M.Sc Thesis

M.Sc StudentAvner Yuval
SubjectOn Non-Linear Precoding Schemes for the Gaussian MIMO
Broadcast Channel
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Shlomo Shamai )Shitz(


In this thesis we consider non linear precoding schemes for the multiple input multiple output Gaussian broadcast channel. In the first part of this thesis we assume perfect side information at the transmitter (CSIT), namely, the values of the channel transfer matrix are perfectly known at the transmitter. For this case, the vector perturbation (VP) transmission method is investigated.

The alphabet relaxation, which is a fundamental tool in the vector perturbation method, is first formalized in terms of nested lattices.

Then, a time-domain generalization of the vector perturbation approach (TDVP) is presented.

Accordingly, the candidates for ``perturbing'' the transmitted signal are all elements belonging to a certain lattice over the time domain.

Since the VP method imposes an optimization problem which is NP-hard, a sub-optimal solution is suggested.

Using this solution, and for any number of users, the TDVP approach is shown to asymptotically achieve the sum capacity of the Gaussian broadcast channel in the high SNR regime, both in terms of degrees-of-freedom (DoF) and power offset.

For the original VP (one shot) scheme, it is shown that the power offset from the asymptotic sum capacity is given by a constant, which is due to the loss of shaping gain,

and does not depend on the channel realization. We then consider the case of a 2-users Gaussian broadcast channel. For this channel, we present a rate region which is achievable using TDVP.

These results shed some light on the close relation between the vector perturbation approach and the dirty paper approach, which is capacity achieving for this channel.

The second part of this thesis considers the case of imperfect CSIT. In order to isolate the main challenge this scenario presents, we focus on a model which is an extension of Costa's ``Writing on Dirty Paper''. In this model, the interference, which is perfectly known at the transmitter in a non-causal manner, is scaled by an i.i.d. ``fading'' process whose statistics are known. The realization of this process is known only at the decoder. For this model, we provide a set of achievable rates. We finally present these achievable rates in the context of a MIMO GBC setting.