We proposed in our previous work an iterative minimum-mean-square-error (MMSE) cooperative positioning
algorithm. MMSE cooperative positioning method achieves better root-mean-square-error (RMSE) performance
than existing classical estimators. And it is implemented in an iterative pattern so as to circumvent the intense
computation burden of the numerical multiple integral computation methods. The basis of the proposed iterative
MMSE method is the single-node MMSE, which is actually the special case of the MMSE cooperative method
when the number of node <i>N</i> being 1. In this work, we study the properties of the single-node MMSE and
accordingly propose three variants of the original algorithm to improve the performance. The single-node MMSE
and its variants can also be used to produce initial position estimation for the maximum likelihood estimator
(MLE), one of the most popular existing classical estimators, and achieve almost the same performance as using
true positions as the initial positions.
We propose and study an iterative minimum-mean-square-error (MMSE) cooperative localization algorithm,
which achieves better root-mean-square-error (RMSE) performance than existing classical estimators. Using
the received signal strength (RSS) measurements, we first derive the formulas for estimating the coordinates
of position-unknown nodes. Then, we investigate the practical solutions to calculate the complicated multiple
integrals involved in the formulas and propose an adaptive and iterative algorithm to circumvent the intense
computation burden incurred by the numerical multiple integral computation methods. We further study the
proposed MMSE cooperative localization algorithm in the scenario where pair-wise range measurements are
incomplete, that is, pair-wise range measurements between certain pairs of nodes are missing. It is observed that
the performance degrades at a slower speed than the reduction of the available range measurements. In other
words, not much performance degradation is caused by comparatively large number of missing measurements.
Therefore, we can improve the efficiency of the iterative MMSE algorithm by intentionally throwing away certain
pair-wise range measurements.
Multiuser multiple-input multiple-output (MIMO) systems are considered in this paper. We continue our research
on uplink transmit beamforming design for multiple users under the assumption that the full multiuser channel
state information, which is the collection of the channel state information between each of the users and the
base station, is known not only to the receiver but also to all the transmitters. We propose an algorithm for
designing optimal beamforming weights in terms of maximizing the signal-to-interference-plus-noise ratio (SINR).
Through statistical modeling, we decouple the original mathematically intractable optimization problem and
achieved a closed-form solution. As in our previous work, the minimum mean-squared error (MMSE) receiver
with successive interference cancellation (SIC) is adopted for multiuser detection. The proposed scheme is
compared with an existing jointly optimized transceiver design, referred to as the joint transceiver in this paper,
and our previously proposed eigen-beamforming algorithm. Simulation results demonstrate that our algorithm,
with much less computational burden, accomplishes almost the same performance as the joint transceiver for
spatially independent MIMO channel and even better performance for spatially correlated MIMO channels. And
it always works better than our previously proposed eigen beamforming algorithm.