Robust Optimization for Multi-Antenna Downlink Transmission in Cellular Networks

Student thesis: Doctoral ThesisDoctor of Philosophy


In multi-cell networks where resources are aggressively reused and the cell
sizes are shrinking to accommodate more users, eliminating interference is
the key factor to reduce the system energy consumption. This growth in
the demand of wireless services has urged the researchers to find new and
efficient ways of increasing coverage and reliability, i.e., coordinated signal
processing across base stations. The optimum exploitation of the benefits
provided by coordinated signal processing can be achieved when a perfect
channel state information at transmitter (CSIT) is available. The assumption
of having perfect knowledge of the channel is, however, often unrealistic
in practice. Noise-prone channel estimation, quantization effects, fast
varying environment combined with delay requirements, and hardware limitations
are some of the most important factors that cause errors. Providing
robustness to imperfect channel state information (CSI) is, therefore, a task
of significant practical interest.
Current robust designs address the channel imperfections with the worstcase
and stochastic approaches. In worst-case analysis, the channel uncertainties
are considered as deterministic and norm-bounded, and the resulting
design is a conservative optimization that guarantees a certain quality of
service (QoS) for every allowable perturbation. The latter approach focuses
on the average performance under the assumption of channel statistics, such
as mean and covariance. The system performance could break down when
persistent extreme errors occur. Thus, an outage probability-based approach
is developed by keeping a low probability that channel condition
falls below an acceptable level. Compared to the worst-case methods, this
approach can optimize the average performance as well as consider the extreme
scenarios proportionally.
In existing literature, robust precoder designs for single-cell downlink transmissions have been extensively investigated, where inter-cell interference
was treated as background noise. However, robust multi-cell signal processing
has not been adequately explored.
In this thesis, we focus on robust design of downlink beamforming vectors
for multiple antenna base stations (BSs) in a multi-cell interference
network. We formulate a robust distributed beamforming (DBF) to independently
design beamformers for the local users of each BS. In DBF, the
combination of each BS’s total transmit power and its resulting interference
power toward other BSs’ users is minimized while the required signal-tointerference-
plus-noise-ratios (SINRs) for its local users are maintained.
In our first approach of solving the proposed robust downlink beamforming
problem for multiple-input-single-output (MISO) system, we assume only
imperfect knowledge of channel covariance is available at the base stations.
The uncertainties in the channel covariance matrices are assumed to be confined
in an ellipsoids of given sizes and shapes. We obtain exact reformulations
of the worst-case quality of service (QoS) and inter-cell interference
constraints based on Lagrange duality, avoiding the coarse approximations
used by previous solutions. The final problem formulations are converted
to convex forms using semidefinite relaxation (SDR). Through simulation
results, we investigate the achievable performance and the impact of parameters
uncertainty on the overall system performance.
In the second approach, in contrast to the ‘average case’ and ‘worst-case’ estimation
error scenarios in the literature, to provide the robustness against
channel imperfections, the outage probability-based approach is proposed
for the aforementioned optimization problem. The outages are due to the
uncertainties that naturally emerge in the estimation of channel covariance
matrices between a BS and its intra-cell local users as well as the
other users of the other cells. We model these uncertainties using random
matrices, analyze their statistical behavior and formulate a tractable
probabilistic approach to the design of optimal robust downlink beamforming
vectors by transforming the probabilistic constraints into a semidefinite
programming (SDP) form with linear matrix inequality (LMI) constraints.
The performance and power efficiency of the proposed probabilistic algorithm
compare to the worst-case approach are assessed and demonstrated
through simulation results.
Finally, we shift to the case where imperfect channel state information is
available both at transmitter and receiver sides; hence we adopt a bounded
deterministic model for the error in instantaneous CSI and design the downlink
beamformers. The robustness criterion is to minimize the transmitted
power while guaranteeing a certain quality of service per user for every possible
realization of the channel that is compatible with the available channel
state information. To derive closed form solutions for the original nonconvex
problem we transform the worst-case constraints into a SDP with
LMI constraints using the standard rank relaxation and the S-procedure.
Superiority of the proposed model is confirmed through simulation results.
Date of Award2015
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorMohammad Nakhai (Supervisor) & Vivien Chu (Supervisor)

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