Achieving near Beamforming Performance with Quantized CSI V. Ganesh Electrical Engineering IIT Madras, Chennai - 600 036 ee04s009@ee.iitm.ac.in Devendra Jalihal Electrical Engineering IIT Madras, Chennai - 600 036 dj@tenet.res.in Abstract Beamforming needs to have the channel state informa- tion (CSI) at the transmitter. The CSI is measured at the receiver and is fed back to the transmitter in the quan- tized form. Quantized CSI affects the BER performance. Casting the problem of quantization as a vector quanti- zation (VQ) problem, we try to quantize the channel in- formation in such a way as to minimize the loss in the performance due to quantization. We examine a reduced parameter feedback of the channel information for beam- forming (maximal ratio transmission or MRT) and show that the performance of MRT is better than that of phase- alone feedback (equal gain transmission or EGT) systems for identical number of bits used. We also derive a new clustering algorithm which aims at maximizing the beam- forming gain and propose a new cost function that mini- mizes the performance loss in using the quantized beam- forming vector for full channel information feedback. 1. Introduction In mobile communications, the adverse effect of chan- nel fading can be mitigated by transmission over differ- ent antennas which see independent channels. A large and growing body has firmly established the potential of orthogonal space time block codes (O-STBC) in multi- input single-output (MISO) systems that use antenna ar- rays at the transmitter to provide spatial diversity and enhanced capacity [1], [2]. Compared with traditional space-time codes, beamforming provides the diversity order and array gain at the expense of requiring chan- nel state information (CSI) at the transmitter in the form of transmit beamforming vector. Unfortunately, in sys- tems where the forward and reverse links are not recipro- cal, CSI should be quantized to accommodate the limited bandwidth feedback channel. When the partial CSI or quantized CSI is known at the transmitter efficient pre- coding can be performed to extract the array gain [6] and [8] which improves the link performance. Since the per- formance of the MISO system depends on the quantized CSI at the transmitter, quantization should be efficient enough to represent the perfect CSI known at the receiver. In this paper, performance degradation due to quantiza- tion is studied using vector quantization (VQ) technique. We propose two new VQ based algorithms for efficient feeding back of quantized channel parameters; the first uses a reduced parameter set and a simple MSE criterion and the second one uses a new cost function and a new stopping criterion for achieving the beamforming gain. This paper is organized as follows. Section II provides a general overview of the system design under consid- eration. Section III describes the quantization schemes and their performance with simulation results. Section IV concludes the paper. 2. System Model Consider a system with N t =2 and 3 transmit antennas and N r =1 receive antenna. Let h, an N t × 1 chan- nel vector, denote the channel. This paper considers 4- QAM modulation scheme with channel h considered as a complex Gaussian with variance σ 2 h =1 and zero mean. At the receiver, white Gaussian noise is added with zero mean and variance σ 2 , which is varied to achieve differ- ent SNRs. With these assumptions, the received symbol at the i th instant with perfect CSI at the transmitter for 2 × 1 system will be given by y i = h i1 w i1 x i + h i2 w i2 x i + n i (1) where w ij is the beamforming weight given by w ij = h ∗ ij ‖h i ‖ (2) where h ij is the channel at i th instant seen by j th an- tenna, ‖h i ‖ 2 = |h i1 | 2 + |h i2 | 2 is the beamforming gain and x i is the transmitted symbol over both antennas at i th instant. We omit subscript i for clarity. 3. Quantized Channel Feedback 3.1. Background We will consider here quantized values of the channel informations assumed to be perfectly known at the re- ceiver. Prior work on this topic is dealt in [6] and where precoding is done over O-STBC with the quantized chan- nel information available at the transmitter. Other work Home Sessions Authors Session 3.1 | | |