Diversity coding is a network restoration technique which offers near-hitless
restoration, while other state-of-the art techniques are signi?cantly slower.
Furthermore, the extra spare capacity requirement of diversity coding is
competitive with the others. Previously, we developed heuristic algorithms to
employ diversity coding structures in networks with arbitrary topology. This
paper presents two algorithms to solve the network design problems using
diversity coding in an optimal manner.
Beamforming techniques employing Singular Value Decomposition (SVD) are
commonly used in Multi-Input Multi-Output (MIMO) wireless communication
systems. For frequency selective channels, Bit-Interleaved Coded Multiple
Beamforming with Orthogonal Frequency Division Multiplexing (BICMB-OFDM) can be
applied to achieve both spatial diversity and multipath diversity. However, the
diversity analysis of BICMB-OFDM is a challenging problem because of its
complicated system structure.
In Singular Value Decomposition (SVD) beamforming, without channel coding,
there is a trade-off between full diversity and full multiplexing. Adding
channel coding, full diversity and full multiplexing can be both achieved, as
long as the code rate Rc and the number of subchannels S satisfy RcS<=1.
The Golden Code is a full-rate full-diversity space-time code, which achieves
maximum coding gain for Multiple-Input Multiple-Output (MIMO) systems with two
transmit and two receive antennas. Since four information symbols taken from an
M-QAM constellation are selected to construct one Golden Code codeword, a
maximum likelihood decoder using sphere decoding has the worst-case complexity
of O(M^4), when the Channel State Information (CSI) is available at the
receiver. Previously, this worst-case complexity was reduced to O(M^(2.5))
without performance degradation.
Beamforming techniques that employ Singular Value Decomposition (SVD) are
commonly used in Multi-Input Multi-Output (MIMO) wireless communication
systems. In the absence of channel coding, when a single symbol is transmitted,
these systems achieve the full diversity order provided by the channel; whereas
when multiple symbols are simultaneously transmitted, this property is lost.
When channel coding is employed, full diversity order can be achieved.
The computational complexity of optimum decoding for an orthogonal space-time
block code G satisfying the orthogonality property that the Hermitian transpose
of G multiplied by G is equal to a constant c times the sum of the squared
symbols of the code times an identity matrix, where c is a positive integer is
quantified. Four equivalent techniques of optimum decoding which have the same
computational complexity are specified. Modifications to the basic formulation
in special cases are calculated and illustrated by means of examples.
The complexity of sphere decoding (SD) has been widely studied in that the
algorithm is vital in providing the optimal Maximum Likelihood performance with
low complexity. In this paper, we propose a proper tree search technique that
reduces overall SD computational complexity without sacrificing performance. We
build a check-table to pre-calculate and store some terms, temporally store
some mid-stage terms, and take advantage of a new lattice representation of our
previous work.
In this paper, we present the diversity order analysis of bit-interleaved
coded multiple beamforming (BICMB) combined with the constellation precoding
scheme. Multiple beamforming is realized by singular value decomposition of the
channel matrix which is assumed to be perfectly known to the transmitter as
well as the receiver. Previously, BICMB is known to have a diversity order
bound related with the product of the code rate and the number of parallel
subchannels, losing the full diversity order in some cases.
In this paper, we present the diversity order analysis of bit-interleaved
coded multiple beamforming (BICMB) combined with the constellation precoding
scheme. Multiple beamforming is realized by singular value decomposition of the
channel matrix which is assumed to be perfectly known to the transmitter as
well as the receiver. Previously, BICMB is known to have a diversity order
bound related with the product of the code rate and the number of parallel
subchannels, losing the full diversity order in some cases.