<PAGE>   1
                                                                     EXHIBIT 3.1

                      RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                                  PROXIM, INC.

     The following Restated Certificate of Incorporation of Proxim, Inc. (the
"Corporation") (i) amends and restates the provisions of the Certificate of
Incorporation of Proxim, Inc. originally filed with the Secretary of State of
the State of Delaware on October 4, 1993, and (ii) supersedes the original
Certificate of Incorporation and all prior amendments and restatements thereto
in their entirety.

                                   ARTICLE I

     The name of this corporation is Proxim, Inc. (the "Corporation").

                                   ARTICLE II

     The address of the Corporation's registered office in the State of Delaware
is 1209 Orange Street, Wilmington, Delaware 19801, County of New Castle. The
name of its registered agent at such address is The Corporation Trust Company.

                                  ARTICLE III

     The nature of the business or purposes to be conducted or promoted by the
Corporation is to engage in any lawful act or activity for which corporations
may be organized under the General Corporation Law of Delaware.

                                   ARTICLE IV

     The Corporation is authorized to issue two classes of stock to be
designated, respectively, Preferred Stock, par value $.001 per share
("Preferred"), and Common Stock, par value $.001 per share ("Common"). The total
number of shares of Common that the Corporation shall have authority to issue is
25,000,000. The total number of shares of Preferred that the Corporation shall
have authority to issue is 5,000,000.

     The Corporation shall from time to time in accordance with the laws of the
State of Delaware increase the authorized amount of its Common if at any time
the number of Common shares remaining unissued and available for issuance shall
not be sufficient to permit conversion of the Preferred.

<PAGE>   2

     The Board of Directors is hereby authorized, subject to limitations
prescribed by law and the provisions of this Article IV, to provide for the
issuance of the shares of Preferred in one or more series, and by filing a
certificate pursuant to the General Corporation Law of the State of Delaware, to
establish from time to time the number of shares to be included in each such
series, and to fix the designation, powers, preferences, and rights of the
shares of each such series and the qualifications, limitations or restrictions
thereof.

     The authority of the Board with respect to each series shall include, but
not be limited to, determination of the following:

     A.   The number of shares constituting that series and the distinctive
designation of that series;

     B.   The dividend rate on the shares of that series, whether dividends
shall be cumulative, and, if so, from which date or dates, and the relative
rights of priority, if any, of payment of dividends on shares of that series;

     C.   Whether that series shall have the voting rights in addition to the
voting rights provided by law, and, if so, the terms of such voting rights;

     D.   Whether that series shall have conversion privileges, and, if so, the
terms and conditions of such privileges, including provision for adjustment of
the conversion rate in such events as the Board of Directors shall determine;

     E.   Whether or not the shares of that series shall be redeemable, and, if
so, the terms and conditions of such redemption, including the date or dates
upon or after which they shall be redeemable, and the amount per share payable
on case of redemption, which amount may vary under different conditions and at
different redemption rates;

     F.   Whether that series shall have a sinking fund for the redemption or
purchase of shares of that series, and, if so, the terms in the amount of such
sinking funds;

     G.   The rights of the shares of that series in the event of voluntary or
involuntary liquidation, dissolution or winding up of the Corporation, and the
relative rights of priority, of any, of payment of shares of that series; and

     H.   Any other relative rights, preferences and limitations of that series.

                                   ARTICLE V

     The Corporation is to have perpetual existence.

                                       2

<PAGE>   3

                                   ARTICLE VI

     For the management of the business and for the conduct of the affairs of
the Corporation, and in further definition, limitation and regulation of the
powers of the Corporation, of its directors and of its stockholders or any class
thereof, as the case may be, it is further provided that:

     A.   The management of the business and the conduct of the affairs of the
Corporation shall be vested in its Board of Directors. The number of directors
which shall constitute the whole Board of Directors shall be fixed exclusively
by one or more resolutions adopted from time to time by the Board of Directors.

     The number of directors which constitute the whole Board of Directors of
the corporation shall be designated in the Bylaws of the corporation. Each
director shall serve until his or her successor is duly elected and qualified or
until his or her death, resignation, or removal. No decrease in the number of
directors constituting the Board of Directors shall shorten the term of any
incumbent director.

     Any vacancies on the Board of Directors resulting from death, resignation,
disqualification, removal, or other causes shall be filled by either (i) the
affirmative vote of the holders of a majority of the voting power of the
then-outstanding shares of voting stock of the corporation entitled to vote
generally in the election of directors (the "Voting Stock") voting together as a
single class; or (ii) by the affirmative vote of a majority of the remaining
directors then in office, even though less than a quorum of the Board of
Directors, in accordance with the Bylaws of the Corporation. Newly created
directorships resulting from any increase in the number of directors shall,
unless the Board of Directors determines by resolution that any such newly
created directorship shall be filled by the stockholders, be filled only by the
affirmative vote of a majority of the directors then in office, even though less
than a quorum of the Board of Directors, in accordance with the Bylaws of the
Corporation.

     B.   In furtherance and not in limitation of the powers conferred by
statute, the Board of Directors is expressly authorized to make, alter, amend,
or repeal the Bylaws of the Corporation.

     C.   The directors of the Corporation need not be elected by written ballot
unless a stockholder demands election by written ballot at the meeting and
before voting begins, or unless the Bylaws so provide.

     D.   No action shall be taken by the stockholders of the Corporation except
(i) at an annual or special meeting of the stockholders called in accordance
with the Bylaws, or (ii) by written consent without meeting made in accordance
with the Bylaws.

     E.   Advance notice of stockholder nomination for the election of directors
and of business to be brought by stockholders before any meeting of the
stockholders of the Corporation shall be given in the manner provided in the
Bylaws of the Corporation.

     F.   Any director, or the entire Board of Directors, may be removed from
office at any time (i) with cause by the affirmative vote of the holders of at
least a majority of the voting power of

                                       3

<PAGE>   4


all of the then-outstanding shares of the Voting Stock, voting together as a
single class; or (ii) without cause by the affirmative vote of the holders of at
least sixty-six and two-thirds percent (66-2/3%) of the voting power of all of
the then-outstanding shares of the Voting Stock.

                                   ARTICLE VII

     Notwithstanding any other provisions of this Restated Certificate of
Incorporation or any provision of law, in addition to an affirmative vote of the
holders of any particular class or series of the Voting Stock required by law,
the affirmative vote of the holders of at least sixty-six and two-thirds percent
(66-2/3 %) of the voting power of all of the then-outstanding shares of the
Voting Stock, voting together as a single class, shall be required to alter,
amend or repeal Article VI or Article VIII of this Restated Certificate of
Incorporation.

                                  ARTICLE VIII

     The Corporation reserves the right to amend, alter, change, or repeal any
provision contained in this Restated Certificate of Incorporation, in the manner
now or hereafter prescribed by statute, except as provided in Article VII of
this Restated Certificate, and all rights conferred upon the stockholders herein
are granted subject to this right.

                                   ARTICLE IX

     A.   To the fullest extent permitted by the Delaware General Corporation
Law as the same exists or as may hereafter be amended, a director of the
Corporation shall not be personally liable to the Corporation or its
stockholders for monetary damages for breach of fiduciary duty as a director.

     B.   The Corporation may indemnify to the fullest extent permitted by law
any person made or threatened to be made a party to an action or proceeding,
whether criminal, civil, administrative or investigative, by reason of the fact
that he, his testator or intestate is or was a director, officer or employee of
the Corporation or any predecessor of the Corporation or serves or served at any
other enterprise as a director, officer or employee at the request of the
corporation or any predecessor to the Corporation.

     C.   Neither any amendment nor repeal of this Article IX, nor the adoption
of any provision of the Corporation's Certificate of Incorporation inconsistent
with this Article IX, shall eliminate or reduce the effect of this Article IX,
in respect of any matter occurring, or any action or proceeding accruing or
arising or that, but for this Article IX, would accrue or arise, prior to such
amendment, repeal, or adoption of an inconsistent provision.

                                       4

<PAGE>   5

                                    ARTICLE X

     Meetings of stockholders may be held within or without the State of
Delaware, as the Bylaws may provide. The books of the Corporation may be kept
(subject to any provision contained in the statutes) outside of the State of
Delaware at such place or places as may be designated from time to time by the
Board of Directors or in the Bylaws of the Corporation.

     The Restated Certificate of Incorporation has been duly adopted by the
stockholders of the Corporation in accordance with the provisions of Sections
242 and 245 of the General Corporation Law of the State of Delaware, as amended.

     IN WITNESS WHEREOF, the undersigned have executed this certificate on
December 21, 1993.


                                       /s/ DAVID C. KING
                                       ----------------------------------------
                                       David C. King, President


                                       /s/ RICHARD C. DEGOLIA
                                       ----------------------------------------
                                       Richard C. DeGolia, Secretary


                                       5

<PAGE>   6

     The undersigned hereby certify under penalty of perjury that they have read
the foregoing Restated Certificate of Incorporation and know the contents
thereof, and that the statements therein are true.

     Executed at Palo Alto, California on December 21, 1993.


                                       /s/ DAVID C. KING
                                       ----------------------------------------
                                       David C. King, President


                                       /s/ RICHARD C. DEGOLIA
                                       ----------------------------------------
                                       Richard C. DeGolia, Secretary


                                       6