control the Person that acquire the proceeds of such
liquidation or dissolution,

                                       24
<PAGE>
 
 (c) any "person" or "group" (within a meaning of Sections 13(d)(3)
and 14(d)(2) of the Exchange Act or any successor provision to either of the
foregoing, including any group acting for the purpose of acquiring, holding or
disposing of securities within the meaning of Rule 13d-5(b)(1) under the
Exchange Act), other than Existing Shareholders, becomes the "beneficial
owner" (as so defined) of more than thirty-five percent (35%) of the total
voting power of all classes of the Voting Stock of the Issuer or a successor
and/or warrants or options to acquire such Voting Stock, calculated on a fully
diluted basis, provided that Existing Shareholders "beneficially own" (as so
defined) in the aggregate a percentage of such Voting Stock or warrants having a
lesser percentage of voting power than such other "person" or "group" and do not
have the right or ability by voting power, contract or otherwise to elect or
designate for election a majority of the Issuer's Board of Directors, or (d)
during any period of two consecutive years, individuals who at the beginning of
such period constituted the Issuer's Board of Directors (together with any new
directors whose election or appointment by such board or whose nomination for
election by the stockholders of the Issuer was approved by a vote of the
Existing Shareholders or a majority of the directors then still in office who
were either directors at the beginning of such period or whose election or
nomination for election was previously so approved) cease for any reason to
constitute a majority of the Issuer's Board of Directors then in office.
Notwithstanding clause (c) above, (i) the acquisition by a Qualified Investor of
forty-nine percent (49%) or less of the Voting Stock of the Issuer shall not
constitute a Change of Control, and (ii) a merger or consolidation that would
otherwise constitute a Change of Control hereunder shall not constitute a Change
of Control if at least ninety percent (90%) of the consideration consists of
common stock that is, or upon issuance, will be traded on a United States
national securities exchange or quoted on the Nasdaq National Market.

          10.5   "Common Stock" means the Issuer's authorized $.01 par value
Common Stock.

          10.6   The "Conversion Date" shall be the date the Issuer or the
Transfer Agent receives the Conversion Notice.

          10.7   The "Conversion Notice" is written notice from the Holder to
the Issuer stating that the Holder elects to convert all or a portion of the
shares of Preferred Stock represented by certificates delivered to the Issuer or
the Transfer Agent contemporaneously.  The Conversion Notice will specify or
include:

                                       25
<PAGE>
 
               (i) The number of shares of Preferred Stock being converted by
     the Holder,

               (ii) The name or names (with address and taxpayer identification
     number) in which a certificate or certificates for shares of Common Stock
     are to be issued,

               (iii) A written instrument or instruments of transfer in form
     reasonably satisfactory to the Issuer or the Transfer Agent, duly executed
     by the Holder or its duly authorized legal representative, or in blank, and

               (iv) Transfer tax stamps or funds thereof, if required pursuant
     to Section 4.9.

          10.8   The "Conversion Price" shall initially be $31.115, subject to
adjustments as set forth in Section 4.3.

          10.9   "Conversion Price Adjustment Events" are any of those events
specified in Section 4.3(a).

          10.10  "Deposit Account" means the account created pursuant to the
Deposit Account Agreement.

          10.11  "Deposit Account Agreement" means the Deposit Account Agreement
dated May 6, 1998 between the Company and The First National Bank of Maryland,
as deposit agent.

          10.12  "Dividend Payment Date" is as defined in Section 2.1, above.

          10.13  "Dividend Payment Record Date" is as defined in Section 2.1,
above.

          10.14  "Equity Interests" means Capital Stock and all warrants,
options or other rights to acquire Capital Stock (but excluding any debt
security that is convertible into, or exchangeable for, Capital Stock).

                                       26
<PAGE>
 
          10.15  "Exchange Act" means the Securities Exchange Act of 1934, as
amended.

          10.16  "Existing Shareholders" means Douglas G. Smith, Madison
Dearborn Capital Partners, L.P. and Allen & Company Incorporated and their
respective Affiliates at May 1, 1998.

          10.17  "Holder" means a Person in whose name shares of Capital Stock
is registered.

          10.18  "Issuer" means Omnipoint Corporation, a Delaware corporation.

          10.19  "Junior Security" is as defined in Section 3.1.

          10.20  "Legal Holiday" means a Saturday, a Sunday or a day on which
banking institutions in the City of New York or at a place payment is to be
received are authorized by law, regulation or executive order to remain closed.
If a payment date is Legal Holiday at a place of payment, payment may be made at
that place on the next succeeding day that is not a Legal Holiday, and no
interest shall accrue for the intervening period.

          10.21  "Liquidation Preference" means $1,000 per share of Preferred
Stock.

          10.22  "Market Capitalization" means the product of the then-current
Market Value times the total number of shares of Common Stock then outstanding.

          10.23  "Market Value" means, as of any date, the average of the daily
closing price for the five consecutive trading days ending on such date.  The
closing price for each day shall be the last sales price or in case no such
reported sales take place on such day, the average of the last reported bid and
asked price, in either case, on the principal national securities exchange on
which the shares of Common Stock are admitted to trading or listed, or if not
listed or admitted to trading on such exchange, the representative closing bid
price as reported by the Nasdaq National Market, or other similar organization
if the Nasdaq National Market is no longer reporting such information, or if not
so available, the fair market price as determined, in good faith, by the Board
of Directors of the Issuer.

                                       27
<PAGE>
 
          10.24  "Parity Security" is as defined in Section 3.1.

          10.25  "Person" means any individual, corporation, partnership, joint
venture, association, joint-stock issuer, interest, trust or unincorporated
organization (including any subdivision or ongoing business of any such entity
or substantially all of the assets of any such entity, subdivision or business).

          10.26  "Preferred Stock" means the Preferred Stock authorized in this
Certificate of Designation.

          10.27  "Qualified Investor" means an investor approved by the Board of
Directors of the Company, which has debt securities rated by a nationally
recognized statistical rating organization in one of its four highest generic
rating categories and either (i) is in the telecommunications industry or (ii)
engages in a business which will benefit from strategic synergies from an
investment in the Company.

          10.28  "Redemption Agent" means that Person, if any, appointed by the
Issuer to hold funds deposited by the Issuer in trust to pay to the Holders of
shares to be redeemed.

          10.29  "Redemption Date" means that certain date set forth in the
Redemption Notice on which date the redemption of the Preferred Stock is
completed.

          10.30  "Redemption Notice" means that notice to be given by the Issuer
to the Holders notifying the Holders as to the redemption, in whole or in part,
of the Preferred Stock pursuant to Article 5 hereof.  The Redemption Notice
shall include the following information:  (i)  the Redemption Date and the time
of day on such date; (ii) the total number of shares of Preferred Stock to be
redeemed and, if fewer than all the shares held by such Holder are to be
redeemed, the number of such shares to be redeemed from such Holder; (iii) the
Redemption Price (whether to be paid in cash or shares of Common Stock); (iv)
the place or places where certificates for such shares are to be surrendered for
payment of the Redemption Price and delivery of certificates representing shares
of Common Stock (if the Issuer so chooses); (v) that dividends on the shares to
be redeemed will cease to accrue on such Redemption Date unless the Issuer
defaults in the payment of the Redemption Price; and (vi) the name of any bank
or trust company, if any, performing the duties of

                                       28
<PAGE>
 
Redemption Agent. Redemption Notice may be given (i) by publication in a
newspaper of general circulation in the Borough of Manhattan, City and State of
New York (if such publication shall be required by applicable law, rule,
regulation or securities exchange requirement) or (ii) by first-class mail to
each record Holder of the shares to be redeemed, at such holder's address as the
same appears on the books of the Company.

          10.31  "Redemption Notice Date" means the date the Redemption Notice
is first mailed or delivered to any Holder.

          10.32  "Redemption Price" means that price established for redemption
of the Preferred Stock established in Section 5.1(b) hereof.

          10.33  "Senior Securities" is as defined in Section 3.1.

          10.34  "Subsidiary" means, with respect to any person, any
corporation, association or other business entity of which more than 50% of the
total voting power of shares of Capital Stock entitled (without regard to the
occurrence of any contingency) to vote in the election of directors, managers or
trustees thereof is at the time owned or controlled, directly or indirectly, by
such person or one or more of the other Subsidiaries of such person or a
combination thereof.

          10.35  The "Transfer Agent" shall be as established pursuant to
Article 11 hereof.

          10.36  "Voting Stock" means with respect to any Person, Capital Stock
of any class or kind ordinarily having the power to vote for the election of
directors, managers or other voting members of the governing body of such
Person.

11.  Transfer Agent and Registrar

     The duly appointed Transfer Agent and registrar for the Preferred Stock
shall be Marine Midland Bank.  The Issuer may, in its sole discretion, remove
the Transfer Agent in accordance with the agreement between the Issuer and the
Transfer Agent; provided that the Issuer shall appoint a successor transfer
agent who shall accept such appointment prior to the effectiveness of such
removal.

                                       29
<PAGE>
 
12.  Other Provisions

          12.1   With respect to any notice to a Holder of shares of the
Preferred Stock required to be provided hereunder, neither failure to mail such
notice, nor any defect therein or in the mailing thereof, to any particular
Holder shall affect the sufficiency of the notice or the validity of the
proceedings referred to in such notice with respect to the other Holders or
affect the legality or validity of any distribution, rights, warrant,
reclassification, consolidation, merger, conveyance, transfer, dissolution,
liquidation or winding up, or the vote upon any such action.  Any notice which
was mailed in the manner herein provided shall be conclusively presumed to have
been duly given whether or not the Holder receives the notice.

          12.2   Shares of Preferred Stock issued and reacquired will be retired
and canceled promptly after reacquisition thereof and, upon compliance with the
applicable requirements of Delaware law, have the status of authorized but
unissued shares of preferred stock of the Issuer undesignated as to series and
may with any and all other authorized but unissued shares of preferred stock of
the Issuer be designated or redesignated and issued or reissued, as the case may
be, as part of any series of preferred stock of the Issuer except that any
issuance or reissuance of shares of Preferred Stock must be in compliance with
this Certificate of Designation.

          12.3   In the Issuer's discretion, no fractional shares of Common
Stock or securities representing fractional shares of Common Stock will be
issued upon conversion, redemption, or as dividends payable in the Preferred
Stock.  Any fractional interest in a share of Common Stock resulting from
conversion, redemption, or dividend payment will be paid in cash based on the
last reported sale price of the Common Stock on the Nasdaq National Market (or
any national securities exchange or authorized quotation system on which the
Common Stock is then listed) at the close of business on the trading day next
preceding the date of conversion or such later time as the Issuer is legally and
contractually able to pay for such fractional shares.

          12.4   The shares of Preferred Stock shall be issuable in whole
shares.

          12.5   All notices periods referred to herein shall commence on the
date of the mailing of the applicable notice.

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<PAGE>
 
          IN WITNESS WHEREOF, Omnipoint Corporation caused this Certificate to
be signed and attested by this 5th day of May, 1998.


                                  OMNIPOINT CORPORATION



                                  By:  /s/ Bradley E. Sparks
                                     -------------------------------
                                  Name:  Bradley E. Sparks
                                  Title: Vice President and
                                         Chief Financial Officer
Attest:

/s/ Edwin M. Martin, Jr.
---------------------------

Name:  Edwin M. Martin, Jr.
Title: Secretary

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