It is widely known that multiple input multiple output (MIMO) communications
provide substantial capacity gains, which are supported by spatial multiplexing and diversity
gains [1]. The study of MIMO communications in underwater environments is scarce in the lit-
erature and usually associated to orthogonal frequency division multiplexing (OFDM) modula-
tions [2{4]. However, OFDM signals present large envelope °uctuations and high peak-to-average
power ratio (PAPR), which can degrade the energy e±ciency of the ampli¯cation process. In
this context, single-carrier modulations such as single-carrier with frequency-domain equalization
are considered an excellent alternative, with identical performances as OFDM schemes [5]. As
with other block transmission techniques, SC-FDE schemes are suitable for reliable transmissions
over severely time-dispersive channels, thanks to the inclusion of the cyclic pre¯x (CP), which
allows a simple frequency-domain equalization (FDE). Conventional SC-FDE schemes employ
a linear FDE optimized under the minimum mean squared error (MMSE) criterion. However,
the residual interference levels might still be too high, leading to performance that is substan-
tially poorer than the matched ¯lter bound (MFB). In that context, attention has been given to
nonlinear equalizers, also known as decision feedback equalizers (DFE), since they are known to
outperform linear equalizers and to have a good performance-complexity tradeo® [6]. In order
to have further performance improvements, there has been signi¯cant interest in the design of
iterative DFE, also known as iterative block decision feedback equalizer (IB-DFE) not only for
single-input single output (SISO) channels, but also for MIMO channels [7, 8]. However, to the
authors' knowledge, the study of IB-DFE schemes in underwater scenarios has not been made
yet.
The underwater channels have challenging aspects that condition the design of communication
schemes [9]. In fact, given the complexity of underwater acoustic medium and the low propagation
speed of sound in water, the underwater acoustic channel is commonly regarded as one of the
most challenging channels for communication. For instance, the speed of the underwater acoustic
waves varies with the water depth and the underwater absorption can have a strong impact on
the attenuation [10, 11]. Moreover, the multipath is usually low, which means that the MIMO
channel presents spatial correlation [12].
In this work, we aim to present the performance evaluation of SC-FDE schemes in underwater
MIMO spatially correlated channels. More concretely, we characterize the performance of IB-DFE
receivers considering di®erent degrees of spatial correlation and we study performance-complexity
tradeo® having in mind not only the parameters of the IB-DFE, but also the size of the MIMO
system. It is shown that although the performance degrades with the spatial correlation, this
degradation can be small if the number of receive antennas is much higher than the number of
receive antennas.