Minimum Energy to Send kk Bits Over Multiple-Antenna Fading Channels

This paper investigates the minimum energy required to transmit $k$ information bits with a given reliability over a multiple-antenna Rayleigh block-fading channel, with and without channel state information (CSI) at the receiver. No feedback is assumed. It is well known that the ratio between the minimum energy per bit and the noise level converges to $-1.59$ dB as $k$ goes to infinity, regardless of whether CSI is available at the receiver or not. This paper shows that lack of CSI at the receiver causes a slowdown in the speed of convergence to $-1.59$ dB as $k\to\infty$ compared to the case of perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap to $-1.59$ dB is proportional to $((\log k) /k)^{1/3}$, whereas when perfect CSI is available at the receiver, this gap is proportional to $1/\sqrt{k}$. In both cases, the gap to $-1.59$ dB is independent of the number of transmit antennas and of the channel's coherence time. Numerically, we observe that, when the receiver is equipped with a single antenna, to achieve an energy per bit of $- 1.5$ dB in the no-CSI case, one needs to transmit at least $7\times 10^7$ information bits, whereas $6\times 10^4$ bits suffice for the case of perfect CSI at the receiver

Interleaving Channel Estimation and Limited Feedback for Point-to-Point Systems with a Large Number of Transmit Antennas

We introduce and investigate the opportunities of multi-antenna communication schemes whose training and feedback stages are interleaved and mutually interacting. Specifically, unlike the traditional schemes where the transmitter first trains all of its antennas at once and then receives a single feedback message, we consider a scenario where the transmitter instead trains its antennas one by one and receives feedback information immediately after training each one of its antennas. The feedback message may ask the transmitter to train another antenna; or, it may terminate the feedback/training phase and provide the quantized codeword (e.g., a beamforming vector) to be utilized for data transmission. As a specific application, we consider a multiple-input single-output system with $t$ transmit antennas, a short-term power constraint $P$, and target data rate $\rho$. We show that for any $t$, the same outage probability as a system with perfect transmitter and receiver channel state information can be achieved with a feedback rate of $R_1$ bits per channel state and via training $R_2$ transmit antennas on average, where $R_1$ and $R_2$ are independent of $t$, and depend only on $\rho$ and $P$. In addition, we design variable-rate quantizers for channel coefficients to further minimize the feedback rate of our scheme.Comment: To appear in IEEE Transactions on Wireless Communication

A New Transmit Diversity Method Using Quantized Random Phases

Wireless communication systems, aside from path-loss, also suffer from small scale up-and- down variations in the power of the received signal. These fluctuations in the received signal power, commonly referred to as multi-path fading, result in a significant perfor- mance degradation of the system. One way to combat fading is diversity. The idea behind diversity is to provide the receiver with multiple independent copies of the transmitted signal, either in time, frequency or space dimension. In broadcast networks with underlying slow-faded channels, an appropriate option for exploiting diversity is transmit diversity, which deploys several antennas in the transmitter terminal. Based on the amount of available channel state information on the transmitter side, various transmit diversity schemes have been proposed in the literature. Because of certain limitations of broadcast networks, a practical assumption in these networks is to provide no channel state information for the transmitter. In this dissertation, a new scheme is proposed to exploit transmit diversity for broad- cast networks, assuming no channel state information in the transmitter. The main idea of our proposed method is to virtually impose time variations to the underlying slow-faded channels by multiplying quantized pseudo-random phases to data symbols before trans- mission. Using this method, all necessary signal processing can be transferred to the RF front-end of the transmitter, and therefore, the implementation cost is much less than that of alternative approaches. Under the proposed method, the outage probability of the system is analyzed and the corresponding achievable diversity order is calculated. Simulation results show that the performance of our proposed scheme falls slightly below that of the optimum (Alamouti type) approach in the low outage probability region

Proof of the Outage Probability Conjecture for MISO Channels

It is conjectured that the covariance matrices minimizing the outage probability under a power constraint for multiple-input multiple-output channels with Gaussian fading are diagonal with either zeros or constant values on the diagonal. In the multiple-input single-output (MISO) setting, this is equivalent to conjecture that the Gaussian quadratic forms having largest tail probability correspond to such diagonal matrices. This paper provides a proof of the conjecture in this MISO setting