ISI Analysis in Network MIMO OFDM Systems
with Insufficient Cyclic Prefix Length
Vincent Kotzsch, Wolfgang Rave and Gerhard Fettweis
Vodafone Chair Mobile Communications Systems, TU-Dresden, Germany
Email: {vincent.kotzsch, rave, fettweis}@ifn.et.tu-dresden.de
Abstract—We consider a cellular network MIMO OFDM sys-
tem where cooperating base stations apply joint signal processing
to the receive signals of several users. In this situation, due
to geometry, the problem of unavoidable differences in time of
arrival between the users’ signals occurs. As a result, symbol
timing offsets can be larger than the cyclic prefix, which leads
to OFDM inter-symbol interference. In addition to the multi-
user interference, a coupling between adjacent subcarriers and
consecutive OFDM symbols is induced in such scenarios. In this
paper, we analyze the multi-user joint detection performance in
systems with distance dependent asynchronous interference and
pathloss environments for different channel delays as well as
fixed cyclic prefix length. To this end we use an exact expression
for the post equalization SINR that is used for the evaluation in
numerical simulations. The system level cell setup considers two
user positioning models based on a hexagonal cell geometry with
varying cell radii.
I. INTRODUCTION
In cooperating space division multiple access (SDMA)
systems which are often referred to as network multiple-input
multiple-output (MIMO) systems, groups of user terminals
(UT) transmit their data on the same time and frequency
resources to geographically separated base stations (BS) which
are connected to each other in order to perform joint signal
processing (e.g. [1], [2]). As we can see in the left-hand side
of Fig. 1 we have different distances d between each UT and
BS that cause different signal path delays τd:
τd =
d
clight
(1)
as well as pathloss ψd:
ψd = Ψ
( d
d0
)−η
(2)
on each wireless communication link where clight is the speed
of light, η is used as pathloss exponent, d0 as the reference
distance and Ψ as an environment propagation factor here.
It has been shown that the orthogonal frequency division
multiplex (OFDM) modulation scheme in SDMA systems is
a promising candidate to fulfill requirements for achieving
high spectral efficiency at adequate computational effort (e.g.
[3]). One advantage of OFDM is the frequency domain data
transmission on orthogonal subcarriers on which flat channels
can be assumed such that common MIMO signal processing
algorithms can be utilized. Since orthogonality is destroyed if
inter-symbol interference (ISI) due to multi-path channels with
impulse response of length τch from previous OFDM symbols
occurs, a cyclic prefix (CP) of duration TCP is used (e.g.
[4]). The aforementioned path delays lead to a misplacement
of the timing point for the receiver window of the discrete
Fourier transform (DFT) that is used for the time frequency
transformation in OFDM. To overcome such misalignments
synchronization procedures are used to compensate those path
delays (e.g. [5] [6]). These techniques are well established for
single user transmission. In network MIMO systems it is only
possible to be synchronized to a single transmitter such that
we have always time differences of arrivals (TDOA) between
the synchronized user and the others.
A possible timing scenario is depicted in the right-hand side
of Fig. 1 where the signals of three users are received by three
base stations taking the links to base station one (BS#1) as an
example. The desired user (UT#1) is synchronized to the base
τd2 , ψd2
t=0
UT #1:
(desired)
UT #2:
UT #3:
Rx DFT Window
Symbol iSymbol (i-1)
t
CP CP
Inter-symbol interference (ISI) from previous symbol
UT#3
BS#1
τd3 , ψd3
τd1 , ψd1
UT#2
UT#1
BS#2
BS#3
Fig. 1: Timing Scenario in Network MIMO OFDM Systems
station while the others are delayed in such a way that the
TDOA of user two lies within the CP but the ISI already leaks
into the DFT window. The third user even violates the CP limit
such that a portion of the previous OFDM symbol lacks into
the DFT span. In the existing literature that kind of interference
is often referred to as asynchronous interference (e.g. [7]). The
upper plot of Fig. 2 depicts the joint distribution of occurring
timing delays after synchronization for different cell radii R,
for the case that three users are uniformly distributed within
a hexagonal cell area that is jointly served by three base
stations. As a reference the duration of the 3GPP/LTE short
CP (TCP = 4.7µs) as well as the long CP (TCP = 16.7µs)
is indicated within the figure by vertical lines. The multi-user
detection (MUD) after asynchronous signal transmission is e.g.
treated in [8], [9] and [10] but without considering cellular
environments where also the distance dependent pathloss (see