Multiclass support vector machines for adaptation in MIMO-OFDM wireless systems

Sungho Yun, Constantine Caramanis
2009 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
In MIMO-OFDM systems, by matching transmitter parameters such as modulation order and coding rate, link adaptation can increase the throughput significantly. However, creating a tractable mathematical mapping model from environmental variables to transmitter parameters that allows the latter to be optimized in any sense, presents serious challenginges due to the large number of variables involved, as well as the complexity required in any model with the ability to accurately capture and explain
more » ... capture and explain all factors that affect performance. Machine learning algorithms, which make no mathematical assumptions and use only past observations to model the input-output relationship, have recently been explored for adaptation in MIMO-OFDM systems. In this paper we propose a novel machine learning algorithm based on multi-class support vector machines (SVMs). Our algorithm has considerably smaller operational overhead (including storage requirements) and better performance for link adaptation. With IEEE 802.11n simulations we show that our new algorithm outperforms existing machine-learning based algorithms. Moreover, we show that our algorithm is (asymptotically) consistent, in the sense that as the number of training data used increases, our algorithm obtains the performance-optimal classifier. I. INTRODUCTION The limited available frequency spectrum and the demand for higher data rate, require future systems to provide significantly enhanced spectral efficiency in order to increase link throughput and network capacity. Multiple-input, multiple-output (MIMO) systems increase the throughput by simultaneously transmitting different streams of data on the different transmit antennas [1], [2] . They can be used to achieve multiple-fold improvement in the peak data rate provided that the MIMO channel is well conditioned. And indeed, this is the case in rich-scattering environments. Frequency-selective fading caused by multipath scattering can be handled by Orthogonal Frequency Division Multiplexing (OFDM). The effects of frequency-selective fading can be considered as flat over an OFDM subcarrier if the subcarrier is sufficiently narrow-banded. This makes equalization much simpler at the receiver in OFDM in comparison to conventional single-carrier modulation. As a result, the combination of MIMO with OFDM is a promising technique to enhance data traffic rate in physical layer. However, maximizing network throughput in higher layers requires systems to meet reliability constraints to reduce overhead caused by retransmissions. Hence, both high data rate and high reliability have to be achieved simultaneously. By matching transmitting parameters such as symbol modulation order, error control coding rate, and spatial multiplexing order to time varying channel conditions, adaptive modulation and coding (AMC) can increase the transmission rate considerably while meeting the reliability constraints at the same time [3], [4] . Unfortunately, the sheer number of environmental parameters such as signal energy, noise variance, channel state information for each subcarrier, time tap, and spatial stream, make it difficult to tune the transmission parameters appropriately. Moreover, many other additional and potentially subtle factors such as quantization error, non-gaussian noise effect, and non-linearity of systems make it almost impossible to obtain a mathematical model which can be tractably optimized to find the optimal (or even near-optimal) parameters to operate the system. Hence, link adaptation to a time-varying channel and environment conditions is challenging. Recently, there have been new flexible approaches to use machine learning algorithms for effective link adaptation [5]- [8] . The authors of [5] have proposed a non-parametric supervised learning algorithm based on k-nearest neighbor (k-NN). There, they show that a subset of ordered post-processing SNR can explain the frame error rate (FER) well, and moreover can do this with very low dimensions. Using this as a feature space, they further show that an adaptation of the k-NN algorithm provides accurate mapping from features to modulation and coding schemes (MCSs) and significantly outperforms other link adaptation algorithms in MIMO-OFDM systems. In this paper we use the feature set extraction scheme shown in [5] , namely ordered post-processing SNR, and develop a new machine learning algorithm based on multi-class support vector machines. The link-adaptation problem, unlike traditional classification problems, is in fact an optimization problem, in the sense that we seek to classify in order to optimize an objective (e.g., expected rate) as opposed to simply aiming to maximizing the probability of determining the "correct label."
doi:10.1109/allerton.2009.5394863 fatcat:6mdspd5aaje4xdcgk35qbegrha