Blind and Semiblind Channel Estimation - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 276

subspace decomposition, or multichannel frequency-domain deconvolution
have been reported in the literature. 43 Typically, assumptions include linear
time-invariant (LTI) systems, infinite SNR, and infinite equalizer length. 46 In
contrast, in real communication systems channels are time varying (TV), SNR
values are rather low in typical operation conditions, and equalizer lengths
are finite.
Using the model described by Equation 8.16, the goal of blind deconvolu-
tion is to estimate transmitted signals using a multichannel linear filter of the
form:

L

W l k y k − l ,

x k = (8.24)

l = 0

where W l k

are the ( m × n ) matrix coefficients of the separating system and L

is the filter order.
In the BSS research community, several methods for solving this problem
have been proposed; see Reference 44. Transmitted signals are assumed to be
statistically independent and non-Gaussian. Typically, the number of trans-
mitters m must be fewer than or equal to the number of receivers n . The
convolution in time domain may be changed into multiplication by doing
the processing in the frequency domain. Then, in the frequency domain we
have an I-MIMO model that may be solved more easily. The I-MIMO mixing
matrix needs to be of full rank. A solution based on BSS and natural gradient
adaptation is proposed in Reference 48. For more detail, see Reference 44.

8.5 Blind Receivers for GSM/EDGE

GSM is one of the most widely used wireless communication systems. GSM
is a TDMA system where each frequency band is shared by eight users, sep-
arated in time by their non-overlapping timeframes. Each frame consists of
two 58-bit data streams and a mid-amble of 26 bits length used for synchro-
nization and channel estimation. At first glance it can be observed that more
than 20% of the data burst is not used for transmitting data bits. Therefore,
schemes that can improve the effective data rate are desired.
Blind equalization is typically designed only for linear modulations, like
QAM. In such a system the received signal from a channel with the impulse
response h

( t ) is

∞

y ( t ) = a k h ( t − kT ) + w( t ) , a k ∈ A , (8.25)

k =−∞