# Ultra-Reliable Link Adaptation for Downlink MISO Transmission in 5G Cellular Networks
## 2 System Model
### SINR Estimation  
Link adaptation is based on the measurement performed by the intended receiver at a time \(t=0\). Known pilot symbols \(z_{k}\) are transmitted with at least \(N_{T}\) orthogonal precoding vectors \(\mathbf{w}_{k}\in\mathbb{C}^{N_{T}\times 1}\), for \(k=1,\ldots,N_{T}\). We assume that all of these transmissions happen essentially simultaneously. With \(J\) transmissions from known interferers, the signal received at the user of interest at \(t=0\) for pilot transmission \(k\)  
\[y_{0,k}=\mathbf{h}_{0}\mathbf{w}_{0,k}z_{k}+\sum_{j=1}^{J}\mathbf{h}_{0,j} \mathbf{v}_{0,j}x_{j}+n \tag{1}\]  
where \(\mathbf{h}_{0}\in\mathbb{C}^{1\times N_{T}}\) is the channel gain vector for the desired transmission, \(\mathbf{h}_{0,j}\) are the interfering channel vectors from transmitter \(j\) to the user of interest, and \(\mathbf{v}_{0,j}\in\mathbb{C}^{N_{T}\times 1}\) are the precoders applied by the interfering transmitters, all at the time of measurement \(t=0\), on the time-frequency resource used for pilot transmission \(k\). Here, \(x_{j}\) are the transmit symbols on \(j\)th transmission. All transmitted symbols are assumed to be of unit average energy, and all precoding vectors are assumed unit norm. As a concrete channel model we consider independent and identically distributed (i.i.d.) Rayleigh fading. The elements in the channel vectors \(\mathbf{h}_{0}\) and \(\mathbf{h}_{0,j}\) are assumed to be drawn from independent complex Gaussian processes with zero mean and variance \(S_{\text{ave}}\) and \(I_{\text{avej}}\), respectively. These variances carry information of the path losses of the signals. The channel realizations developed under fading processes after the measurement are drawn from the same distribution as the channels at a given measurement instance, and are conditioned on the measurement results. Additive White Gaussian Noise (AWGN) with variance \(N_{0}\) is denoted by \(n\). This variable may also model interference from other than the \(J\) known sources, which is assumed Gaussian. We assume multiple orthogonal pilot transmissions of the form Equation (1) extending over multiple transmissions within a coherence time and bandwidth of the channels. This enables the receiver to reliably estimate the channel \(\mathbf{h}_{0}\). Canceling the transmissions of the known pilot signals over the estimated channels from signals of Equation (1), interference plus noise powers can be estimated, and accordingly SINRs. Finally, we assume that the receiver knows the pilot signals of the \(J\) known interferers as well. In a communication frame at measurement time \(t=0\), there would thus be received signals of the type Equation (1) for the pilots of the \(J\) known interferers, making it possible to separate the contributions of the interferers to interference plus noise power at the time of measurement. Collecting statistics over longer periods, it is possible to estimate characteristics of the statistical distributions of the channels. Here, we assume these statistics are perfectly known. Collecting such statistics would be possible in environments where the channels remain wide sense stationary for extended periods of time, e.g., in factory environments [19]. For a forthcoming transmission to the user of interest, a precoder \(\mathbf{v}_{0}\) is selected, either based on the measurements at time \(t=0\), or by some other means. If the transmitter selects the precoder, it is informed to the user. As a result, we have an estimated SINR  
\[\gamma_{0}=\frac{|\mathbf{h}_{0}\mathbf{v}_{0}|^{2}}{\sum_{j=1}^{J}|\mathbf{h }_{0,j}\mathbf{v}_{0,j}|^{2}+N_{0}} \tag{2}\]  
for a forthcoming transmission. If the precoder is selected based on the user channel only, a typical choice would be to take \(\mathbf{v}_{0}\) to be a normalized version of \(\mathbf{h}_{0}^{H}\), or a quantized version thereof. Otherwise it may be, e.g., a common precoder which is used to serve all users in the cell in order to stabilize inter-cell interference. The \(J\) interfering transmissions are assumed to be independent.