Thursday, November 20, 2008

Interference Cancellation: III A Signal Subspace Perspective

[ Interference Cancellation. I. A Short Overview of Multiusr Detection ]
[ Interference Cancellation: II. A Conventional Receiver Design Perspective ]
[ Interference Cancellation: IV. A Blind Receiver Design Perspective ]

In realities it is known to be difficult to directly and precisely estimate the signal signatures {sk : k ≠ 1} for taking advantage of well-developed optimum or conventional multiuser detection schemes. In Figure 1, the design of a linear MMSE interference cancellation receiver for CDMA systems is shown as an example. As we can see, there are at least two challenges in the implementation. The first one is you need know the signal signatures of all involved users. The second one is it requires the computation-intensive matrix inverse operation. Design challenges like these make the conventional interference cancellation methodology unattractive in practical applications.

Figure 1. The challenges in employing conventional interference cancellation design. An example of linear MMSE interference cancellation

Now it is known that interference cancellation is able to be designed with a signal subspace model and statistic signal processing techniques for reconstructing the conventional detectors. Signal subspace methods are empirical linear approaches for dimensionality reduction and noise reduction in signal processing. They have attracted significant interest and investigation in the context of antenna array signal processing and speech signal processing for a long time. In later 1970s and early 1980s, G. Bienvenu and L. Kopp (1980) and R. O. Schmidt published their pioneer work applying signal subspace approaches on array signal processing. It is worth mentioning the well-known multiple signal classification (MUSIC) scheme introduced by R. O. Schmidt has been widely studied for estimating direction of arrivals (DOA) or frequency of arrivals (FOA). In 1901, Karl Pearson suggested the principal component analysis (PCA) approach, which essentially is similar to signal subspace approaches and widely applied in audio and speech signal processing. It is notable that Xiaodong Wang and Vincent Poor suggested further applying this concept on blind multiuser receiver design in 1998. The basic idea behind signal subspace approaches is to transform a series of samples, e.g., time-domain correlated samples, into a set of usually uncorrelated or less correlated representations in a linear subspace.

In the subspace signal model, the received signal vector r is modelled by a combination of the signal subspace bases {usk : 1 ≤ k ≤ K} according to

r = Us φ + n

where Us = [ us1 us2 . . . usK ], φ is a vector defined by

φ = Φ A b

With Φ being a K × K matrix. The original signal signature matrix S can now be expressed as

S = Us Φ .

One most attractive feature of the subspace signal model is that the signal subspace bases {usk : 1 ≤ k ≤ K} are much easier to be blindly estimated than the actual signal signature waveform so that the blind receiver design can be simplified. In theory, these signal bases can be estimated by applying subspace decomposition on the autocorrelation matrix R

R = E{ rrH } = [ Us Un ] diag{[Λs Λn]} [ Us Un ]H

where Un denotes the noise subspace bases.

Figure 2. Mathematical illustration of signal subspace linear MMSE interference cancellation

With the signal subspace approach, the linear MMSE interference cancellation shown in Figure 1 now can be redesigned in a different way. This is shown in Figure 2 and 3.  The estimation and separation of signal and noise subspaces essentially help identify the signal signature of the desired components from the received signals. On  the other conventional MMSE receiver can be blindly constructed with the signal and noise subspaces bases.  No explicit signal signature estimation is necessary.

Figure 3. The receiver structure of signal subspace linear MMSE interference cancellation

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