30,184 research outputs found
Inner Structure of Spin^{c}(4) Gauge Potential on 4-Dimensional Manifolds
The decomposition of gauge potential in terms of the Dirac 4%
-spinor is investigated, where an important characterizing equation has been discovered. Here is the vacuum
expectation value of the spinor field, , and
the twisting U(1) potential. It is found that when takes
constant values, the characterizing equation becomes an eigenvalue problem of
the Laplacian operator. It provides a revenue to determine the modulus of the
spinor field by using the Laplacian spectral theory. The above study could be
useful in determining the spinor field and twisting potential in the
Seiberg-Witten equations. Moreover, topological characteristic numbers of
instantons in the self-dual sub-space are also discussed.Comment: 11 page
Transmit Optimization with Improper Gaussian Signaling for Interference Channels
This paper studies the achievable rates of Gaussian interference channels
with additive white Gaussian noise (AWGN), when improper or circularly
asymmetric complex Gaussian signaling is applied. For the Gaussian
multiple-input multiple-output interference channel (MIMO-IC) with the
interference treated as Gaussian noise, we show that the user's achievable rate
can be expressed as a summation of the rate achievable by the conventional
proper or circularly symmetric complex Gaussian signaling in terms of the
users' transmit covariance matrices, and an additional term, which is a
function of both the users' transmit covariance and pseudo-covariance matrices.
The additional degrees of freedom in the pseudo-covariance matrix, which is
conventionally set to be zero for the case of proper Gaussian signaling,
provide an opportunity to further improve the achievable rates of Gaussian
MIMO-ICs by employing improper Gaussian signaling. To this end, this paper
proposes widely linear precoding, which efficiently maps proper
information-bearing signals to improper transmitted signals at each transmitter
for any given pair of transmit covariance and pseudo-covariance matrices. In
particular, for the case of two-user Gaussian single-input single-output
interference channel (SISO-IC), we propose a joint covariance and
pseudo-covariance optimization algorithm with improper Gaussian signaling to
achieve the Pareto-optimal rates. By utilizing the separable structure of the
achievable rate expression, an alternative algorithm with separate covariance
and pseudo-covariance optimization is also proposed, which guarantees the rate
improvement over conventional proper Gaussian signaling.Comment: Accepted by IEEE Transactions on Signal Processin
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