Semi-Blind Equalization for OFDM using Space-Time Block Coding and Channel Shortening Final Report Multidimensional Digital Signal Processing Spring 2008 Alvin Leung and Yang You May 9, 2008 Abstract Multiple input multiple output (MIMO) communications has become a stalwart in high speed communication systems. By using multiple antennas along with space-time coding, one can leverage spatial diversity gain, or multiple propagation paths, for transmitted signals. This in turn can improve reliability in communication systems. Channel shortening is necessary when the channel impulse response is longer than the cyclic prefix (CP) in a multi-carrier modulation scheme. This precludes low complexity signal recovery, also known as equalization, in the frequency domain. Equalization at the receiver can only be achieved by properly estimating the channel. While known symbols can be transmitted in order to achieve channel shortening and estimation, frequently sending out these pilot symbols may consume precious bandwidth. As an alternative, semi-blind approaches, which use known symbol structure and limited pilot symbols, have been receiving more attention. We propose a cascaded receiver design, which first performs channel shortening with a blind algorithm, using only the structure of the CP, developed by Martin et al. in [1]. The receiver then estimates the channel using a semi-blind technique [2], and uses the resulting channel estimate to perform frequency domain equalization. In this paper, we evaluate the combination of a blind channel shortening algorithm and semi-blind channel estimation in a linearly precoded space-time (ST) orthogonal frequency division multiplexing (OFDM) system.I. Introduction As the demand to stay constantly connected with the world grows, the necessity for high data rate communication systems has become ubiquitous. Using multiple antennas in a communication system introduces spatial diversity or multiple propagation paths for the transmitted signals, which creates new opportunities to increase the data rate of the system. In multiple input multiple output (MIMO) communication systems, the multiple antennas allow the designer to encode the transmitted signal over space as well as time. This technique, known as space-time coding, is a powerful way to leverage spatial diversity gain and improve transmission reliability with lower bit-error rates. In most wireless communication systems, we contend with a multipath channel which exhibits inter-symbol interference (ISI). That is, symbols being transmitted at different times can arrive simultaneously at the receiving antenna after traversing different paths. The multipath phenomenon can be attributed to propagation effects on radio frequency signals such as reflection and refraction. Many wireless standards which incorporate MIMO, such as IEEE 802.11n, IEEE 802.16e, 3rd Generation Partnership Project – Long Term Evolution (3GPP LTE), and IEEE 802.20, use orthogonal frequency division multiplexing (OFDM) due to its simplified equalization and resilience in multipath effects [3]. In multi-carrier systems, channel equalization is simplified because we can partition the channel into many narrowband flat-fading sub-channels that can be equalized individually. This is accomplished by pre-pending a cyclic prefix (CP) from the end of the transmitted OFDM symbol to the front of the transmitted OFDM symbol; to ensure that the convolution of the OFDM symbol with a multipath channel can be viewed as pointwise multiplication in frequency. In this report, we consider a MIMO OFDM system model using space-time coding. We evaluate the combination of a blind channel shortening algorithm proposed in [4] and the subspace based channel estimator in [5] using a realistic model of a time-varying channel. This report is organized as follows. After introducing basic concepts pertinent to our system such as blind channel shortening, and semi-blind channel estimation in Section II, we present our full system model in Section III. Section IV describes the model we used for a slowly time-varying channel,while Section V details the implementation of our project. Section VI provides concluding remarks and insights and summarizes this paper. II. Background A. Channel Shortening Frequency domain channel equalization is a popular technique used in recovering the transmitted signal at the receiver. However, in an OFDM communication system, channel shortening is necessary whenever the channel impulse response is longer than the cyclic prefix. After shortening, a frequency domain equalizer (FEQ), which is composed of a complex-valued gain for each frequency bin, corrects the residual amplitude scaling and phase rotation. The two traditional approaches to channel shortening are training-based and blind, extensively studied by Martin et al. in [6] and Melsa et al. in [7]. While the training-based approach usually yields faster equalizer convergence, the system can suffer from a decrease in throughput due to the need for frequent transmission of pilot tones in a time-varying channel. Blind methods excel in this regard, but may not converge as quickly as trained equalizers, nor do they provide a straightforward way to compute the optimal FEQ [1]. B. Semi-blind Channel Estimation To perform frequency domain equalization, we must still obtain a channel estimate at the receiver. The approaches to this problem are analogous to that of channel shortening. Sending out pilot tones intermittently for a training-based approach may consume precious bandwidth and decrease capacity, while purely blind schemes have trouble resolving an accurate channel estimate. Semi-blind approaches take advantage of the known structure in the transmitted sequence, and combine it with limited pilot tones in order to accurately estimate channels with minimal training overhead.III. System Model Fig 1. Space-time coded multiple input single output OFDM system model. Precoding is added by Θ1 and Θ2, followed by Alamouti space-time coding. The signals are then transmitted in parallel through channels D1 and D2, combined with Gaussian noise, and received by a single antenna. The signal is then filtered by the channel shortener, Alamouti decoded, and equalized by M and Γ. [5] Fig. 1 above illustrates the system model which we used for this project. We assume the use of a 4-QAM (Quadrature Amplitude Modulation) constellation for our symbols sequence