Fund DevelopmentThis chapter will present the basics of fundra.docx

Fund Development
This chapter will present the basics of fundraising, including
the annual campaign, direct mail, special events, major gifts,
and planned gifts. The concept of moving donors from annual
giving to major gifts and planned gifts will be presented. This
chapter will also explore donor motivation and present a
fundraising strategy based on the concept of providing donors
with opportunities rather than approaching fundraising as a
“begging” activity. Begging is not a strategy to raise funds. The
alternative to begging for funds is to have a well-developed
fundraising program. Even if the organization employs a
professional fundraiser, the administrator is still the chief
fundraising officer and, as such, will develop professional
fundraising skills or risk becoming the chief beggar for the
organization. Securing resources for the organization is
ultimately the responsibility of the board of directors, but it is
the administrator’s responsibility to develop and oversee a well-
developed fundraising program. Effective fundraisers work from
a strategic fundraising plan that is long term, has specific goals,
and uses a variety of fundraising methods and techniques. The
organization’s financial strength can be developed and
maintained only through a fundraising strategy that is
diversified by using many different fundraising approaches
appropriate for their various categories of donors. Fundraising
must be approached as any other major project in that it requires
the administrator to develop a plan. The planning process for
fundraising includes the same steps as any other planning
process. As the administrator, you must set goals, allocate
resources, develop action steps and timelines. and then evaluate
the process. There are many “truisms” in fundraising, but the
one most important to remember is that “people give to people,
not to organizations.” This is another way to say that
fundraising is really “friend-raising.” The people that will give

money to your organization are those who share a passion for
the mission of the organization and who trust that their money
will be used wisely. It is the responsibility of the administrator
to develop and nurture relationships that will financially sustain
the organization. Another truism is that people will not give
anything to meet your agency needs, but they will give when
presented with the opportunity to invest in an organization that
will make a difference in the lives of others. People will give
when they think they can make a positive difference in
something they care about. At whatever level of fundraising
activity, your approach should be to present opportunities that
will make a positive impact in the lives of the people your
organization serves and not to present the “needs” of the
agency.
11Fund Development
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May not be reproduced in any form without permission from the
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and Skills
124 LEADERSHIP SKILLS
Remember that people want to give to successful causes. You
want to give the donor not only the opportunity to give but also
a reason to contribute to a cause that will support success. Your
appeal is not that your organization has great needs, but that it
is successful in meeting the needs of your clients. Before we
explore the many levels of activities in a fundraising program,
we will look at the factors that motivate people to give.
DONOR MOTIVATION
Why do people give? Often, you will hear that most people give
a donation because they will get a tax break. It is very seldom
that tax donations are the major reason for making a donation.

You may need funds to hire a new counselor, but the
fundraising approach should be to secure funds to serve more
clients. You must tell the potential donor why the clients need
this service and what difference it will make in their lives if the
services are provided. The approach should NOT be that your
organization needs a new counselor.
A new executive director was excited to learn that an elderly
couple had decided to leave their 1,000-acre ranch to the
organization in their will. The executive went to visit the couple
and raised the possibility that they could use a planned giving
vehicle to go ahead and make their gift to the agency and at the
same time enjoy a tremendous tax advantage, plus increase their
income for the rest of their lives. In fact, through this gift, the
couple could be rich. After listening politely, the elderly woman
said, “Young man, I don’t want to be rich. I want to go to our
ranch and hunt birds!” It is important to know what motivates a
donor. In this case, it was certainly not a tax break or more
income.
So why do people give? In a review of over 500 articles on
charitable giving, Bekkers and Wiepking (2011) found eight
mechanisms as the most important forces that determine a
person’s decision to give. These are (1) awareness of need, (2)
solicitation, (3) costs and benefits, (4) altruism, (5) reputation,
(6) psychological benefits, (7) values, and (8) efficacy. People
will give only when they are interested and involved in your
cause. Of course, there are different levels of giving. The new
donor, responding to a direct mail piece, will be very different
from a board member donor with years of experience with the
organization. People will respond to different kinds of appeals
because they have different reasons. So, why do they give?
Giving behavior is just as complex as any other behavior. In his
book Tested Ways to Successful Fund Raising, George A.
Brakeley, Jr. (as cited in “8 Rules of Thumb,” 2012) wrote that
virtually every fundraising campaign and development program
depends on nine factors in motivating donors to support their
organization:

1. The right person or persons ask them, at the right time, and in
the right circumstances. 2. People have a sincere desire to help
other people.
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Fund Development 125
Whatever their other motivations, people will give only when
they are interested and involved, and when they are asked. To
determine how to ask for a gift, we must know where our donors
fit on the “donor pyramid.”
THE DONOR PYRAMID
Fundraising professionals often use the donor pyramid as a way
to conceptualize the fundraising program (see Figure 11.1).
Each level in the pyramid builds on the level beneath it. For
example, direct mail solicitation is appropriate to attract new
donors to your organization, but once they have responded with
even a small gift, your goal is to move them up to the next level
of the pyramid. You want your new direct mail donors to
become major givers. Of course, some donors will always be
small givers or even stop giving to your organization, but most
of your future major gift donors of tomorrow are your small gift
givers today. Also, remember that all those small gifts add up
and are very important to your overall fundraising plan. The
Association of Fundraising Professionals (AFP) Fundraising
Dictionary (2004) describes the donor pyramid as:
A diagrammatic description of the hierarchy of donors by size
of gifts. The diagram reflects that: as the size of donations
increases, the number of donations decreases; as the number of
years a donor is asked to renew increases, the number of donors

decreases; as campaign sophistication progresses from annual
giving to planned giving, the number of donors decreases; as
donor involvement increases, the size of the donor’s
contribution increases and the response to campaign
sophistication increases.
As you work through this chapter, refer back to the donor
pyramid. In a sophisticated fundraising program, donors will be
treated differently depending on where they are on the donor
pyramid. Donors will move up the donor pyramid through
involvement with the organization and through receiving
personal attention from the board and staff of the organization.
Notice that, as you move up in the pyramid, the fundraising
techniques become increasingly more personalized. What seems
to be a simple and obvious truism is, “No one gives at any level
unless they are asked!” As uncomfortable as it may be at times,
eventually someone has to ask for the gift, but, if you and your
board believe in your mission and truly believe you are giving
others the opportunity to participate in your important work,
then the “ask” will be less difficult.
Annual Campaign
The annual campaign consists of the fundraising activities that
are conducted for the purpose of supporting the organization’s
annual operating budget. Even though these funds will be used
for the organization’s operating budget, your approach will
focus on the services to be provided, not on the need for things
like staff raises or paying the electric bill. The operating
expenses support the services your organization provides. Ask
your donors to help serve your clients. Generally, the largest
number of donors will be giving to the annual campaign. Some
organizations may not think of their many and diverse
fundraising activities as an “annual campaign,” but whether it is
thought of in these terms or not, it is in effect the annual
campaign for the organization. The approaches used in the
annual campaign may include direct mail, phonathons, or
special events such as golf tournaments or galas. The defining
feature of annual fund activities is that they are activities

intended to raise gift income, every year. It is expected that you
will approach the same donors every year and, sometimes,
several times within the same year. Funds donated to the annual
campaign are intended to support operational costs such as
salaries, supplies, utilities, and client needs. The purpose is to
support any part of the organization’s operation that requires
continuous and regular support. Most donors will come into
your organization through the annual campaign. It is rare that a
person’s first gift to the organization will be a major gift. More
likely, those who become major donors are those who have been
consistent annual campaign donors.
Direct Mail
You probably know about direct mail fundraising from your
personal experience. Direct bulk mail is used to ask millions of
people for money, and most people receive solicitations in their
mail on a regular basis. What rate of return should you expect
for your direct mail campaign? Typically, the response is
somewhere in the range of 1%. Even though the return is small,
it is an economical way to get your message before thousands of
potential donors and a key strategy in bringing new people into
the bottom of your pyramid. The typical direct mail package
includes the carrier (outside), the letter, a reply device, and a
return envelope. The carrier or outside envelope should be
designed with one objective in mind: to get the recipient to open
it. If the piece goes into the trash, your chance of getting a
donation is zero. The goal is to make the pieces look as much as
possible like a personal letter and to make it look different from
other solicitations in the mail box that day. Ideally, the
envelope could be hand addressed, but since direct mail is a
strategy of large numbers, this is rarely possible. Pre-cancelled
bulk mail stamps give a more personal look than the standard
postal indicia used on most bulk mail. The other strategy is to
use an envelope other than the standard “number 10” business
envelope that many fundraisers refer to as “the number 10
ugly.” Choose an envelope that is smaller, larger, or a different
shape. You may also want to consider using color or a see-

through window to peak your potential donor’s interest. Once
you get the potential donors to open the letter, your task is to
capture their attention long enough to consider making a gift to
your cause. The task here is not to write a scholarly piece or to
impress anyone with your vocabulary. The letter should strike
an informal tone and be easy to read and understand. Kim Klein
(2000) proposes a set of principles to remember as you develop
your letter:
1. People have a very short attention span. Sentences should be
short and take no more than six to fifteen seconds to read.
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and Skills
2. People love to read about themselves. The letter should refer
to the reader at least twice as often and up to four times as often
as it refers to the organization sending it. For example, “You
may have read . . . ” or “If you are like me, you care deeply
about . . . ” 3. People must find the letter easy to look at. The
page should contain a lot of white space and wide margins, and
be in a clear and simple font. Paragraphs should be short, no
more than two or three sentences. You should feel free to use
contractions (won’t, you’re, can’t, we’re) as this will add a
more informal tone to your letter. 4. People read the letter in a
certain order. First, they read the salutation and the opening
paragraph, but then, no matter how long the letter is, they read
the closing paragraph and then the postscript. Only a small
number of people will read the entire letter.
The opening paragraph of your letter is critical. It must capture
the attention of your readers and make them want to read on.

Remember the truism that people will not give anything to meet
your agency needs, but they will give when they have an
opportunity to invest in a service that is of interest to them.
Your letter must be about the people you serve, not the needs of
your organization. Also, people do not relate well when you talk
about the thousands of people you serve. Your letter should tell
the story of one person helped by your organization and how
this potential donor can make a difference in the life of
someone else. How long the letter should be is always a debate.
Our natural instincts tell us that the letter should be short and to
the point, but many fundraising consultants counsel that long
letters are better and claim that a two-page letter will get a
better response than a one-page letter, and that even three- and
four-page letters will often outperform a shorter letter. There
are many theories about why you should consider writing a
longer letter. Some will say that it gives the impression that
your organization has a lot to say, while others believe that
more pieces of paper and longer letters give an opportunity for
the potential donor to feel more involved with your
organization. In the closing paragraph, you ask for the money.
Tell the reader what you want them to do. They have read your
letter, now what do you want them to do about it? For example,
say, “Send your gift of $25, $50 or $100 today.” It needs to be
direct and specific. No one gives unless they are asked. The
postscript is that small P.S. at the end of the letter. The reader
will read the P.S. if they do not read anything else in the letter.
This is your final opportunity to ask for the gift. Examples are,
“ Send your check today” or “Johnny needs your help.” Finally,
the reply device is a small card that gives the potential donor
the opportunity to respond. It will typically have a box to check
that says something like, “Yes! I’ll help” and then gives several
options of giving—$10, $25, $50, $100, or more. The donor
completes the card, encloses the check, and returns it in the
enclosed return envelope. With that, your campaign is a
success—at least with this donor. Special events are limited
only by your imagination. The events may be galas, golf

tournaments, walk-a-thons, performances—the possibilities are
endless. Many times, special events do not raise large sums of
money for the first few years but, over time, grow into major
events that raise large amounts of money. When planning a
special event, there are considerations other than the amount of
money to be raised. The special event may be the activity that
will raise the visibility of your organization in the community
and an opportunity to involve more volunteers in your work.
Special events are by their nature very labor intensive and can
take a great deal of your time and staff time. Before deciding on
a special event, it is important to consider the volunteer and
staff resources necessary for a successful event. Any special
event will require a major investment of time in planning,
marketing, and execution.
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130 LEADERSHIP SKILLS
Major Gifts
Major gifts are the larger gifts that you will solicit for your
cause. These gifts will typically come from those individuals,
foundations, and corporations with whom you have developed a
long-term ongoing relationship. Many times, major gifts are
solicited within the framework of a “capital campaign” for the
purpose of capital improvement, such as building a new
building or, in some cases, to develop or strengthen the
endowment of an organization. An organization will often
contract with a consulting firm to conduct a capital campaign.
You, your board, and your staff will still have to solicit the
gifts, but a good consultant can help structure and focus a

successful campaign. Major gifts require personal solicitation
and the preparation of a proposal. A foundation may require a
fully developed proposal, but an individual donor may prefer a
short, well-developed statement of the purpose of the proposed
donation. These donors are higher on the “pyramid” and, in
most cases, know about your organization, believe in your work,
and are willing to make a major contribution. When seeking a
foundation or corporate gift, it is important to research the
previous gifts and areas of interest of the foundation or
corporation. As in all fundraising, finding a personal connection
between your organization and the foundation or corporation is
a great asset in your attempt to secure a gift.
Planned Gifts
Planned giving is a complex area. The bequest is the simplest
form of planned giving. This means that someone has named
your organization in a will and that, on passing away, a portion
or sometimes all of that person’s estate will come to your
organization. As the administrator, you have an awesome
responsibility to see that a person’s life work is used for the
intended purposes. Other planned giving arrangements include
charitable gift annuities, revocable and non-revocable trusts,
and other financial vehicles to transfer funds from the donor to
the organization. These gifts have tax implications for the donor
and are in many cases a part of the estate planning process. Any
gift of this type will involve an attorney or certified public
accountant. The role of the administrator is to see that the
organization has the structure and the advisors necessary to
accept gifts of this nature.
Say Thank You!
It is impossible to say thank you too much to your donors. The
acknowledgement or “thank you” is a vital part of your
fundraising system. Donors should be thanked in writing as
quickly as possible for their gift, and, whenever possible,
donors should be thanked with a telephone call. For large
donations, you as the administrator or your board chairman
should make a phone call or a visit to thank donors for their

gifts. Since successful fundraising is based on relationships, it
is important to nurture and sustain relationships by showing
gratitude to those who invest in the mission of your
organization.
SUMMARY
Effective fundraisers work from a strategic fundraising plan that
is long term, has specific goals, and uses a variety of
fundraising methods and techniques. The organization’s
financial strength can be developed and maintained only
through a fundraising strategy that is diversified by using many
different fundraising approaches appropriate for their various
categories of donors. Fundraising must be approached as any
other major project in that it requires the
copyright law.
and Skills
Administrator to set goals, allocate resources, develop action
steps and timelines, and then evaluate the process.
Helpful Terms:
Annual campaign—the fundraising activities that are conducted
for the purpose of supporting the organization’s annual
operating budget.
Direct mail—a fundraising approach using bulk mail to reach
potential donors. The typical direct mail package includes the
carrier (outside), the letter, a reply device, and a return
envelope.
Donor pyramid—a diagrammatic description of the hierarchy of
donors by size of gifts. The diagram reflects that: as the size of
donations increases, the number of donations decreases; as the

number of years a donor is asked to renew increases, the number
of donors decreases; as campaign sophistication progresses from
annual giving to planned giving, the number of donors
decreases; as donor involvement increases, the size of the
donor’s contribution increases, and the response to campaign
sophistication increases.
Major gifts—the larger gifts that typically come from
individuals, foundations, and corporations with whom the
organization has developed a long-term, ongoing relationship.
Some major gifts are solicited within the framework of a
“capital campaign” for the purpose of capital improvement,
such as building a new building or, in some cases, to develop or
strengthen the endowment of an organization.
Planned gifts—The bequest is the simplest form of planned
giving. Other planned giving arrangements include charitable
gift annuities, revocable and non-revocable trusts, and other
financial vehicles to transfer funds from the donor to the
organization. These gifts have tax implications for the donor
and are, in many cases, a part of their estate planning process.
Special events—events such as galas, golf tournaments, walk-a-
thons, performances, and so on; very labor-intensive activities
that have the advantage of increased volunteer participation and
the opportunity to increase the visibility of the sponsoring
organization.
REFERENCES
Bekkers, R., & Wiepking, P. (2011). A literature review of
empirical studies of philanthropy: Eight mechanisms that drive
charitable giving. Nonprofit and Voluntary Sector Quarterly,
40(5), 924–973. 8 rules of thumb when soliciting prospects.
(2012, May 23). The NonProfit Times. Retrieved from
http://www.thenonprofittimes.com/management-tips/8-rules-of-
thumb-when-soliciting-prospects Hoffman, M. (2011).
Americans give $241 billion to charity in 2003. Foundation for
the Carolinas. Retrieved from
http://fftc.pgdc.com/pgdc/americans-give-241-billion-charity-
2003 Klein, K. (2000) Fundraising for social change (4th ed.).

Oakland, CA: Chardon Press.
Generalized Semi-Orthogonal Multiple-Access for
Massive MIMO
Majid Nasiri Khormuji
Huawei Technologies Sweden AB, Stockholm
Emails: [email protected]
Abstract—We propose a novel framework to enable concurrent
transmission of multiple users to an access node equipped with
a
massive multiple-input multiple-output (mMIMO), which
encom-
passes and extends the conventional time-division duplex
(TDD)
protocol and the recently proposed semi-orthogonal multiple-
access (SOMA). The new solution is referred to generalized
semi-
orthogonal multiple-access (GSOMA). To enable GSOMA, the
users are grouped such that the users within each group are
assigned mutually orthogonal pilot sequences. However the
pilot
sequences can be reused in different groups and the users in
different group are coordinated such that their pilot sequences
do not interfere by a semi-orthogonal mechanism enabled by a
resource-offset sequence. We describe the general framework
and
analyze a case of GSOMA and show that a properly designed
GSOMA can outperform the conventional TDD and SOMA.
I. INTRODUCTION TO MMIMO

Massive multiple-input multiple-output (mMIMO) commu-
nication is considered as one of promising physical-layer
solutions to enable multi-user communication for future com-
munications systems [1]–[4] in response to ever-increased
demand for high data rate applications as well as to a more
homogenous quality-of-service across the service area. Time-
division duplex (TDD) protocol in which the uplink pilot
symbols are used to estimate both uplink and downlink is
proposed to cope with the pilot overhead for mMIMO arrays.
In TDD protocol [1]–[4], the transmission time over each
coherence time is divided into four non-overlapping phases:
Channel training to learn the channel between the users and the
base station, each user transmits some known pilot symbols;
Uplink Data: the uplink data of all users are transmitted
over the same time–frequency resources in a non-orthogonal
fashion such that the base station receives a superposition of
all transmitted symbols; Processing Time: the time which is
needed to perform the channel estimation and precode the
users data for the downlink transmission; and Downlink Data:
finally the downlink data of all users are precoded using
the estimated channels and transmitted over the same time–
frequency resources in a non-orthogonal fashion. The duration
of uplink and downlink transmissions may vary and can be
adjusted based on the amount of the users’ data and the traffic
demands.
In this paper, we investigate the communication of K single-
antenna users to a common receiver with a massive antenna
array over an uplink shared channel. To estimate the channel
between two antenna ports, the transmitting node sends pilot
symbols which are known at the receive node (the time–
frequency location and the associated value are generally
preset). The pilot symbols from each user should have the
periodicity of N = TcBc symbols in order to track the channel
variation over the time and frequency where Tc and Bc denote

the coherence time and bandwidth, respectively. It is desirable
to coordinate as many users as possible for uplink transmission
such that the receiver can perform spatial-division multiple-
access (SDMA); i.e. the receiver is able to obtain interference-
free signals associated to each user via spatial filtering (e.g.
projection of the received signals in the space that is spanned
by the associated channels from the users to the antenna
array). In mMIMO, the receiver can asymptotically separate
the uplink data of different users without inter-user interfer-
ence if the spatial channels are for example independent [1].
Hence ignoring the processing time, the maximum number
of the coordinated users, under successful decoding, can be
obtained by maximizing the total number of transmitted data
symbols that are separable at the receiver, which is given by
K(BcTc − K), where the maximum is taken over the active
number of users, K, for a given coherence interval spanning N
symbols. Under assumption that all data symbols contain equal
information; i.e. all users employ the same modulation order,
this concludes that the coherence interval should be equally
divided between the channel training and data transmission
as considered in [1]. So the optimal number of active users
operating over the same time–frequency resources should be
set to
⌊
1
2
N
⌋
and the total number of data symbols that can be
transmitted hence becomes
⌊
1
2

N
⌋
·
⌈
1
2
N
⌉
symbols.
In [5], it is shown that the above number of users and the
associated aggregate rate can be improved by the so-called a
semi-orthogonal feature. In this paper, we further extend this
concept and present a generalized one which can bridge both
SOMA and the conventional TDD [1] and provide an enhanced
aggregate throughput.
The remainder of the paper is organized as follows.
Section II briefly reviews semi-orthogonal multiple-access
(SOMA) described in [5]. Section III generalizes SOMA
scheme to enhance its potential performance. Section IV
discusses two realizations of GSOMA and presents an iterative
receiver. This section also analyzes the sum-rate for two
modes of GSOMA using matched filtering (MF) and zero-
forcing (ZF) receiver. Section V presents numerical results
and Section VI finally concludes the paper.
978-1-4799-8088-8/15/$31.00 ©2015 IEEE
User 1
User 2

User K
Pilot symbol
Baseline UL data symbol
NEW UL data symbol
Blank symbol
... ...
Channel Training
UL Data
... ...
... ...
Coherence Interval
... ...
... ...
...
User K+1
User K+2
User N-1
NEW UL data symbol

of NEW users
Fig. 1. Illustration of Semi-Orthogonal Multiple-Access
(SOMA) transmission.
II. SOMA
We next briefly discuss the semi-orthogonal multiple-access
in [5] which is designed to address the uplink capacity shortage
problem in mMIMO. SOMA coordinates up to K ≤ N − 1
users, where N = TcBc is the number of resources in time and
frequency over which the channel is approximately constant,
i.e. the coherence interval. Fig. 1 depicts an example of how
the uplink transmission is configured in which K = N − 1
users are scheduled. Over each coherence block, the user
1 ≤ j ≤ N − 1, transmits one pilot symbol and N − j data
symbols such that the pilot symbols of users are transmit-
ted over orthogonal time–frequency resources, and the data
symbols of user j, for all 1 ≤ j ≤ N − 1, consume all the
time–frequency resources of users j + 1 ≤ k ≤ N −1, which
are used for both pilot and data transmission. The received
signals at the access node in a coherence window is illustrated
in Fig. 1. In a given time-slot, some of the users are silent
and appears orthogonal while some other users transmit non-
orthogonally. For example, in time slot one, only user one
transmits its pilot and all other users appear orthogonal and
in the second time slot the first user transmits its data symbol
and second user transmits its pilot symbol and so forth; cf.
semi-orthogonal feature. SOMA when used with an access
node with a very high number of antennas can schedule K
users where user k can transmit N − k asymptotically error-
free symbols. Therefore, for very large antenna arrays, SOMA
solution nearly doubles the throughput as compared to the
baseline TDD with optimal number of users. The receiver is
constructed using a sequential channel estimation and data
detection enabled by the designed semi-orthogonal feature

embedded in the transmitted signals.
III. GENERALIZED SOMA
We next present the generalized SOMA (GSOMA). Fig. 2
depicts multi-user GSOMA transmission in which the users
are grouped into J groups where each group contains kj
users for j ∈ {1, 2, . . . , J} and K =
∑J
j=1 kj is the total
number of the users. The user i in group j uses the pilot
sequences si for all j ∈ {1, 2, . . . , J}. That is the pilot
sequences are reused. The pilot sequences within each group
are orthogonal such that it allows interference-free channel
estimation for the users in each group. The maximum number
of pilot sequences therefore is maxj kj . The conventional
reuse of pilot sequences where the pilot symbols interference
with one another results to “pilot contaminations” which
severely degrades the performance of the users. However with
this new solution, it is allowed to reuse the pilot sequences
in a controlled fashion. A pilot reuse is performed semi-
orthogonally to boost the spectral efficiency of the system.
However, the interference is controlled by a transmission of
a resource-offset (e.g. timing-offset or frequency-offset) such
that the received packets at the access node have the following
structure
• The pilot signals of different groups are received non-
orthogonally (for example non-overlapping time slots
with timing-offset)
• The pilot sequences of the group j ∈ {1, 2, . . . , J}, are
only interfered by data symbols of users in the groups
1 to j − 1. The pilot sequences of the first group are

received interference-free. That is the other users appear
silent at the receiver side.
With GSOMA, the user may use partial blanking which has
the same granularity as the length of pilot region to control
to the inter-group interference. GSOMA includes both SOMA
scheme described in [5] and the conventional TDD solution
proposed by Marzetta in [1] as special cases. When each group
contains one user and no blanking is used, GSOMA reduces to
SOMA. When there is only one group with maximum number
of users, then GSOMA reduces to the conventional TDD
wherein only orthogonal pilot sequences are used. Therefore,
a properly designed GSOMA can combine the advantages
of both SOMA and conventional TDD. The advantage of
GSOMA with respect to the conventional TDD is that it sched-
ules more groups, which enhances the aggregate rate. Since
DataPilot 1 Pilot 1 DataPilot 1 Data Pilot 1 DataPilot 1 Data
Pilot 1 Data
DataPilot 1 Pilot 1 DataPilot 1 Data Pilot 1 DataPilot 1 Data
Pilot 1 Data
Pilot 1 Data Pilot 1 DataPilot 1 Data Pilot 1 Data
Pilot 1 Data Pilot 1 DataU
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s
e
(i
.e
.
n
o
n
o
rt
h
o
g
o
n
a
l

p
il
o
t
s
e
q
u
e
n
c
e
s
)
Group 1: users with orthogonal pilot sequences
Resource (Time/Frequency)
2
r
1L
r
1L
r

L
r
..
.
3
r
Resource-offset between group1 and group 2
1
r
.
.
.
.
.
.
.
.
.
Group 2
Group J-1
Group J

Controller
Resource-Offset Sequence
Pilot Sequence Index
Access Node
Blanking Pattern
Channel Estimation Uplink data and pilot signals over
shared channels
Spatial FilteringDetection
D
M
U
X
Blank
Blank
Blank
� �
�
�
�
Users

Fig. 2. Generalized Semi-Orthogonal Multiple-Access
(GSOMA) transmission.
within each group the pilot sequences are mutually orthogonal
as that in the conventional TDD, it allows performing joint
channel estimation without interference for all users in each
group and employing joint spatial filtering such as zero-forcing
per group to suppress the inter-user interference among the
users in each group. This also increases the aggregate rate.
IV. TWO-GROUP GSOMA
In this section, we tailor the design of GSOMA to the cases
with two groups and discuss two modes of transmission.
A. Mode 1: without blanking
Fig. 3 shows the transmission protocol and the receiver for
the case with two groups where there is no blanking. The
users are grouped into two groups such that each group is
designed according the conventional TDD wherein the half of
the coherence time, i.e. 1
2
Tc, is used for pilot transmission and
the other half is consumed for the data transmission. To enable
the channel estimation without interference, a time-offset equal
to 1
2
Tc is used. The receiver first estimates the channel of the
users in the first group using the knowledge of the orthogonal
pilot sequences and then performs joint spatial filtering to

decode the data of the first group. The decoded data are fed
back to the channel estimator of the second group to perform
interference cancellation prior to the channel estimation. After
the interfere cancellation, the channels of the second group are
estimated using the known orthogonal pilot sequences used for
the users in the second group. The decoded data of the second
group is used to cancel the interference over the pilot symbols
of first group. This sequential channel estimation and decoding
is iteratively continued until all data are successfully decoded.
We next present the single-cell uplink throughput for the
protocol in Fig. 4 with L consecutive sub-frames when the
receiver has nt antennas and the channels are i.i.d. Rayleigh
fading with unit variance. We first consider matched-filtering
(MF) and then zero-forcing (ZF). The proofs, which are
omitted due the space limitation, can be obtained by similar
approaches as those in [5].
Proposition 1: The transmission protocol in Fig. 3 where
each group contains K users and the receiver employs MF
achieves the sum-rate
RMF∑,1 = K2L + 1
L∑
l=1
(R1,l + R2,l) (1)
where
R1,l = log
(
1 +

(nt −1)(1−Ne1,l)Pd1,l
N0 + Ne1,lPd1,l + Pp2,l + (K −1)Pd1,l
)
R2,l =log
(
1 +
(nt −1)(1−Ne2,l)Pd2,l
N0 + Ne2,lPd2,l + Pp1,l+1 + (K −1)Pd2,l
)
Ne1,l =
N0 + KNe2,l−1Pd2,l−1
N0 + Pp1,l + KNe2,l−1Pd2,l−1
Ne2,l =
N0 + KNe1,lPd1,l
N0 + Pp2,l + KNe1,lPd2,l
and Ppj,l , Pdj,l denote the average power consumed for the
pilot and data symbols of the users in group j ∈ {1, 2} and
sub-frame l ∈ {1, 2, . . . , L}, and Nej,l and N0 respectively de-
Pilot 1 Data Pilot 1 Data
Pilot 1 Data Pilot 1 DataPilot 1
Group 1 with BcTc/2 users with orthogonal pilot sequences
Group 2

Data Pilot 1 Data
Pilot 1 Data Pilot 1 Data
Pilot 1 Data Pilot 1 DataPilot 1 Data Pilot 1 Data
Channel Estimation
Group 1
Spatial Filtering, Data
Detection or Decoding
Channel Estimation
Group 2
Spatial Filtering, Data
Detection or Decoding
Timing offset
Tc Tc/2
a) Transmission Protocol
b) Receiver
D
M
U
X
Fig. 3. Two-Group GSOMA without blanking.

note variance of AWGN at the receiver and channel estimation
error, and Ne1,0 = Pd1,0 = Pp1,L+1 = 0.
each group contains K users and the receiver employs ZF
RZF∑,1 = K2L + 1
L∑
l=1
log
(
1 +
(nt −K)(1−Ne1,l)Pd1,l
N0 + KNe1,lPd1,l + Pp2,l
)
+ log
(
1 +
(nt −K)(1−Ne2,l)Pd2,l
N0 + KNe2,lPd2,l + Pp1,l+1
)
(2)
where Nej,l is defined in Prop. 1.
B. Mode 2: with blanking

For the case the array contains not so many antenna
elements with respect to the scheduled number of users in
each group, it is beneficial to partially blank some part of
sub-frames to enhance the channel estimation and to improve
consequently the performance of spatial filtering which in turn
improves the spectral efficiency of the system. The blanking
pattern, should be chosen based on the inter-user interference
when for higher interference a blanking pattern with a higher
density is selected and similarly a sparser blanking pattern
should be selected for lower interference to improve the
spectral efficiency of the system. Fig. 4 shows the transmission
protocol and the receiver for the case with two groups where
the blanking is used. The users are grouped into two groups
and transmission is arranged such that the pilot symbols of first
group do not experience any interference. This is useful for the
case that one to enhance the channel estimation for the users in
the first group, this also enhances the interference cancelation
for channel estimation of the second group. Additionally, this
arrangement is also useful for the case where first and second
groups compromise far and near users, respectively.
each group contains K users and the receiver employs MF
RMF∑,2 = 13K log
(
1 +
(nt −1)(1−Ne1)Pd1
N0 + Ne1Pd1 + Pp2 + (K −1)Pd1
)
+

1
3
K log
(
1 +
(nt −1)(1−Ne2)Pd2
N0 + Ne2Pd2 + (K −1)Pd2
)
(3)
where Ppj , Pdj denote the average power consumed for the
pilot and data symbols of the users in group j ∈ {1, 2}, and
N0 denotes variance of AWGN at the receiver. The quantity
Nej = Nej,1 denotes the variance of channel estimation error
for users in group j ∈ {1, 2}.
each group contains K users and the receiver employs ZF
RZF∑,2 = 13K log
(
1 +
(nt −K)(1−Ne1)Pd1
N0 + KNe1Pd1 + Pp2
)
+
1

3
K log
(
1 +
N0 + KNe2Pd2
)
(4)
where Nej = Nej,1 for j ∈ {1, 2} is given in Prop. 3.
From the sum-rates in Propositions 1–4, one can see that
the imperfections due to inter-user interference, the channel
estimation error and AWGN are linearly reduced by the
factor of 1
nt−1
and 1
nt−K
for MF and ZF, respectively. We
additionally see that ZF removes the inter-user interference
in each group due the data transmission which is one of the
advantages of GSOMA with respect to SOMA.
V. NUMERICAL EVALUATIONS
For comparison, we consider time-shared TDD as a baseline
when the resources are shared between two groups of users
when each group is designed according to the conventional
TDD. This, using ZF, gives the sum-rate

RZF∑,TS = 14K log
(
1 +
N0 + KNe1Pd1
)
+
1
4
K log
(
1 +
N0 + KNe2Pd2
)
(5)
Pilot 1
Pilot 1Pilot 1 Data Pilot 1
Pilot 1 Data Pilot 1Pilot 1
Group 1 with BcTc/2 users with orthogonal pilot sequences
Group 2Data Pilot 1
Pilot 1 Data Pilot 1

Pilot 1 Data Pilot 1Pilot 1 Data Pilot 1
Blank
Blank
Timing offset
Partially Blanked
Tc Tc/2
Fig. 4. Two-Group GSOMA with blanking.
where Nej =
N0
N0+Ppj
.
We next discuss two numerical examples of the sum-rate.
Fig. 5 and 6 show the sum-rate of the schemes as a function of
number of antennas for N = BcTc = 100, where the number
of users in each group is K = 1
2
N = 50. We set Pd1,l = Pd1 ,
Pd2,l = Pd2 (i.e. uniform power allocation across the sub-
frames) and N0 = 0 dB and the power of the associated
pilots are set 10 dB higher than the data for all users to
ensure a good channel estimation. In each figure, four schemes
are considered: time-shared TDD with ZF, SOMA with MF,
GSOMA with transmission protocol in Fig. 3 (i.e. Mode 1)
with ZF and L = 100, GSOMA with transmission protocol
in Fig. 4 with ZF (i.e. Mode 2). In Fig. 5 we set Pd1 = 0,

Pd2 = −20 dB and in Fig. 6 we set Pd1 = 10, Pd2 = −5
dB. In both cases, GSOMA provides an enhanced aggregate
rate as compared to the time-shared TDD. The gain is more
pronounced for the case that the groups are higher difference
in the received signal strength for which Mode 1 performs
better. Fig. 6, Mode 2 performs better than Mode 1 due to the
fact that the channel estimation for the high-power users in
group 1 is less degraded as compared to that in Mode 1.
VI. CONCLUSIONS
We presented a new multiple-access solution and analyzed
its aggregate rate. The new solution is constructed using a
semi-orthogonal feature for a group of users wherein each
group employs the conventional TDD. The numerical eval-
uation showed that the new proposal can provide a higher
aggregate rate as compared to the conventional TDD solution.
REFERENCES
[1] T. L. Marzetta, “Noncooperative cellular wireless with
unlimited numbers
of base station antennas,” IEEE Transactions on Wireless
Communica-
tions, vol. 9, no. 11, pp. 3590–3600, 2010.
[2] E. G. Larsson, F. Tufvesson, O. Edfors, and T. L. Marzetta,
“Massive
MIMO for next generation wireless systems,” IEEE
Communications
Magazine, pp. 186–195, 2014.
[3] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L.
Marzetta, O. Edfors,
and F. Tufvesson, “Scaling up MIMO: Opportunities and
challenges with

very large arrays,” Signal Processing Magazine, IEEE, vol. 30,
no. 1, pp.
40–60, 2013.
[4] J. Hoydis, S. Ten Brink, and M. Debbah, “Massive MIMO in
the UL/DL
of cellular networks: How many antennas do we need?” IEEE
Journal
on Selected Areas in Communications, vol. 31, no. 2, pp. 160–
171, 2013.
[5] M. N. Khormuji and B. M. Popović, “Semi-orthogonal
multiple-access for
massive MIMO,” Submitted to IEEE Trans on Wireless
Communications,
2014.
0 200 400 600 800 1000
0
20
40
60
80
100
120
140
160

180
Number of antennas: n
t
S
u
m
−
ra
te
[
b
it
/s
/H
z]
Time−shared TDD
SOMA
GSOMA: Mode 1
GSOMA: Mode 2
Fig. 5. The sum-rate of the schemes for Pd1 = 0, Pd2 = −20 dB.
0 200 400 600 800 1000
0
50

100
150
200
Number of antennas: n
t
S
u
m
−
ra
te
[
b
it
/s
/H
z]
Time−shared TDD
SOMA
GSOMA: Mode 1
GSOMA: Mode 2
Fig. 6. The sum-rate of the schemes for Pd1 = 10, Pd2 = −5 dB.

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