Interference Analysis in Time and Frequency
Asynchronous Network MIMO OFDM Systems
Vincent Kotzsch and Gerhard Fettweis
Vodafone Chair Mobile Communications Systems, TU-Dresden, Germany
Email: {vincent.kotzsch, fettweis}@ifn.et.tu-dresden.de
Abstract—It is well known that symbol timing offsets larger
than the cyclic prefix as well as carrier frequency offsets between
transmitter and receiver stations destroy the orthogonality among
OFDM subcarriers and induce additional interference. In con-
junction with MIMO transmission on frequency selective fading
channels where different users interfere with each other, these
effects strongly degrades the signal detection performance. In
this paper we consider fully asynchronous spatially multiplexed
transmission with different symbol timing and carrier frequency
offsets on each transmitter-receiver link which appear in dis-
tributed MIMO systems with multiple users and base stations.
We derive a factorized system model for signal transmission in
frequency domain where the different effects of inter-carrier,
inter-symbol and inter-block interference are separated and an-
alyzed in terms of signal-to-interference-noise-ratio degradation.
Finally, we evaluate the interference levels at a receiver station
for different link-level as well as system-level simulation setups.
I. INTRODUCTION
It has been shown in many publications that the orthogonal
frequency division multiplex (OFDM) modulation scheme in
multiple-input multiple-output (MIMO) systems is a promising
candidate to fulfil requirements for achieving high spectral
efficiency at adequate computational effort (e.g. [1], [2]).
In recent standardisation processes OFDM has been chosen
for application in cellular mobile communications, namely
orthogonal frequency division multiple access (OFDMA). In
conjunction with space division multiple access (SDMA) tech-
niques it is possible to assign time-frequency-space resources
to users fairly flexibly (e.g. [3]). In such systems, separate base
stations (BS) and user terminals (UT) suffer from inaccuracies
in terms of synchronization mismatches in time and frequency
(e.g. [4], [2]). Symbol timing offsets (STO) between users are
caused by propagation delays through transmission channels.
Carrier frequency offsets (CFO) occur due to unsynchronized
local oscillators at each UT in the network as well as Doppler
shifts from relative movements w.r.t to the BS respectively.
Approaches for future mobile communication systems include
clusters of base stations that work in a cooperative manner
in order to improve the spectral efficiency in cellular environ-
ments (e.g. [3]). In such distributed systems there are high
requirements on the time/frequency alignment of the users to
the BS network to achieve the anticipated gains.
There has been a lot of work in the field of the interference
analysis in order to describe the effects of STOs and CFOs
so far (e.g. [2], [5], [6]), as well as to understand the effects
of insufficient CP length in the case of large STOs (e.g. [7],
[8], [9]), but often there are limitations in such a way that
it is difficult to map a asynchronous network MIMO OFDM
system to the existing error models. In this paper, we provide
a generalized frequency domain transmission model where K
asynchronous users transmit their data over the same channel
resource and will be received by M asynchronous base sta-
tions. We derive a convenient approximation for the overall
interference power that includes the effects of STOs, CFOs
and insufficient CP length, which is used for an extensive
interference analysis.
The paper is organized as follows: In section II we derive
our network MIMO OFDM system model. A SINR approxi-
mation for all subcarriers is given in section III. Performance
evaluations and simulation results are provided in section IV,
before in section V concluding remarks summarize the main
results.
Notation: Boldface letters denote matrices and underlined
letters vectors respectively. We use [.] for indexing an element
of a vector or matrix. Lowercase letters describe variables in
the time domain and uppercase letters variables in frequency
domain respectively. (.)T is used as transpose and (.)H as
conjugate transpose operator. The operator E(.) expresses the
expectation value.
II. SYSTEM MODEL
We consider the uplink of a cellular system with K active
users which are connected to their serving base station each.
For the joint multi-user detection process we use a cluster of
base stations which receive the user signals at an appropriate
power level. The users simultaneously transmit their data on
a set of OFDM subcarriers D in frequency domain. In order
to avoid OFDM inter-symbol interference (ISI) and self inter-
carrier interference (ICI) we use a cyclic prefix (CP) of NCP
samples. As a result one OFDM symbol block consists then
of NB = N + NCP time domain samples. The representation
of the base band signal for user k is given as IDFT operation:
xki [n] =
1
√
N
∑
l∈D
Xki [l] e
j2πln
N , −NCP ≤ n ≤ N − 1 (1)
where Xki [l] = 0 ∀ l /∈ D and N represents the DFT size. The
OFDM symbol index is denoted by i = 0, ..., NS − 1. After
the transmission over the channel with the impulse response
vector h which consists of L discrete channel taps, the signal