In multi-user multiple-input multiple-output (MUMIMO) systems, channel state information at the transmitter (CSIT) allows for multi-user spatial multiplexing and thus increases the system throughput. We assume that CSIT is obtained by means of a finite-rate feedback channel through channel vector quantization (CVQ) at the receiver. In this paper we use real channel measurements to study the effect of CVQ on the sum rate of a MU-MIMO system employing linear precoding. The measurement data has been acquired using Eurecom's MIMO Openair Sounder (EMOS). The EMOS can perform realtime MIMO channel measurements synchronously over multiple users. We consider CVQ using a Fourier codebook, a random codebook and a random codebook exploiting the second order statistics of the channel. For comparison, we also show the capacity of a single-user system using time division multiple access (TDMA) with no CSIT at all. The results show that the Fourier codebook shows very poor performance in the measured channels. Random codebooks--although suboptimal--provide a much better performance in the measured channels.