MULTIPLE ANTENNA METHOD FOR REDUCING INTER -CELL INTERFERENCE IN MULTI-USER
WIRELESS SYSTEMS
Field of the Invention
The invention relates generally to wireless communication networks in which
user terminals transmit pilot signals to a base station for the purpose of measuring
propagation characteristics. The invention relates more particularly to mobile
wireless systems employing Time-Division Duplexing (TDD).
Art Background
In a typical mobile wireless multi-user system, a plurality of radio cells cover
an extensive geographical area. A base station (BS) is centrally located within each
cell. The BS receives and transmits data to those mobile user terminals, referred to
hereinafter as "mobiles" or "mobile stations", that are located in the same cell as the
BS.
However, signals transmitted by a given base station will propagate not only
to the mobiles within its own cell, but also to mobiles in the neighboring cells. As a
consequence, downlink transmissions from each base station will tend to create noise,
referred to as "intercell interference," at the mobiles of neighboring cells. Similarly,
signals transmitted by each mobile within a given cell will propagate not only to the
base station serving that cell, but also to the base stations serving neighboring cells.
As a consequence, uplink transmissions from each mobile will tend to create intercell
interference at the base stations serving neighboring cells.
For example, FIG. 1 illustrates a portion of a cellular network in which
downlink transmissions from the base station of Cell 1 interfere with mobile stations
in Cell 2 .
Intercell interference, as described above, is a major obstacle to increasing the
rate of data transmission in modern wireless systems. In particular, intercell
interference degrades the gains in transmission rate that can otherwise be made by
employing multiple antennas at the base station. That is, the theoretical maximum
feasible transmission rate on the downlink increases linearly with the number of base
station antennas. However, the amount of intercell interference increases with the
number of base station antennas in such a way that only a sublinear increase is
achieved.
Summary of the Invention
We have found an efficient way to reduce inter-cell interference in mobile
wireless systems, and particularly in Time Division Duplexing (TDD) wireless
systems.
In an embodiment, a base station serving one or more mobile terminals
receives a pilot signal from at least one of the served mobile terminals at a plurality of
base station antennas, which include at least some main antennas and at least some
auxiliary antennas. In response to the pilot signal as received at each of the antennas,
an output is provided from each antenna of the antenna plurality. The antenna outputs
are processed to obtain a set of precoding weights for a transmission from the main
antennas. The processing includes nulling at least one interfering signal using the
outputs from at least the auxiliary antennas.
Brief Description of the Drawing
FIG. 1 is a schematic drawing of a portion of a typical cellular network having
hexagonal geometry, illustrating inter-cell interference between the cells numbered 1
and 2 in the figure.
FIG. 2 is a timing diagram illustrating the synchronous transmission of pilot
signals from mobile stations in a group of neighboring cells.
FIG. 3 is a timing diagram illustrting an alternative to the format of FIG. 2, in
which there is a timing offset between the pilot transmissions in different cells.
FIG. 4 is a schematic diagram of a portion of a network in which two base
stations are equipped with main and auxiliary antennas according to an embodiment
of the invention.
FIG. 5 is a graph of simulation results showing throughput in a model network
versus the number of auxiliary antennas.
Detailed Description
Channel Coefficients.
For purposes of illustration, we will base our description on a network in
which OFDM data transmission is used. The invention is not limited in application to
OFDM networks, however, but instead is applicable to any type of network in which
uplink pilot signals are used for the purpose of measuring characteristics of the
propagation channel.
For simplicity of presentation, we will limit the following discussion to one of
the plurality of orthogonal subchannels used in OFDM systems for data transmission.
Extension of the below discussion to the full set of OFDM subchannels is
straightforward.
In the below discussion, signals and coefficients will be indexed using the
following symbols:
j identifies a particular cell in which a mobile is present;
/ identifies a particular base station and by extension, the cell served by that
particular base station;
k identifies a particular mobile within a given cell; and
m identifies a particular antenna at a given base station.
We will assume that there are L cells in a group consisting of a given cell and
its neighboring cells, with K mobiles in each cell. We will assume that all base
stations haveM antennas for transmission and reception and that each mobile has one
antenna. We denote signals transmitted by the k-t mobile of the -th cell by x k .
Signals received by the m-t antenna of the /-th base station we denote by y lm . By
pMS and pBS we denote transmitted power levels of mobiles and base stations
respectively. For illustrative purposes, we will make the simplifying assumption that
all mobiles have the same power and that all base stations have the same power.
During transmission, the effect of the propagation channel is to multiply each
signal from the mobile of the -th cell to the w-th antenna of the /-th base station
by the complex-valued channel coefficient h jlkm . The respective channel coefficients
from the mobile of the -th cell to theM antennas of the l-th cell form the
channel vector
jik = hjikM ) •
(Herein, the bold font is used to denote vectors.) The channel coefficients
h jlkm are modeled as random variables. The channel coefficients h jlkm remain
approximately constant during the coherence interval T. The length of the coherence
interval T depends on the speed of a mobile. The faster a mobile is moving, the
shorter the coherence interval for its channel coefficients h ¾ = h ,..., hjlkM ) . For
mobiles moving with a speed of 50 or 70 km/h the coherence interval J is
approximately equal to the time needed for transmission of 20 or 10 OFDM symbols,
respectively.
Because in our example the same frequency subchannel is used on both the
downlink and the uplink, reciprocity applies and a signal transmitted from the m-th
antenna of the /-th base station base station to the mobile is likewise multiplied by the
same channel coefficient hjlkm .
Shadowing Coefficients.
Practical experience has shown that in modeling a wireless network, it is
useful to include a relatively slowly varying, generally real-valued coefficient to
represent attenuation of transmitted signals due to distance or other factors such as
intervening topographical features, buildings, or other physical obstructions. That is,
a signal transmitted from the k-th mobile of the -th cell to any antenna of the /-th base
station is multiplied by the shadowing coefficient k .The shadowing coefficients
take random values. Unlike the channel coefficients, the shadowing coefficients
stay constant much longer. For this reason a base station can, at least in principle,
accurately estimate the shadowing coefficients to all the mobiles of the neighboring
cells.
Accordingly, we will assume in the following discussion that the shadowing
coefficients fi k , j = ,..., , k =\,...,K, are known to the l-t base station. It is also
important to note that the shadow coefficient will, in general, be strongly
correlated with the distance between the l-th base station and the k-th mobile of the j -
th cell. The larger the distance, the smaller (typically) will be the value of .
Knowledge of the channel coefficients allows a base station to reduce the
intra-cell interference and the inter-cell interference by using interference cancellation
precoding.
To allow the base stations to estimate the channel coefficients jlkm , all
mobiles, in all cells, synchronously (in the present example) transmit training pilot
signals k ,j =\,...,L,k =\,...,K, of symbols each. Thus, each pilot signal is a r -
tuple of scalar-valued symbols, and as such is a r -dimensional vector. As a
consequence of a pilot signal having been transmitted, a r -dimensional vector
y lm is received at the m-th antenna of the l-th cell, having the form
where the r - tuple lm represents additive noise.
We now introduce the following definitions, expressed in terms of quantities
defined above:
From Eqn. (1), the signal received at the /-th base station is
= & ¾ + (Y, is a r x matrix)
It will be understood that Y/ is a matrix, each of whose columns corresponds
to one of theM antennas at the /-th base station. Each column of Y/ is a r - tuple of
scalar values. Each of the scalar values corresponds to one of the symbols of the
transmitted pilot signal, and represents a sum, at the m-t antenna, of the various
versions of the symbol as received from the respective mobiles occupying the served
cell and neighboring cells, plus additive noise.
When the pilot signals are designed to be mutually orthogonal (as is
typically the case), their orthogonality properties can be used in an appropriately
designed receiver to recover estimates of the individual channel coefficients
h = (h ,...,h M at the l-t base station. Even if there are small deviations from
complete orthogonality, it may be possible to employ the same techniques to obtain
estimates of the channel coefficients. Accordingly, it should be understood that when
we speak herein of "orthogonal" pilot signals, we mean to include pilot signals that
may deviate somewhat from complete orthogonality, but not so much as to render
ineffective the estimation of individual channel coefficients.
Thus, for example, an MMSE estimator uses prior knowledge of the pilot
signals and the orthogonality property that *= to recover an estimate H of
the matrix H defined above. is the KxK unity matrix.
That is, the MMSE estimator of H given Y is
Data Transmission from Base Stations to Mobiles.
Using the estimates H , _ = l,...,L, the /-th base station can use either linear or
nonlinear precoding to provide mobiles from the /-th cell with strong signals and to
limit intra-cell interference and inter-cell interference to mobiles from its own cell and
to mobiles from other cells. In particular, a linear precoding can be done as follows.
Let qlK be signals that should be transmitted by the /-th base station to
the corresponding mobiles from the /-th cell. Using the estimates H , _ =l,...,L, the
/-th base station forms anMxK precoding matrix A and transmits signals
The signal received by the k- mobile from the -th cell is
where z represents additive noise.
There are many different efficient precoding matrices, that allow one to
significantly reduce the intra-cell interference and the inter-cell interference. One
possible way is to use as A the pseudoinverse of H « .
Pilot Signals and their Assignment to Mobiles
As mentioned above, precoding may be employed to significantly reduce the
interference. However, as a general rule, the precoding works well only if the
estimates h =l,...,L,k =l,...,K, are accurate and uncorrected. In order to obtain
fully accurate and uncorrected estimates, the pilot signals (also referred to below as
"pilots") f k ,j =\,...,L,k =\,...,K, must be orthogonal. Unfortunately it is not
generally possible, as a practical matter, to satisfy this requirement simultaneously
over all mobiles in a given cell and its neighboring cells.
That is, mobiles may move with high speeds, e.g. vehicular speeds, and may
consequently have short coherence intervals, i.e., low values of T. The channel
coefficients, which the base station learns with the help of the pilots, remain
effectively constant only during a given coherence interval. As a consequence, the
maximum interval available to the the base station for transmitting data to the mobiles
is T - . Therefore, it is advantageous to make , the length of the pilot signals
measured in symbol intervals, as small as possible.
Typically, r can take values from 4 to 12, depending on the speed of the
mobiles in a particular wireless network. Elementary vector analysis teaches that a set
of mutually orthogonal r -dimensional vectors cannot contain more than r elements;
otherwise, at least one pair of vectors will be non-orthogonal. Consequently, the
maximum number of mobiles that can have orthogonal pilot signals at a given time is
equal to .
The number J of cells in a group consisting of a given cell and the cells
neighboring the given cell in a typical hexagonal network is 7 as shown, e.g., in FIG.
1, and it will be taken as 7 in our illustrative example. For example, as will be seen in
FIG. 1, a cell 1 may be surrounded by neighbor cells 2-7. Thus it will be clear that if
two or more mobiles are simultaneously served by their respective base stations in a
given cell and each of its six neighbors, the pilots being used cannot all be mutually
orthogonal, even if is as high as 12.
Mitigation of intra-cell interference is generally considered to be more
important than mitigation of inter-cell interference. Intra-cell interference can be
efficiently mitigated by requiring that all the pilots used within a given cell be
orthogonal. Accordingly, it will be assumed in the example discussed below that pilot
signals used for the mobiles within a given cell are orthogonal.
Without loss of generality, consider two different cells Cell 1 and Cell 2, a
pilot signal belonging to the k'th mobile of Cell 1, and a pilot signal 
belonging to the q'th mobile of Cell 2 . If these two pilot signals are not orthogonal,
then the estimates of the channel vectors k and 22q will be inaccurate, and in
particular, they will be at least partially correlated. This will result in a bad precoding
matrix A2 . That is, using such estimates, the base station of index 1=2 will generate a
precoding matrix A2whose entries are at least partially adapted to aid the
transmission of data from the 1=2 base station to the k-t mobile of Cell 1. In other
words, the signal s generated according to Eqn. (2) will arrive at the k-t mobile of
Cell 1 with relatively high strength. Stated differently, the product | h t s | , wherej=and 1=2, will be large. Thus the 1=2 base station will unavoidably beamform the
downlink signal for the 'th mobile of Cell 2 so as to create a directed interference at
the &'th mobile of Cell 1. Referring again to FIG. 1, it will be seen that the signals
shown arriving at two mobile stations of Cell 2 cause interference of the kind
described here.
To obtain the precoding matrix, one conventional approach has all the mobile
stations in a group of neighboring cells synchronously send pilot signals to their
respective base stations, as illustrated in FIG. 2 . By "synchronously" is meant that all
pilot transmissions in the synchronous group of mobile stations begin together and
end together.
It should be noted, however, that to preserve intra-cell orthogonality, at most 
mobiles of a given cell can synchronously transmit pilot signals, being, as noted, the
number of symbol intervals in a pilot signal. Thus, although FIG. 2 (as well as FIG.
3) shows synchronous transmissions from immobile stations, it should be understood
that if K , then to preserve intra-cell orthogonality, fewer than all mobile stations in
the cell will be active at one time.
The base stations use these pilots to estimate the channel coefficients to each
of their corresponding mobile stations, and they use the estimated channel coefficients
to compute the precoding matrices. However, each channel estimate based on the
pilot from a given mobile station may be contaminated by one or more synchronously
transmitted non-orthogonal pilots from different mobile stations (which will typically
be transmitting from other, neighboring cells). As noted above, such contamination
may lead to downlink interference that is significantly stronger than the interference
from a random signal of the same power. This can result in significant reduction of
downlink transmission rate in Multi-Cell Multi-User wireless systems.
An alternative protocol is illustrated in FIG. 3 . In this protocol K
mobiles from a given cell use K orthogonal pilots and send them
synchronously. At the same time, mobiles from different cells send shiftedin-
time pilots, as shown in the figure. In this case, pilots from different cells
will not contaminate each other.
New Approach
However, such an approach suffers from the problem that signals
transmitted by base stations are significantly stronger than signals
transmitted by mobiles. Thus, the base station BS 1 will have to estimate the
channel coefficients of the mobiles from cell 1 in the presence of strong
downlink signals transmitted by BS 2 and the base stations of other
neighboring cells.
We will now describe a new approach we have developed to address
this problem.
We note first that because there is a timing offset of the pilot
transmissions from neighboring (and thus, potentially interfering) cells, we
can limit the discussion, below, to the mobiles of only a given cell.
Accordingly, the notational symbol h i m that we have used, above, to
represent the channel coefficient from mobile k of cell j to base station
antenna m of cell / will now be simplified to the form h m, representing the
channel coefficient from mobile k to base station antenna m .
Exemplary implementations of our new approach are achieved
through the following steps:
1. Equip base stations with an additional set of N auxiliary antennas, which are
passive antennas in the sense that they are used for reception but not for
transmission.
2 . Employ a communication protocol and a signal processing algorithm that
allow the base station to estimate the channel coefficients hkm between the
active antennas and the mobiles even in the presence of strong downlink
signals from other base stations. The protocol and signal processing algorithm,
which are discussed below, are based on the use ofM active antennas, which
we refer to as "main" antennas, and the N passive antennas, which we refer to
as "auxiliary" antennas.
3 . Optionally, optimize the respective numbers of active and passive antennas.
Mathematical Details
A generic situation is shown for purposes of illustration in FIG. 4 . In
the figure, base station BS 1 serves cell 1, and base station BS 2 serves
cell 2 . In cell 1 there are immobile stations. (Only one mobile, i.e.,
mobile k, is shown in the figure.) A set of r of these mobiles
simultaneously transmit r orthogonal pilots. Mobiles from different
cells send shifted-in-time pilots, as shown in FIG.3.
The &'th mobile of cell 1 transmits pilot At the t'th
instant of time, let BS 2 transmit signals sT=(si, .. . , SM) from itsM active
antennas to mobiles located in cell 2 . (Here, the superscript "T"
indicates matrix transposition.) The signal sT=(si, ..., is not known
to BS 1.
The channel coefficients between the k t mobiles andM active
antennas of BS 1 are k h^.
We denote by k =( k ...,h¾ ) the 1 x M vector formed by the
channel coefficients of the &'th mobile.
The channel coefficients between theM active antennas of BS 2 and
the M+N antennas of BS 1 are g ,j =1, ... +N r=1, ...JM. t
G=[g ]
be the (M+N) xM matrix formed by the channel coefficients g between
BS 1 and BS .
At the th time instant, BS 1 receives 1 x (M+N) vector
y =(Gs) T + i i + ... + K + additive noise.
As noted above, intra-cell orthogonality is preserved only if K .
Accordingly, for cells that contain more than mobile stations, K should be
understood for purposes of this discussion as the number of mobile stations in a subset
that contains no more than mobile stations.
The channel matrix G does not change or changes very slowly, since the base
stations do not move. Hence, by sending appropriate pilots, G can be accurately
estimated and periodically updated.
Let all base stations transmit signals with power p BS . Assume that all
mobiles transmit with power p MS . (The algorithm is readily extended to apply to the
case in which different mobiles and base stations transmit with different powers.) To
simplify our notation, we assume that all base stations have the same power and that
all mobiles have the same power. Extensions to more general cases are
straightforward.
The standard assumption in wireless systems is that ~ CN(0, I{M+N}),
where M+N } is the (M+N) x (M+N) identity matrix. That is, it is assumed that the
channel vectors have the complex Gaussian distribution with the covariance matrix
M+N} If the channel vectors have a different distribution, the algorithm described
here is readily modified accordingly.
BS 1 can now perform the following procedure:
1. Using a good estimate of G allows BS 1 to accurately estimate the vector s
transmitted by BS 2 . This is done, e.g., using estimation techniques known from linear
regression analysis, in which the terms + ... + K are treated as additional
noise. In particular, BS 1 can use the Bayesian MMSE estimator to obtain theM x 1
vector
Sest = [1/(^+1)] IPBS IM)+ (1/(^+1)) G* G )]- 1 G* y T
Here * denotes the Hermitian conjugate, I denotes the MxM identity matrix,
and s est is the estimated version of the vector s transmitted by BS 2 .
2 . BS 1 subtracts the vector (G s est ) T from y , so as to obtain the (M+N x 1) vector
w = y - (G s est ) T = t hi + ... + Kt K + (G(s-s est)) T + additive noise
3 . Accumulating vectors w for t=l,.., r ( r is the length of the pilots ), BS 1 can
estimate the channel coefficients km. This can be done in the following way. Let z be
the xl vector formed by the firstM entries of w . Let Z be the r xM matrix
formed by Z ,...,z ; that is,
Assuming that the term G(s-s e t) is small and using the standard MMSE estimation
method we obtain, for mobile station :
hi,e t = c , where c=sqrt(> pMS ) .
4 . Using the obtained estimates h, e t of h, , BS 1 can conduct an interference
cancellation precoding (for instance zero-forcing precoding) without creating a
directed interference to cell 2 .
As explained above at steps 1 and 2, base station BS 1 estimates the vector s
and subtracts the vector (G sest ) T from y , so that the channel coefficients km can be
estimated without degradation by the signal s . This is an example of nulling, by
which we mean any method which reduces or removes the degrading effect of s on
the channel-coefficient estimates.
Note that the performance of the algorithm can be further improved if steps 1-
3 are iterated several times. This can be done, e.g., if the base stations are equipped
with fast computational devices and can conduct steps 1-3 several times within a
suitable timeframe. Appropriate computational devices include special purpose
digital processors, but they are not so limited and may alternatively include other
special-purpose or general-purpose computational devices operating under hardware,
firmware, or software control.
In the case when several base stations from the neighboring cells transmit
signals the above-described approach can likewise be used.
It is not difficult to see that the larger the number of passive antennas N, the
better the estimates of the channel coefficients that BS 1 can obtain. Indeed let us
assume that N tends to infinity. Then using the N passive antennas BS can obtain an
arbitrarily accurate estimate of the vector s transmitted by BS 2 . (This directly
follows from linear regression analysis.) In such case we have sest=s and therefore
w = y - (G sest ) T = t hi + . . . + ί hK + additive noise ,
which corresponds to the case when K mobiles from cell 1 transmit orthogonal pilots
and no other base stations or mobiles from cell 2 transmit any signals at all. This is a
very favorable situation for BS 1. In this case, BS 1 can accurately estimate the
channel vectors hi, . . ., K and transmit to mobiles from cell 1 without creating any
directed interference to mobiles located in cell 2 .
Of course there will always be practical limits on the total number of antennas
L (including both active and passive antennas) that can be deployed. It is therefore
advantageous to choose an optimal number of active M and passive N antennas.
One optimization method that is useful in this regard involves estimating the
sum rate (i.e., the system throughput) for various combinations of and N by
computer simulation. Methods for estimating the sum rate are known and need not be
described here in detail. One exemplary such method is described in T. L. Marzetta,
"How much training is required for multiuser MEVIO," Proc. of Signal, Systems, and
Computers , ACSS 2006, Fortieth Asilomar Conference, pp. 359-363 (Nov. 2006).
According to our exemplary optimization method, computer simulation is used
to estimate the sum rate for different values M and N that satisfy the constraint
M+N=L. A search of the results can identify the numbers opt and N0pt (such that
Pt +Nopt =L ) of active and passive antennas that maximize the sum rate.
It should be noted that passive antennas do not require signals amplifiers and
therefore they are less expensive than active antennas. Thus, if the total number of
antennas is L and we deploy an optimal number of passive antennas N (M=L-N) then
we simultaneously increase the data transmission rate and decrease the cost of the
system.
In some embodiments, the number of antennas to be designated as main
antennas, and the number to be designated as auxiliary antennas may be variable, and
thus may be adapted to changing conditions. Whether a given antenna is to be
designated as "main" or "auxiliary" may also be selectable. For example, switches
may be used to connect selected antennas to transmit chains while connecting other
selected antennas to receive chains only, and to designate how the output from a given
antenna (operating in receive mode) is to be processed, i.e., whether for full
communication or only for interference mitigation.
It can also be made a matter of choice to use only auxiliary antennas, or a
combination of main and auxiliary antennas, for estimating the interfering signals
from the neighboring base stations.
Example
FIG. 5 presents the results of a numerical simulation that we performed for the
case of seven neighboring cells, as illustrated, e.g., in FIG. 1. We assume that in each
cell there are four mobiles and that the mobiles use the same set of orthogonal pilots,
each pilot consisting of n=4 symbols. More precisely we assume that the these four
pilots form rows of the Hadamard matrix of size 4 .
From top to bottom, the three curves represent, respectively, our new method,
with results that are dependent on the number N of passive antennas; the method using
time-offset pilot transmissions as described with reference to FIG. 3; and the method
using synchronous pilot transmissions without a time offset, as described with
reference to FIG. 2 .
It is evident that the protocol in which mobiles from different cells send
shifted-in-time pilots exhibits gains over the protocol in which all mobiles in all cells
send pilots synchronously. (Only M active antennas are used in both cases). One can
also see that the proposed scheme with N passive antennas gives further significant
improvement.
CLAIMS
What is claimed is:
1. A method performed by a base station serving one or more mobile terminals,
comprising:
(a) receiving a pilot signal from at least one of the served mobile terminals at a
plurality of base station antennas, said plurality including at least some main antennas
and at least some auxiliary antennas;
(b) providing an output from each antenna of the plurality, said outputs being
in response to the received pilot signal; and
(c) processing the antenna outputs to obtain a set of precoding weights for a
transmission from the main antennas, said processing including nulling at least one
interfering signal using the outputs from at least the auxiliary antennas.
2 . The method of claim 1, further comprising transmitting data to one or more of the
served mobile terminals using the precoding weights, said transmission taking place
from the main antennas while no transmission is made from the auxiliary antennas.
3 . The method of claim 2, wherein the data transmission is made simultaneously to a
plurality of served mobile terminals.
4 . The method of claim 1, wherein a pilot signal is received simultaneously from a
plurality of served mobile terminals.
5 . The method of claim 1, wherein the step of receiving a pilot signal is performed at
least partly during a transmission from at least one neighboring base station, and
outputs from at least the auxiliary antennas are used to null at least one said
neighboring base station transmission.
6 . The method of claim 1, wherein the outputs from the main antennas and the outputs
from the auxiliary antennas are used to null at least one said interfering signal.
7 . The method of claim 1, further comprising selecting some antennas of said plurality
to be the main antennas, and selecting some other antennas of said plurality to be the
auxiliary antennas.