*2.1. Millimeter-Wave Propagation*

For a point-to-point LOS mmWave link, the received power *PB* (dBm) may be related to the transmitted power *PT* (dBm); the antenna gains *GT* (dBi) and *GR* (dBi); and the propagation path loss (*PL*), atmospheric loss (*AL*) and other losses (*OL*). The link can be written as:

$$P\_B = P\_T + G\_T + G\_R - PL - AL - OL \tag{1}$$

The propagation path loss can be expressed as [34]:

$$\text{PL}(f\_{\mathbb{C}}, d) = 32.4 + 20 \log 10 \text{(f\_{\mathbb{C}})} + 10n \log 10 \text{(d/d\_0)} + \chi\_{\mathbb{C}}, d \ge 1m \tag{2}$$

where *fc* denotes the carrier frequency in GHz, *d* is the transmitter and receiver separation distance, the reference distance *d0* is 1 m, and *n* represents the path loss exponent. Here, χσ is a zero-mean Gaussian random variable with a standard deviation σ in dB.

#### *2.2. LOS-MIMO-Based mmWave Backhaul System*

The principle ofa2x2 LOS-MIMO microwave backhaul link is to design a MIMO channel with a phase difference of 90 degrees between short and long paths to make the signal streams orthogonal to each other. The channel is denoted by a *N* × *M* matrix **H**, and each element represents the channel from the *m*th transmit (Tx) antenna to the receive (Rx) antenna *n*th. Note that *N* = *M* = 2 in our measurement setup. Each element of the channel matrix can be written as *Hmn* = *ej*θ*mn* , where θ*mn* is the phase of the sub-channel. For the phase of the sub-channel from the *n*th transmit antenna to the *m*th receive antenna, θ*mn* <sup>=</sup>2π*rmn*/λ, where λ is the wavelength and *rmn* is the propagation distance between the transmit antenna *n* and receive antenna *m* [19,20]. This can be achieved by designing the antenna separation distance at the transmitter *d*1 and receiver *d*2 to fulfill, *d*1 x *d*2 = λ*L*/*N,* where *L* is the path length between the transmit site and receive site. Let **X** and **Y** denote the transmit and receive signal vector, respectively. The *N* × 1 received signal vector can be written as:

$$\begin{aligned} \mathbf{Y} &= \sqrt{\mathcal{P}\_{\overline{R}}} \mathbf{H} \mathbf{X} + \mathbf{W} \\ \begin{bmatrix} Y\_1 \\ Y\_2 \end{bmatrix} &= \sqrt{\mathcal{P}\_{\overline{R}}} \begin{bmatrix} H\_{11} & H\_{12} \\ H\_{21} & H\_{22} \end{bmatrix} \begin{bmatrix} X\_{A1} \\ X\_{A2} \end{bmatrix} + \begin{bmatrix} W\_1 \\ W\_2 \end{bmatrix} \end{aligned} \tag{3}$$

where **W** is the *N* × 1 complex additive white Gaussian noise vector and its variance equals *No*; *PR* is the average received power, expressed in watts, where *PR* = 10*PB*/10.

In practice, a sub-optimal linear zero-forcing algorithm can be applied to simply invert the channel and independently decode the data streams at the receiver to recover the spatially multiplexed signals:

$$\mathbf{G} = P\_R^{-1/2} \mathbf{H}^+ = P\_R^{-1/2} \left( \mathbf{H}^\text{H} \mathbf{H} \right)^{-1} \mathbf{H}^\text{H} \tag{4}$$

The character + denotes the pseudo-inverse operation. By applying the pseudo-inverse of the channel matrix to the received signal we get:

$$\begin{aligned} \overline{\mathbf{X}} &= \mathbf{G} \Big( P\_{\overline{R}}^{-1/2} \mathbf{H} \mathbf{X} + \mathbf{W} \Big) = \mathbf{X} + \mathbf{G} \mathbf{W} \\ &= \mathbf{X} + P\_{\overline{R}}^{-1/2} \mathbf{H}^{+} \mathbf{W} \end{aligned} \tag{5}$$

The SNR after interference cancellation for the *i*th sub-channel is given as:

$$SNR\_i = \frac{P\_R}{N\_0 \left[ \left( \mathbf{H}^H \mathbf{H} \right)^{-1} \right]\_{i,i}} \tag{6}$$

Here, **H** *H* **H** -−1 *i*,*i* refers to the (i, i)th elements of **H** *H* **H** -−1. The independent and identical (i.i.d) MIMO channel capacity, assuming equal transmit power, is given as:

$$C = \sum\_{i=1}^{N} \log\_2(1 + SNR\_i) \tag{7}$$

where (·) *H* denotes the Hermitian transpose.
