Precoder design for MIMO systems over spatially correlated Ricean fading channels
空間相關的萊斯衰落信道下 MIMO 系統的預編碼設計
Student thesis: Doctoral Thesis
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Award date  3 Oct 2014 
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Permanent Link  https://scholars.cityu.edu.hk/en/theses/theses(76893b7f401f4227ba92a01c8ce15b25).html 

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Abstract
In response to the considerable increase in mobile data tra±c driven by multimedia
and cloudbased services, multiple input multiple output (MIMO) is one of the most
powerful communication technologies to deal with this continuously growing demand.
By using a precoder, to be designed with the knowledge of channel state information
(CSI) at the transmitter (CSIT) to transform the input signal prior to MIMO transmission, the bit error rate (BER) and data rate can be improved. A precoder designed
with perfect instantaneous CSI can achieve either best BER performance or best data
rate performance. However, perfect CSI is practically unavailable because of estimation errors, feedback delay, and quantization errors. Imperfect CSI can substantially
degrade the system performance. Furthermore, the frequent feedback of instantaneous CSI costs expensive bandwidth overhead. Statistical CSIT, including channel
mean and spatial correlation, is an e±cient measure to CSI. Its slowly varying nature
does not need frequent CSI feedback to the transmitter, so that it can save much
bandwidth overhead. So, the design of an optimal precoder based on statistical CSIT
is of vital importance.
The objective of this thesis is to investigate precoder design methods over spatially
correlated Ricean fading channels for MIMO systems with statistical CSI. Regarding
the statistical CSI feedback, the spatial correlation requires more feedback overhead
than the mean. Also, the estimation of the spatial correlation using training data will
consume bandwidth and will incur delay, apart from computations. Therefore, analytical spatial correlation analysis to derive a correlation expression for given spatial
antenna configurations can reduce feedback and bandwidth in training data.
Clustered channels with a hierarchical angle structure to describe azimuth angle
in terms of the direction of departures (DOD) at the transmitter antenna array and the direction of arrival (DOA) at the receiver antenna array have been used to model
communication channels in standards such as the 3GPP spatial channel model (SCM).
The cluster is a resolvable channel path composed of a number of unresolvable subpaths. In the hierarchical angle structure, the DOAs and DODs of the subpaths are
expressed as the sum of the cluster's centered angle and the subpaths' angle offsets. In
this thesis, two different hierarchical angle models are investigated to derive analytical
spatial correlation formulas for clustered channels. The first model assumes that the
centered angles of the clusters are independent Gaussian random variables while the
subpaths' angle offsets are deterministic as defined by 3GPP SCM. For the above
angle model, existing methods either require many expansion terms or limit clustered
angle spread within a small range to achieve the desired accuracy. This thesis derives
a simplified spatial correlation analysis by using the GaussHermite quadrature, to
avoid numerical integration for uniform linear array (ULA) and uniform circular array
(UCA). Compared with the existing expansion solutions, the number of terms, e.g.,
less than 10, required to generate accurate spatial correlations is much reduced.
The second hierarchical angle model treats the cluster's centered angle and subpaths' angle offsets as random variables. Hence the hierarchical angle is a bivariate,
which is different from the single random variable approach of the first model and
existing methods. It is assumed that the centered angle is Gaussian distributed while
the angle offset is Laplacian distributed. An analytical correlation formula is derived
for the above angle model for ULA and UCA . Computer evaluation shows that the
derived formula matches well with the simulated correlations with channel parameters
defined in the 3GPP SCM. The analytical spatial correlation expressions are useful
for system performance evaluation and precoder design.
In the literature, several precoder design methods using statistical CSIT over correlated Ricean fading channels were proposed. However, these methods can only provide either asymptotic solutions with degraded performance or noneigenstructured
iterative solutions with slow convergence and high computational complexity. In this
thesis, the eigenstructure of the precoder is exploited to improve the convergence
and computations. This eigenstructure approach is to convert the precoder design
into a joint power allocation and unitary beamforming design problem.
Kronecker correlation model is commonly used for modeling the spatial covariance matrix. Two transmit precoding schemes are proposed for MIMO systems over
correlated Ricean channels with Kronecker covariance matrix. The first scheme deals
with the case of correlated receive antennas' received data and uncorrelated transmit
antennas' transmitted waveform. It is known that the optimal BER based precoder is
the onedimensional scheme using the largest eigenmode (rank one) and equal power
control scheme for low and high signaltonoise ratios (SNRs), respectively. Based on
these asymptotic solutions at low and high SNRs, a simple scheme is proposed that
assumes only two values for power allocation. A bigger value is assigned to the largest
eigenbeam and a smaller value to the rest of eigenbeams. The two power control
values are optimized to minimize a pair error probability (PEP) bound. Simulations
show that the simplified solution can achieve a performance close to the existing
optimal solution with fast convergence speed.
The second scheme handles the general case of correlated transmit and receive
antennas. For this general correlation problem, the PEP bound is used as design
criterion with an average power constraint. Expressing the constrained optimization problem in terms of power control matrix and unitary matrix of the precoder,
the objective function and power constraint become nonlinear functions of the power
control parameters and unitary matrix. This optimization problem suffers from local
solution and convergence. By defining a new set of power constraint variables, the
power constraint is now a linear function of the new power control variables. For
given unitary matrix, the constrained optimization is a convex problem and the new
power parameters can be solved by numerical methods namely interior point method.
For given the power control parameters, we propose to employ the Riemannian optimization method to solve for the unitary beamforming matrix from the Lie group of
unitary space. The above iterative optimization procedure is shown to achieve local
optimal solution and guarantee convergence by computer simulation.
A generalized precoding scheme is proposed to handle the channel covariance
matrix of no specified spatial correlation structure. This general correlation structure can cover any double correlated channel including those of distributed antenna
systems. The existing iterative method that needs to search a fullrank precoding
matrix of large dimension has high computational complexity and slow convergence. Unfortunately, the convergence cannot be guaranteed. Our precoding scheme is also
an eigenstructure based solution composed of power allocation and unitary beamforming. Using a formulation similar to the Kronecker case, power allocation can be
solved as a sequential quadratic programming (SQP) problem and the unitary matrix obtained from the optimization method on Riemannian manifold. In comparing
with the existing method, the proposed method has a much lower matrix dimension
and thus has significant less computation. Simulation results show that the proposed
method can give a local optimal solution with guaranteed convergence.
 Wireless communication systems, MIMO systems, Coding theory