An Efficient Feedback Scheme with Adaptive Bit Allocation for Dispersive MISO Channels Leonid G. Krasny and Dennis Hui Ericsson Research, 8001 Development Drive, RTP, NC 27709, USA leonid.krasny@ericsson.com, dennis.hui@ericsson.com Abstract—In this paper, we focus on a cellular system with M transmit antennas at the base station (BTS) and one receive antenna at the mobile (i.e. an M-input/single-output (MISO) channel), where the BTS commands each mobile to transmit its channel state information back to the BTS. Our main result is a specific feedback scheme with adaptive bit allocation, where a binary tree-structured vector quantizer is used to separately quantize each channel tap at a different level of quantization. We show that the proposed feedback scheme allows us to exploit the different statistics of the channel taps and results in a performance very close (within 1dB) to the performance that can be obtained with perfect channel knowledge at the BTS. I. I NTRODUCTION The focus of this paper is communication over dispersive multiple-input/single-output (MISO) channels where the re- ceiver informs the transmitter of the state of these downlink channels, and these channels are block fading (i.e. the fading coefficients are constant during each coding block, but they change independently from block to block). The problem of feeding back detailed channel information has been studied by a number of authors. In [1]- [3] a codebook design criterion has been proposed for quantizing the transmit beamforming vectors in flat MIMO channels. It has been shown that for a flat channel the near-optimal beamformer codebooks can be constructed by minimizing the maximum inner product between any two beamforming vectors in the codebook. This design criterion is similar to the design criterion of signal constellations for Gaussian channels, which maximizes the minimum Euclidean distance between any two signal points in the constellation. However, the design criterion does not apply to dispersive MISO channels. The feedback method that can work in dispersive MISO channels has been proposed in [4]. This feedback method is particularly well-suited for wireless packet data cellular systems on the downlink where the entire downlink channel is allocated to one downlink user at a time. Meanwhile, the feedback scheme of [4] consumes a large proportion of uplink resources to achieve high level of performance. For example, it was shown in [4] that for a 4-tap channel, the mobile should send 160 bits to the BTS to get reasonable performance. In this paper, we present a more effective feedback scheme with adaptive bit allocation, where a binary tree-structured vector quantizer (TSVQ) is used to separately quantize each channel tap at a different level of quantization. We show that such approach allows us to exploit the different statistics of the channel taps in order to reduce the amount of feedback. This results in a performance very close to the performance that is obtained with perfect channel knowledge at the transmitter. The outline of the rest of this paper is as follows. In section II, a model for the MISO channel is presented along with a transmitter structure. In Section III, we propose the feedback scheme with adaptive bit allocation. Then, we show that the feedback scheme proposed in [4] can be viewed as an instance of a conventional TSVQ. In Section IV, Monte- Carlo simulations are used to show that our feedback method results in a performance (in terms of maximum data rate that can be reliably transmitted to each mobile) very close to the performance that can be obtained with perfect channel knowledge at the BTS. Finally, Section V concludes the paper. II. SYSTEM MODEL Our system model is presented in Fig.1. In this figure, b[n]’s are the information bits at the transmitter which are coded and modulated to get the analog, complex, baseband signal s(t). The base station (BTS) transmitter has M transmit antennas, and on the m-th antenna the signal s(t) is passed through a pre-filter with impulse response h(t, m). The impulse response of the downlink channel from the m-th transmit antenna to the single receive antenna at the mobile is assumed to be linear time invariant and is denoted by g(t, m). Therefore, the received baseband signal at the receiver can be expressed by: r(t)= M  m=1 h(t, m) ⋆g(t, m) ⋆s + v(t), (1) where “⋆” denotes convolution, and v(t) is the baseband noise. For closed-loop MISO antenna systems (cf. [5]), the pre- filters h(t, m) in Fig.1 are just the scaled versions of the filters matched to the forward channels g(t, m), i.e., h(t, m)= αg * (−t, m), (2) where α is a real, positive scaling factor used to ensure that the total transmit power σ 2 X is constant, regardless of the actual channel realization. One can see that the closed-loop MISO scheme requires that the forward link channel knowledge be fed back explicitly from the receiver to the transmitter.. 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP