3:30, SPCOM-L9.1
CONVEXITY IN SISO BLIND EQUALIZATION
M. CORLAY, M. CHARBIT, P. DUHAMEL
In [1], a new class of blind equalization cost functions was proposed. They have the particularity of being unimodal, and some of them, sectionally convex in the Combined System Domain (CDS), both properties seeming very attractive for a cost function, though no proof (or specific definition) was given of the sectional convexity. In this paper we show, using a particular case of this class, that sectional convexity not only implies to fix a delay, but that it also requires to fix the value of the coefficient associated to such delay. We show that the CMA criterion shares the same property, and the difficulty of maintaining this property in actual algorithms.

3:50, SPCOM-L9.2
FIR CHANNEL IDENTIFICATION IN MULTIRATE COMMUNICATION SYSTEMS WITH A SUBSPACE METHOD
H. YAN, S. ROY
The problem of blind channel identification for multirate, multi-user communication systems is addressed. By exploiting symbol rate differences, it is shown that users can be separated based on the autocorrelation of the received signal, thus reducing the problem to the familiar single rate setting. A subspace method is then developed to identify the channel associated with each user. Simulations are used to explore algorithm performance as a function of key factors such as signal to noise ratio (SNR) and signal to interference ratio (SIR).

4:10, SPCOM-L9.3
INTERACTING MULTIPLE MODEL FOR SINGLE-USER CHANNEL ESTIMATION AND EQUALIZATION
M. JAWARD, V. KADIRKAMANATHAN
In this paper, a blind sequence estimation algorithm based on interacting multiple model is introduced to estimate the channel and the transmitted sequence corrupted by ISI (intersymbol interference) and noise. The proposed algorithm avoids the exponential growth complexity caused by increasing channel memory length. The performance of the IMM (interacting multiple model) based equalizer is studied and compared with the well known algorithm like DDFSE (Delayed Decision-Feedback Sequence Estimation).

4:30, SPCOM-L9.4
OPTIMAL TRAINING FOR FREQUENCY-SELECTIVE FADING CHANNELS
H. VIKALO, B. HASSIBI, B. HOCHWALD, T. KAILATH
Many communications systems employ training, i.e., the transmission of known signals, so that the channel parameters may be learned at the receiver. This has a dual effect: too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. In this paper we use an information-theoretic approach to find the optimal amount of training for frequency selective channels described by a block-fading model. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the length of the channel impulse response. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger. We further show that at high SNR training-based schemes are capable of capturing most of the channel capacity, whereas at low SNR they are highly suboptimal.

4:50, SPCOM-L9.5
OPTIMAL DESIGN AND PLACEMENT OF PILOT SYMBOLS FOR CHANNEL ESTIMATION
M. DONG, L. TONG
The problem of design and placing pilot symbols for the estimation of frequency selective random channels is considered. For both SISO and MIMO channels, the Cramer-Rao Bound (CRB) on the mean square error of channel estimators is derived and minimized with respect to the pilot symbols and their placement. It is shown that placing pilot symbols, possibly in multiple clusters, in the middle of the data packet leads to minimum CRB.

5:10, SPCOM-L9.6
STRUCTURED MMSE EQUALIZATION FOR SYNCHRONOUS CDMA WITH SPARSE MULTIPATH CHANNELS
S. CHOWDHURY, M. ZOLTOWSKI, J. GOLDSTEIN
We present chip-level MMSE equalizers for the forward link in CDMA that exploit the underlying channel structure, specifically the fact that the channel impulse response is sparse. The assumption we make is that the channel vector lies in the subspace assciated with the pulse shaping filter convolution matrix. We can then project the chip-level MMSE equalizers onto a much lower dimensional subspace due to the sparseness of the channel. The simulations demonstrate that this low-rank MMSE equalizer converges very quickly to the asymptotic SINR, even where the underlying assumption is not valid.