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a complex conjugate of x₁, respectively. Thus, as shown in Figure 2.10, the symbols x₁ and x₂ are transmitted using first and second transmitter outputs y₁ and y₂ at first and second times, respectively, as may be expressed by Eq. 2.1:

(2.1)

      wherein for each transmitter output at each time, a top element is a symbol transmitted using a first antenna, and a bottom element is a symbol transmitted using a second antenna. Notably, the first symbol x₁ is transmitted at a different time than the complex conjugate of the first symbol , and the second symbol x₂ is transmitted at a different time than the negative complex conjugate of the second symbol −x₂ [2].

First and second received symbols r₁ and r₂ at a receiver having two antennas may be expressed by Eq. 2.2:

(2.2)

      where h_ab is a path gain for a path including an ath transmitting antenna and a bth receiving antenna, and n₁ and n₂ represent first and second additive white noise, respectively. The receiver can recover the transmitted symbols x₁ and x₂ using linear processing [2].

TABLE 2.6 802.11 Cheat Sheet

Topic	Description
Observation	Band, Channel, and Stream have their special definitions.
Band	There are two general public shared bands 2.4 and 5 GHz for Wi‐Fi operation.
Channel	Channel is the divided small portions of frequency within each band. For example, there are 11 channels in 2.4 GHz as originally used in 802.11b which utilize 20 MHz per channel, with 15 MHz overlapping to cross over 100 MHz.
Stream	Stream is used since 802.11n (the first implementation of MIMO and known as Wi‐Fi 4). One stream in a single 2.4 GHz band and 40 MHz channel (with 400 ns GI) can deliver a maximum of 150 Mbps. A four‐stream Wi‐Fi 802.11n AP can deliver up to 4 × 150 Mbps = 600 Mbps (one needs to equip with 4 × 4 antenna in such AP).
Practical/commercial example	802.11 ac (known as Wi‐Fi 5) still maintains the same 802.11n maximum of 4 streams per band. It operates in 5 GHz band; thus, the throughput increases to 433 Gbps per stream (often called “450” – it is almost 3 times data rate than 802.11n). Most commercial 802.11ac AP in the market are dual‐band. They only implement three streams in 5 GHz band (even though in the specification, it can support 4 streams), complemented by four streams in the 2.4 GHz band. Thus, such a Wi‐Fi AP could support 1900 Mbps of system throughput capacity with the following configuration: 3 × 433 (= 1300 Gbps) + 4 x 150 (= 600 Mbps).

      2.5.5 Product Waves

The Wi‐Fi Alliance separated the introduction of 802.11ac wireless products into two phases (“wave”), named “Wave 1” and “Wave 2”. Initially, (2013) products were based on the IEEE 802.11ac Draft 3.0; it supported three spatial streams (with three antennas). Wave 2 certification became available in 2016; Wave 2 products achieve higher bandwidth and system capacity than Wave 1 products. Wave 2 included newer features such as MU‐MIMO, wider 160 MHz channel width support, additional 5 GHz channels, and four spatial streams (with four antennas; compared to three in Wave 1 and 802.11n) (IEEE's 802.11ax supports eight.) See Table 2.6 for a “Cheat Sheet” on 802.11ac concepts and system throughput.

2.6 BRIEF PREVIEW OF IEEE 802.11AX

      As a quick initial comparison, note that an amendment to the IEEE Std 802.11 (the IEEE 802.11ax amendment) was being developed at press time by the IEEE 802.11ax Task Group. The amendment defines a high‐efficiency WLAN for enhancing the system throughput in high‐density scenarios. Unlike previous amendments that focused on improving aggregate throughput, the IEEE 802.11ax amendment is focused on improving metrics that reflect the user experience, such as average per station throughput, the fifth percentile of per station throughput of a group of stations, and area throughput. Improvements aimed at targeting environments such as wireless corporate offices, outdoor hotspots, dense residential apartments, and stadiums. The principal focus of the IEEE 802.11ax amendment is on indoor and outdoor operation of the WLAN. The target for increases in average throughput per station is in the range of 5–10 times, depending on a given technology and scenario of the WLAN. Outdoor operation is limited to stationary and pedestrian speeds [2]. This HEW system marketed as Wi‐Fi 6 by Wi‐Fi Alliance saw initial deployment in late 2019.

As is the case in other 802.11 standards, 802.11ax is designed to operate in the Industrial Scientific and Medical (ISM) bands located between 1 and 6 GHz, including the 2.4 and 5 GHz bands traditionally utilized; additional bands between 1 and 6 GHz may be added as they become available. An aggregate theoretical data rate exceeding 10 Gbps is achievable. For dense deployments, throughput speeds can be four times higher than the throughput speed achieved with IEEE 802.11ac systems (the nominal data rate, however, is only around 37% faster under optimal circumstances). Another key goal of 802.11ax is to improve spectrum efficient utilization. To achieve this goal, better power‐control methods are utilized to minimize or avoid interference with neighboring networks. Also, OFDMA, higher order modulation at 1024‐QAM (see Table 2.7), and UL of MIMO and MU‐MIMO combined with DL of MIMO and MU‐MIMO are all utilized to further increase throughput. Additionally, dependability improvements of power consumption and enhanced security protocols, specifically, WPA3 were added.

TABLE 2.7 Modulation and Coding Schemes for Single Spatial Stream

Modulation and Coding Scheme (MCS)	ModulationScheme	Coding Rate	20 MHz Channels 1600 ns GI Data Rate (Mbps)	40 MHz Channels 1600 ns GI Data Rate (Mbps)	80 MHz Channels 1600 ns GI Data Rate (Mbps)	160 MHz Channels 1600 ns GI Data Rate (Mbps)
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