# <center><i class="fa fa-edit"></i>Background Knowledge</center>
###### tags: `Internship`
:::success
The study objectives were to:
- Gain deeper knowledge about Multi-user (MU) transmission, OFDMA, and Joint MU-MIMO OFDMA
- Understand in detail about the system method related to 802.11ax
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**Reference:**
- [About OFDMA](https://www.cisco.com/c/en/us/products/wireless/what-is-ofdma.html?dtid=osscdc000283)

:::spoiler Click to view the fundamentals knowledge in detail, you can skip this if you already understand
### Multi-user (MU) transmission
Multi-user (MU) transmission in WiFi network is an important feature which can improve the system throughput greatly. It was first introduced in 802.11ac standard. The MU transmission in 802.11ac relies on downlink MU-MIMO, which makes use of spatial diversity to cancel the interference between users. In one MU-MIMO transmission, the frame takes the whole bandwidth.
> 802.11ax supports three types of MU transmissions: MU-MIMO, OFDMA and Joint MU-MIMO and OFDMA
### Orthogonal Frequency-Division ultiple access (OFDMA)
OFDMA (orthogonal frequency-division multiple access), a technology in Wi-Fi 6 (IEEE 802.11ax), improves wireless network performance by establishing independently modulating subcarriers within frequencies. This approach allows simultaneous transmissions to and from multiple clients.
> In the OFDMA transmission of 802.11ax, the whole bandwidth is divided into multiple subsets of subcarriers, each subset called a resource unit (RU). Each RU is assigned with a user or a user group which is typically referred to as user scheduling
### The Difference between OFDM and OFDMA
OFDM (orthogonal frequency-division multiplexing) is an older, related technology for increasing wireless capacity and efficiency. OFDM has been used in areas such as cellular networking and broadcast media and in previous versions of Wi-Fi. OFDMA is essentially a type of OFDM for multiple users. It allocates in both the time domain and the frequency domain, allowing for multiple users—even those with widely varying use patterns or data loads. By comparison, OFDM can allocate only sequentially.
### How Does OFDMA work?
One way to understand OFDMA is to use delivery trucks as an analogy.

With Wi-Fi 5, each "truck" could carry only a single user's cargo. But with Wi-Fi 6 and OFDMA, the truck can be loaded with multiple users' cargo loads. Also, its drop-off schedule can be optimized for speed and efficiency.

OFDMA divides a Wi-Fi channel into smaller frequency allocations, called resource units (RUs). An access point can communicate with multiple clients by assigning them to specific RUs.

Wi-Fi 5 divides channels into 64 312.5-kHz subcarriers, all of which are used to transmit data to a single client. By spacing these carriers orthogonally, OFDMA allows Wi-Fi 6 to divide channels into smaller units without interference.

The number of RUs assigned to each client is determined by factors such as device constraints, quality-of-service (QoS) requirements, and packet size. The flexibility in scheduling along with the parallel nature of OFDMA increases the productive Air Time efficiency.
### The Varying Nature of the Channel and its Capacity
In a wireless network, wireless signals from APs propagate to the users through different paths and thus incur different path losses. Generally speaking, users with small path loss have higher received power and their data rate is higher. However, wireless networks usually operate in a multipath environment where the coherent bandwidth is small such that the wireless channel for the whole bandwidth is considered as a frequency selective channel.

The channel capacity on a subcarrier is not only decided by the path loss, but also influenced by the multipath effect. If the variations over subcarriers are high enough, a user with larger path loss may have higher channel capacity than others even if their path loss is smaller.
### Importance of Scheduling and Resource Allocation in 802.11ax
OFDMA is a multiple access technique based on orthogonal frequency-division multiplexing (OFDM). OFDMA divides the whole bandwidth into subcarriers. The subcarrier spacing is small enough such that each subcarrier can be seen as a narrowband subchannel, even if the whole bandwidth is a frequency selective channel.

802.11ax introduced OFDMA to alleviate the intensive contentions in dense scenarios and improve the efficiency of resources. The variation of channel capacity over users and subcarriers makes it important to select a good user schedule.
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# Module 1 : Background

$Figure\ 1$
- The channel capacity of a frequency selective channel is illustrated above
- Figure 1 shows the channel capacity of two MU-MIMO groups in a wireless network where an AP and users are equipped with 4 and 1 antennas respectively, under a typical indoors wireless channel.
- The path loss of users in user group 1 is smaller and the average channel capacity of the two user groups is 9.2 bps/Hz and 6.8 bps/Hz respectively
- The channel capacity of user group 2 is higher than user group 1 on some subcarriers due to variations of CSI.
- In summary, the channel capacity is a function of both large scale fading and small scale fading, and it changes over users and subcarriers.

$Figure\ 2$
- Sum rate distribution and average value from the simulation is illustrated above:
- if the users are scheduled randomly without optimization, the sum rate of the system is significantly reduced, especially for joint OFDMA and MU-MIMO transmissions.
# MODULE 2 : System Model
## A. 802.11 Ax Primer
802.11ax supports the following bands: 20MHz, 40MHz, 80MHz, 80+80MHz (combines two 80 MHz channels) and 160MHz (a single 160 MHz channel). In an OFDMA transmission, the spectrum band is divided into multiple RUs. In the time domain, an RU spans the entire data portion of a high efficiency (HE) PLCP protocol data unit (PPDU). In the frequency domain, it consists of a subset of contiguous subcarriers except the RUs which “straddle DC” (where some nulls are placed in the middle of the band). The size of an RU in frequency domain can be 26, 52, 106, 242, 484 or 996 subcarriers. The RUs in an HE MU PPDU using OFDMA transmission can only be any of these sizes. The locations of RUs in an HE PPDU are fixed. Each RU of size larger than 26 can be further divided into 2 smaller RUs.
## B. Physical Layer Modeling
### 1) The Channel Model
Consider an 802.11ax BSS where the AP and users are equipped with $N_{T}$ and $N_{R}$ ($N_{T}$>$N_{R}$) antennas respectively. the downlink CSI to all users is transmitted to the AP through channel sounding (CSIT). Then the AP applies ZFBF for SU-MIMO or MU-MIMO. The users are indexed by the set $U={1,2,…,N}$. In a downlink transmission, the AP decides to transmit to a set of users $U_{s}⊂U$ on subcarrier s. The received signal at user $k$ on subcarrier $s$ is \begin{equation*} yk,s=h_{k,sk,s}w\sqrt{P_{k,s}}x_{k,s}+\sum\limits_{\substack{j\in U_{s}\\ j\neq k}} h_{k,s^{W}j,s}\sqrt{P_{j,s}}x_{j,s}+z_{k,s},\tag{1}\end{equation*} \begin{equation*}\ P_{s}=\sum\ _{k∈U_{s}γ^{−1}_{k,s}P_{k,s}} \tag{2} \end{equation*} is constant over all subcarriers, where \begin{equation*} \gamma_{k,s}=\frac{1}{\Vert w_{k,s}\Vert^{2}}. \tag{3} \end{equation*}
| Variable | Meaning |
| -------- | -------- |
| $x_{k,s}$ | data symbol |
| $h_{k,s}$ | channel response |
| $w_{k,s}$ | beamforming weight vector |
| $P_{k,s}$ | transmit power |
| $z_{k,s}$ | additive white Gaussian noise $(AWGN)$ |


$Figure\ 3\ :$ RU locations in a 40MHz HE PPDU

The beamforming matrix $W_{s}$=$[w_{k,s},k∈U_{s}]$, consisting of all beamforming weight vectors $w_{k,s}$ , is the pseudo-inverse of $H_{s}$=$[h^T_{k,s},k∈U_{s}]^T$, that is
\begin{equation*} W_{s}=H_{s}^{H}(H_{s}H_{s}^{H})^{-1}. \tag{4} \end{equation*}
Last, the sum rate on subcarrier s equals
\begin{equation*} R_{ZFBF}(s)=\sum\limits_{k\in U_{s}}\log_{2}(1+P_{k,s}), \tag{5} \end{equation*}
where $P_{k,s}$ can be optimized by waterfilling, or set by equal power allocation for simplicity. (Recall that the noise power is normalized to one.)
### 2) User Grouping of MU-MIMO
If the AP transmits in joint MU-MIMO and OFDMA mode, the scheduling and resource allocation requires to perform user grouping.
### 3) Abstraction of RUs
Each $RU$ is denoted by $RU(l,i)$, where i is the number of splits from the original $RU$ to the current one and $i$ is the index of an $RU$ at its level. Note that $RU(0,0)$ refers to the $RU$ occupying the whole bandwidth. The whole bandwidth can be split into $2^l$ $RU_s$ of equal size at level $l(l∈{0,1,…,L−1})$, labeled as $0,1,…,2^l−1$. Each $RU$ $RU(l,i)$ with $l<L−1$ can be split into two $RU_s$ $RU(l+1,2i)$ and $RU(l+1,2i+1)$.

$Figure\ 4\ :$ Rus of a 20MHz HE PPDU
### 4) Scheduling and Resource Allocation
In one OFDMA transmission, the whole bandwidth is divided into a combination of RUs from different levels. Let $p={pj…}$ be a valid partition of the whole bandwidth where $pj=RU(l_j,i_j)$ is the $j^th$ $RU$ in $p$ and let $P$ be the universal set of all partitions.


$Figure\ 5\ :$ A valid partition of the bandwidth

Having obtained a valid partition of the bandwidth, we need to allocate users to RUs. Say $g={(p_j,u_j)}$ is a valid user schedule where $p_j=RU(l_j,i_j)$ is the $j_th$ RU in a valid partition of the whole bandwidth and $u_j$ is the user set allocated to $p_j$.

$Table\ 1\ :$ A valid user schedule

The $ZFBF$ capacity on an $RU(l, i)$ can be computed by summing the achieved rates at each subcarrier which is part of this RU, that is,

\begin{equation*} R_{ZFBF}(RU(l, i))=\sum_{s\in RU(l,i)}R_{ZFBF}(s). \tag{6} \end{equation*}

Then, the ZFBF capacity of g is

\begin{align*} R_{ZFBF}(g) & =\sum\limits_{j}R_{ZFBF}(p_{j})\\ & =\sum\limits_{j}\sum\limits_{s\in p_{j}}\sum\limits_{k\in U_{s}}\log_{2}(1+P_{k,s}).\tag{7} \end{align*}