Cooperative Transmission Mechanisms in Next Generation WiFi: IEEE 802.11ac

Abstract

Very high throughput (VHT) WLAN, known as IEEE 802.11ac, can provide compelling performance and has attracted extensive attention for achieving transmission rate over 1 G bps for 5 GHz band owing to involving the MU-MIMO and maximum 160 MHz bandwidth transmission. Despite extensive studies and dramatic performance, the conventional carrier sensing mechanism emerges some drawbacks especially in the overlapping BSS scenario responsible for employment of MU-MIMO and bandwidth expansion. In order to address the issue of conventional carrier sensing mechanism, namely, redundant or useless network allocation vector (NAV) setting, this paper proposes an enhanced NAV transmission mechanism, which not only needs little modifications to current standard draft but also can achieve performance improvement significantly. On this basis, in order to solve the SINR inaccuracy calculated based on null data packet (NDP) in the actual MU-MIMO transmission, the SINR feedback mechanism is proposed and the frame structure modifications are displayed in detail. Furthermore, theoretical analysis is also performed on the proposed mechanism and the formulas of the achieved gains are also derived. Numerical results confirm the validation of our theoretical analysis and further substantiate that the proposed scheme obtains obvious throughput gain over the conventional mechanism.

1. Introduction

With the development of modern broadband communication systems, there is growing evidence that the timeless and convenience of the information acquisition become more and more important to user experience. It has gained popularity recently due to its easy and quick deployment with low cost. In wireless local area network (WLANs), the wireless channel is shared by all the nodes and hence a medium access control (MAC) protocol is needed to coordinate their transmissions to reduce the collision. Although it was initially standardized for WLANs, IEEE 802.11DCF (Distributed Coordination Function) was known as carrier sense multiple access with collision avoidance (CSMA/CA), with an optional use of RTS/CTS [1]. However, the employment of multiple user multiple input multiple output (MU-MIMO) and bandwidth expansion mechanism makes the existing mechanism of IEEE 802.11 emerge some drawbacks. For instance, when multiple stations are simultaneously active and have different packet lengths to send, the network allocation vector (NAV) should be set as the longest duration to avoid interference; “NAV” is the time that the neighboring node will finish its ongoing transmission. But for the station in the neighboring BSS which only interferes with part of the active users, it is very possible that its NAV setting is redundant; that is, thus, even those transmissions that will not interfere with the ongoing one are still blocked. Therefore, how to address these issues and improve the performance of VHT WLANs is of particular importance. Motivated by this, the paper aims to find solutions to these problems in the framework of TXOP sharing mechanism adopted in the current standard [2]. The proposed scheme could solve these drawbacks with some subtle frame structure modifications to WLAN IEEE 802.11ac draft.

It is worth noting that the fundamental access method of the IEEE 802.11 MAC is a DCF known as carrier sense multiple access with collision avoidance (CSMA/CA) with an option of RTS/CTS, which is a little similar to carrier sense multiple access with collision detection (CSMA/CD). The four-way handshake procedure (RTS/CTS/DATA/ACK), which is used to deal with the hidden terminal problem, is as follows. Before a node begins to transmit, it should first sense the channel to determine whether there is any ongoing transmission. If the channel is busy, the node will defer until the channel is sensed idle for a period of DIFS. Then the node randomly chooses a backoff period according to the contention window and starts a back-off timer to backoff. The back-off timer decreases by 1 after the channel is idle for the duration of a slot. If the channel is sensed busy during any slot in the back-off interval, the back-off timer will be suspended. It can be resumed only after the channel is idle for a period of DIFS again. After the back-off timer reduces to 0, the sender transmits a RTS omnidirectionally. This transmission ends after the receiver correctly receives the data and responses with an ACK. All four kinds of frames contain an estimated duration of the rest time of the transmission. Other nodes that receive these frames update their NAVs (network allocation vectors) with the duration. Every NAV decreases by 1 after a time slot. Those nodes are only allowed to transmit after they sense the channel idle for a period of DIFS after their NAVs expire [3].

Another kind of access method of IEEE 802.11 MAC is a EDCA (enhanced distributed channel acess). With EDCA, high-priority traffic has a higher chance of being sent than low-priority traffic: a station with high-priority traffic waits a little less before it sends its packet, on average, than a station with low-priority traffic. This is accomplished by using a shorter contention window (CW) and shorter arbitration interframe space (AIFS) for higher priority packets. The exact values depend on the physical layer that is used to transmit the data. In addition, EDCA provides contention-free access to the channel for a period called a transmit opportunity (TXOP). A TXOP is a bounded time interval during which a station can send as many frames as possible (as long as the duration of the transmissions does not extend beyond the maximum duration of the TXOP). If a frame is too large to be transmitted in a single TXOP, it should be fragmented into smaller frames. The use of TXOPs reduces the problem of low rate stations gaining an inordinate amount of channel time in the legacy 802.11 DCF MAC. A TXOP time interval of 0 means it is limited to a single MAC service data unit (MSDU) or MAC management protocol data unit (MMPDU) [2].

Though WLAN has been extensively studied, some parts of them still focus on the conventional DCF mechanism of IEEE 802.11. The performance analysis of DCF mechanism of 802.11 was firstly researched by Bianchi in [4] on JSAC 2000, which described the access protocol of CSMA using bidimensional chains of Markov and analyzed the throughput performance of IEEE 802.11a. The theoretical upper bound of IEEE 802.11a capacity was derived by Cali et al. in [5]. Reference [6] investigated the MU-MIMO transmission schemes based on WLAN 802.11n, which considered an opportunistic channel-aware scheduling policy to achieve simultaneous downlink transmission to multiple users and one of the drawbacks of this scheme proposed was random beam-forming technique at the physical layer. Reference [7] gave some research about the MU-MIMO transmission under IEEE 802.11n. The contention window of WLAN IEEE 802.11 was also studied based on DCF to maximize throughput by Weng et al. [8] and Babich and Comisso [9]. References [10–12] gave a network allocation vector analysis for IEEE 802.11 based on DCF mechanism.

On the other hand, there are also some papers focusing on EDCA (enhanced distributed channel access) mechanism, which is an enhanced mechanism for DCF. Reference [13] presented the throughput performance of EDCA and compared the case of full NAV setting and packet by packet NAV setting with and without NAV clear mechanism. The results showed that EDCA in the case of packet by packet NAV setting outperforms that in the case of full NAV setting and EDCA with NAV clear mechanism outperforms that without NAV clear mechanism. Reference [14] presented a NAV scheme to improve the system throughput, the proposed scheme displayed considerable throughput gains. The author in [15] proposed and investigated a scheme that modified network allocation vector update process of voice terminals based on EDCA. Mario and coauthors proposed a priority based CSMA/CA mechanism to support deadline aware scheduling in home automation applications using IEEE 802.15.4 [16]. The authors in [17] also presented an adaptive energy-management framework for sensor nodes with constrained energy scavenging profiles; the scheme proposed boosts the system throughput to some extent.

Up to now, to the best of our knowledge, the research on the performance analysis of TXOP sharing with MU-MIMO and solving problems as similar as Figure 1 is still an open problem. For example, as shown in Figure 1, when multiple stations are simultaneously active and have different packet lengths to send, the NAV should be set as the longest duration to avoid interference; “NAV” is the time that the neighboring node will finish its ongoing transmission. But for the station in the neighboring BSS which only interferes with part of the active users, it is very possible that its NAV settings is redundant; that is, the duration in the NAV is longer than the actual interfering duration. More seriously, if the station in the overlapping area responds to the MU-MIMO polling but finally fails to obtain the transmission opportunity, the overlapping nonserving BSS will be set NAV mistakenly. This will result in some performance loss. Motivated by this, we will propose a two-level NAV mechanism to address this issue after elucidating that the problem is how to form and further provide theoretical analysis on its achieved performance.

Figure 1

IEEE 802.11ac overlapping BSS scenario.

2. Problem Formulation

It is known that the available channel in IEEE 802.11ac could only support up to two 160 MHz or five 80 MHz bandwidths simultaneously. Furthermore, the introduction of MU-MIMO in IEEE 802.11ac will result in inefficient use of the limited frequency resource with the conventional enhanced distributed channel access (EDCA) mechanism, becoming of redundant or useless NAV setting. The problem will be elaborated as follows.

As shown in Figure 1, the two-BSS overlapping network considered in this paper is as follows: the two BSSs involve different stations showed in Figure 1, respectively. It is worth noting that the STA3 locates in the overlapping BSS (it is the so-called OBSS scenario) position and associates with AP1. According to IEEE 802.11ac standard, AP1 may transmit RTS to poll STA1, STA2, and STA3 in order to realize MU-MIMO and decide how wide the bandwidth to use. It is critical that the STA3 may be polled by AP1 and respond to the polling with CTS sending to AP1, the action of which will lead to STA4 and AP2 set NAV to avoid interference. However, the bandwidth and duration in NAV are determined such that each STA in the following MU-MIMO transmission is protected according to the TXOP mechanism in EDCA. It is likely that this makes the NAV setting for STA4 and AP2 become redundant or useless. There are two typical scenarios for the issue of mistaken or redundant NAV setting for the overlapping BSS.

For the first case, two neighboring BSSs have different primary channels; namely, the primary channel of BSS2 overlaps the secondary channel of BSS1, which is a frequent scenario for several BSSs usually. In this case, STA3 will suffer interference from different BSSs due to its location in the overlapping area (the more the BSS number increases, the stronger interference OBSS station received); it is most likely that it cannot satisfy the condition required by AP1 and will be excluded in the list of the following MU-MIMO transmission such as the unequal bandwidth or other algorithms for achieving an objective. If this happens, the NAV setting for STA4 and AP2 becomes mistaken due to the polling response of STA3 and cannot be cleared based on conventional mechanism, resulting in noticeable throughput loss of the VHT WLANs.

For the second case, the scenario of adjacent BSS has the same primary channel; namely, the primary channel of BSS2 overlaps the primary channel of BSS1, which occurs regularly in practical generally. Nevertheless, different STAs may have different lengths of packets to transmit in practical, then AP1 can clear the redundant TXOP duration through CF-END frame when STA3 finishes the transmission; however, STA4 and AP2 cannot receive the CF-END frame (CF-END is a no response frame), resulting in that the BSS2 is out of work in the redundant TXOP duration and decreasing the throughput of VHT WLANs inevitably.

Furthermore, the accuracy of the SINR feedback in Downlink MU-MIMO of IEEE 802.11ac plays a key role in improving the performance of MU-MIMO transmission. The SINR calculated based on NDP is usually far from accuracy, since at that moment (in the sounding process) the possible interuser interference in the actual MU-MIMO transmission cannot be estimated effectively. Generally speaking, there are several continuous data frames for each STA in a TXOP; it is therefore possible to correct the SINR estimation during the process of data transmission via BA frame.

Focusing on these cases above, we will propose solutions to solve the problems above in the next section.

3. Proposed Solutions

3.1. Enhanced NAV Mechanism

Here we would like to elaborate a two-level NAV mechanism to solve the above-mentioned two redundant NAV setting cases. Though the description of the proposed schemes may seem to only address the special cases shown in Figure 1, the extension to a more general case is straightforward.

Case 1.

Firstly, AP1 obtains the available channel use for MU-MIMO implementation and may transmit RTS/data to poll the stations to be served. STA3 may respond with CTS/BA; then AP2 and STA4 in BSS2 will set NAV to enter power saving state. AP1 can decide transmit bandwidth after receiving all the response frame and AP1 also needs to calculate which bandwidth can maximize the throughput (different algorithms may be adopted and this is not the focus in this paper). If AP1 finally decides that STA3 will not be served for unequal bandwidth or other reasons, then AP2 and STA4 may still be mistakenly in NAV setting. We propose the following two steps to address this issue.

Secondly, AP2 and STA4 in BSS2 need to wait a timeout duration (such as DIFS, SIFS) to make sure that they are in this mistaken NAV duration case.

Thirdly, to clear the mistaken NAV setting while guaranteed no interference on others, AP2 and STA4 need to check two conditions to clear NAV setting after receiving the final frame announcement. One is the timeout; the other is as shown in Figure 2; the NAV duration to be cleared should be in the range between the longest duration and the second longest duration.

Figure 2

BA frame correction process.

Case 2.

Firstly, similar to the first case, AP2 and STA4 in BSS2 will set NAV after overhearing CTS/BA frame. If the packet length of STA3 is much shorter than the TXOP duration, at the end of STA3's packet transmission, the redundant NAV duration for AP2 and STA4 actually can be used without causing any interference. But according to conventional mechanism, AP2 and STA4 have to wait until the TXOP duration is ended. We propose the following solution to address this issue. In our solution the final BAR frame needs to carry the information of the last frame, and the response BA frame of STA3 also needs to carry information to announce AP2 and STA4. The last frame announcement can be obtained through two methods. One is via “more data” field indication; namely, “more data” equal to 1 represents the last frame announcement, otherwise not the last frame; another can be realized through BAR control field, which has 9 reserved bits to be used and any of these bits available equal to 1 indicates the last frame announcement, otherwise not the last frame.

Secondly, STA3 needs to inform the last frame announcement to its surroundings so as to clear useless NAV settings, which can be implemented through reserved bits in control field of BA frame; namely, a reserved bit in BA control field of STA3 equal to 1 represents the last frame announcement, otherwise not the last frame.

Thirdly, AP2 and STA4 check two conditions to see whether their NAV setting can be cleared or not, which is the same as that in the first case. Based on that, AP2 and STA4 can clear the possible useless NAV after waiting SIFS without causing interference to other STAs.

3.2. SINR Correctness Feedback Mechanism

The accuracy of the SINR feedback in downlink MU-MIMO of IEEE 802.11ac plays a key role in improving the performance of MU-MIMO. The SINR calculated based on NDP is usually far from accuracy, since at that moment (in the sounding process) the possible interuser interference in the actual MU-MIMO transmission cannot be estimated. In general there are several continuous data frames for each STA in a TXOP; it is therefore possible to correct the SINR estimation during the process of data transmission via BA frame, as illustrated in Figure 2.

Therefore, we propose the SINR correctness feedback mechanism in order to satisfy the channel state information (CSI) accuracy requirement for MU-MIMO. Namely, the transmitter can update the precoding matrix adaptively through the SINR feedback. Especially, the secondary access category (AC) users can join the MU-MIMO transmission when the TXOP is not expired; then, the CSI of the secondary AC users are not accurate enough, which can have great effect on the MU-MIMO transmission. So we can give a SINR correctness feedback mechanism to solve the problem above-mentioned and the steps of correcting the estimated SINR during TXOP can be seen as follows.

• (i)

AP transmits the first data frame in an MU-MIMO TXOP using an MCS lower than that indicated by the feedback SINR during sounding.

(ii)

STA reestimates the SINR based on the first data frame, in which the interuser interference can be incorporated.

(iii)

Based on the SINR reestimation, STA sends the SINR correction information (usually defined as a difference between the originally estimated and the reestimated SINR) to AP through the subsequent BA frame, as illustrated in Figures 3 and 4.

(iv)

On receiving the SINR correction information, AP transmits the remaining data frames in this TXOP using a corrected MCS.

Figure 3

BA frame modification Scheme  1.

Figure 4

BA frame modification Scheme  2.

In order to trigger a STA to reestimate the SINR in the process of data transmission in a TXOP, an indication is needed in the data frame. There are two ways:

• (i)

using one reserved bit in the VHT-SIGA field to explicitly indicate this;

(ii)

alternatively, using scrambling to implicitly indicate this, that is, using a particular scrambling initialization in the service field to trigger the SNR reestimation.

Then STA reobtain the SINR per space stream per subcarrier and can calculate the average value; namely, STA sums the SINR per stream per subcarrier and then subtracts the stream number to obtain the total average SINR, which can be compared with the former feedback average SINR to obtain the SINR correction. The SINR correction can be quantized to four bits and feedback to the transmitter through BA frame. The four bits (B3 to B6) can represent this correction. Due to each STA at most can receive four space streams, so the group can feedback four average SINR correction and needs eight bits (B3 to B10) to indicate.

B3 and B4 indicate the first space stream, B5 and B6 indicate the second space stream, B7 and B8 indicate the third space stream, and B9 and B10 indicate the fourth space stream. The main process can be seen in Figure 2. Firstly, the transmitter can send the first MU-MIMO frame in TXOP duration with low modulation and coding scheme (MCS); secondly, the STA can recalculate the SINR after receiving the first MU-MIMO frame; thirdly, the STA feedback the SINR correction to the transmitter through BA frame; fourthly, the transmitter can update the precoding matrix adaptively and give better power allocation after overhearing the BA frame with SINR correction to maximize the system throughput.

The advantages of this scheme mainly conclude that the system does not need the control package frame; this not only reduces the complexity; but also does not increase frame exchange, which makes the transmitter obtain the more accurate SINR and thus improves the MU-MIMO performance. Certainly, the scheme proposed occupies four reserved bits in order to implement the enhancement of the MU-MIMO transmission.

4. Performance Analysis

4.1. The Performance of Enhanced NAV Mechanism

In this section, we analyze the performance of the proposed enhanced NAV mechanism.

It is assumed that the service time X of one frame transmission completed in a TXOP follows exponential distribution with parameter λ; then m frames transmission completion are independent identically distributed and can be obtained $Y=X_{\mathrm{1}}+\cdots +X_m$ which follows m-Erlang distribution [18]; namely,

$$\begin{array}{cc}& f_y\left(y\right)=\frac{\lambda e^{-\lambda y}{\left(\lambda y\right)}^{m-\mathrm{1}}}{\left(m-\mathrm{1}\right)!},\hspace{1em}y\ge \mathrm{0}.\end{array}$$

(1)

It is assumed that the business arrival Z follows the Poisson distribution with parameter $\tilde{\lambda }$ as (4):

$$\begin{array}{cc}& \text{Pois}\left(\tilde{\lambda }\right)=\frac{{\tilde{\lambda }}^k}{k!}{e}^{-\tilde{\lambda }},\hspace{1em}k\in \mathrm{0,1},\mathrm{2,3},\dots .\end{array}$$

(2)

Based on the above model, then, the average length of the packet payload can be calculated through computing the expectation of distribution as follows:

$$\begin{array}{cc}& E\left[y\right]={{\displaystyle \int }}_{\mathrm{0}}^{\infty }yf\left(y\right)dy=\frac{m}{\lambda }.\end{array}$$

(3)

Let $P_u$ represent the user's packet payload; then the average packet length $E{P}_u$ is constant and can be expressed as $E{P}_u={\lambda }_s=m_u/\lambda$ ; let $P_u^{\text{Possion}}$ note the uth user business arrival probability, which follows Possion distribution. TXOP is called transmit opportunity, which is a duration and stations can be won through contention; however, different stations have different data volumes and then different stations have different redundant times $T_{\text{redundan}{\text{t}}_t}$ in a TXOP duration.

The redundant time $T_{\text{redundan}{\text{t}}_t}$ in a TXOP duration when the transmission mode is SU-MIMO and frame numbers are m can be written as

$$\begin{array}{cc}& T_{\text{redundan}{\text{t}}_t}=\text{TXOP}-\Delta -Y,\end{array}$$

(4)

where the $\Delta =\text{RTS}/s_{\text{Data}}+\text{SIFS}+\delta +\text{CTS}/\text{ACK}+\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{SIFS}+\delta$ because every transmission starting needs TXOP initialization and needs RTS/CTS or short data polling. δ is transmission delay time.

Then we give the throughput gains $G_a$ expression as

$$\begin{array}{cc}& G_a=\frac{{{\displaystyle \sum }}_{u=\mathrm{1}}^{\stackrel{-}{𝒩}}E\left[P_u\right]P_u^{\text{Possion}}}{T_{\text{redundan}{\text{t}}_t}},\end{array}$$

(5)

where $\stackrel{-}{𝒩}$ is user number, which refers to users released when OBSS stations finish frame transmission as the proposed solution procedure and can be calculated using campel theorem as [19, 20].

We have elaborated the redundant time $T_{\text{redundan}{\text{t}}_t}$ in a TXOP duration when transmission mode is SU-MIMO and frame number is m, however, MU-MIMO transmission mode has some difference compared with SU-MIMO mode. It is assumed that a station service time of m frames interaction in SU-MIMO mode follows m-Erlang distribution as the network model, nevertheless, MU-MIMO transmission should need to wait some extra times to complete interaction when each adding a station, the extra time can be expressed as $\text{extra}\_\text{time}=\text{SIFS}+\delta +\text{BAR}+\delta +\text{SIFS}+\delta +\text{BA}+\delta$ , we can assume that the MU-MIMO transmission has G stations, then the redundant time in MU-MIMO transmission mode can be expressed as $T_{\text{MU}\_\text{redun}}=\text{TXOP}-\Delta -\text{extra}\_\text{time}·{\sum }_{u=\mathrm{2}}^G‍{\lambda }_u-X$ , where X expresses all the transmission frames in MU-MIMO mode.

Then we will give some propositions to evaluate the performance of the proposed scheme.

Firstly, we can calculate the distribution of the redundant time as Proposition 1.

Proposition 1.

The distribution about the redundant time $T_{redundan{t}_t}$ in a TXOP duration when the transmission mode is SU-MIMO and frame number is m can be obtained in the following:

$$\begin{array}{cc}& f_{SU\_redundant}\left(x\right)=\frac{\lambda e^{-\lambda \left(t-\Delta x\right)}{\left[\lambda \left(t-\Delta -x\right)\right]}^{m-\mathrm{1}}}{\left(m-\mathrm{1}\right)!}.\end{array}$$

(6)

Then on the basis of Proposition 1, we can obtain the distribution of SU-MIMO throughput gains using the proposed enhanced NAV scheme as Proposition 2.

Proposition 2.

The distribution of the throughput gains using proposed enhanced NAV scheme can be obtained as follows when the transmission mode is SU-MIMO:

$$\begin{array}{l}{f}_{SU\_gains}\left(x\right)={\displaystyle \sum }_{k=\mathrm{0}}^{\lfloor x\left(t-\delta \right)\rfloor }‍\frac{\lambda e^{-\lambda \left(t-\Delta \right)}}{\left(m-\mathrm{1}\right)!}{e}^{-\lambda \overline{𝒩}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\times \frac{{\lambda }_{\overline{𝒩}}^k}{\left(k-\mathrm{1}\right)!}\frac{k}{x}{e}^{\left(\lambda {\lambda }_{s}k\right)/x}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{1em}\times {\left[\lambda \left(t-\Delta -\frac{{\lambda }_{s}k}{x}\right)\right]}^{m-\mathrm{1}},\end{array}$$

(7)

where ${\lambda }_{\overline{𝒩}}={\sum }_{u=\mathrm{1}}^{\overline{𝒩}}‍{\lambda }_u$ .

The proof of Proposition 2 can be seen in Appendix A.

Furthermore, we can give the expectation of throughput gains in SU-MIMO mode as Corollary 1.

Corollary 1.

The expectation of throughput gains in SU mode can be obtained as

$$\begin{array}{l}{E}_{SU\_gains}\\ \hspace{1em}=\frac{{\lambda }_s{\lambda }_{\overline{𝒩}}}{\left(m-\mathrm{1}\right)!}{\displaystyle \sum }_{k=\mathrm{1}}^{\infty }‍{\left(\frac{\mathrm{1}}{t-\Delta }\right)}^k{\left(\frac{\mathrm{1}}{\lambda }\right)}^{k-\mathrm{1}}\gamma \left(m+k+\mathrm{1},\lambda \left(t-\Delta \right)\right),\end{array}$$

(8)

where $\gamma (·,·)$ is an incomplete gamma function [21].

The proof of Corollary 1 can be seen in Appendix B.

Based on this section's beginning, the distribution of the redundant time in MU-MIMO mode can be obtained as Proposition 3.

Proposition 3.

The distribution of the redundant time $T_{MU\_redun}$ in a TXOP duration when transmission mode is MU-MIMO and frame number is m can be obtained in the following:

$$\begin{array}{l}{f}_{MU\_redun}\left(x\right)=e^{-{\lambda }_G}\frac{{\lambda }^m}{(m-\mathrm{1})!}{\displaystyle \sum }_{k=\mathrm{0}}^{\lfloor \left(t-\Delta -x\right)\rfloor }\frac{{\lambda }_G^k}{k!}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times e^{-\lambda \left(t-\Delta -x-k\right)}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times {\left(t-\Delta -x-k\right)}^{m-\mathrm{1}},\end{array}$$

(9)

where ${\lambda }_G=con\_t{\sum }_{u=\mathrm{2}}^G‍{\lambda }_u$ .

The proof of Proposition 3 can be seen in Appendix C.

Similar to the SU-MIMO mode, we can also calculate the distribution of throughput gains using the proposed scheme in MU-MIMO mode as Proposition 4.

Proposition 4.

The distribution of throughput gains using the proposed scheme can be obtained as follows when transmission mode is MU-MIMO:

$$\begin{array}{l}{f}_{MU\_gains}\left(x\right)=e^{-{\lambda }_{\overline{𝒩}}}{e}^{-{\lambda }_G}\frac{{\lambda }^m}{\left(m-\mathrm{1}\right)!}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times {\displaystyle \sum }_{l=\mathrm{0}}^{\lfloor x\left(t-\delta \right)\rfloor }{\displaystyle \sum }_{k=\mathrm{0}}^{\lfloor \left(t-\delta -l/x\right)\rfloor }\frac{{\lambda }_{\overline{𝒩}}^l}{l!}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\phantom{0000000000000000}\times \frac{l}{x}\frac{{\lambda }_G^k}{k!}{e}^{-\lambda \left(t-\Delta -\left(l{\lambda }_s/x\right)-k\right)}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\phantom{0000000000000000}\times {\left(t-\Delta -\frac{l{\lambda }_s}{x}-k\right)}^{m-\mathrm{1}}.\end{array}$$

(10)

The calculating method of Proposition 4 is similar to Proposition 3.

Furthermore, the expectation of the throughput gains in MU-MIMO can be obtained as Corollary 2.

Corollary 2.

The expectation of the throughput gains in MU-MIMO transmission mode can be calculated as follows:

$$\begin{array}{cc}& E_{MU\_gains}=e^{-{\lambda }_G}\frac{{\lambda }^m}{\left(m-\mathrm{1}\right)!}{\displaystyle \sum }_{k=\mathrm{0}}^{\lfloor t-\Delta \rfloor }\frac{{\lambda }_G^k}{k!}\left(I_{\mathrm{1}}-I_{\mathrm{2}}\right),\end{array}$$

(11)

where $I_{\mathrm{1}}=(-\mathrm{1}{)}^{m-\mathrm{2}}{k}^{m-\mathrm{1}}{e}^{\lambda k}Ei(-\lambda k)+{\sum }_{i=\mathrm{1}}^{m-\mathrm{1}}‍(i-\mathrm{1})!(-k{)}^{m-\mathrm{1}-i}{\lambda }^{(-i)}$ and $I_{\mathrm{2}}=e^{\lambda k}{\sum }_{j=\mathrm{0}}^{m-\mathrm{1}}‍C_{m-\mathrm{1}}^j(t-\delta -k{)}^j(t-\Delta {)}^{m-\mathrm{1}-j}\Gamma (m-j)\Gamma (-(m-\mathrm{1}-j),\lambda (t-\Delta ))$ .

The proof of Corollary 2 can be seen in Appendix D.

It is noted that the redundant time $T_{{redundant}_t}$ may be the whole TXOP duration when the primary channel of one BSS overlaps the secondary channel of another BSS, namely, Case 1.

4.2. The Performance Analysis of the MU-MIMO in IEEE 802.11ac

In this section, we will analyze the MU-MIMO performance in IEEE 802.11ac. Assume that $\stackrel{-}{X}$ is the average transmission frame length and $\stackrel{-}{T}$ is the average transmission time. If $P_{\text{AP}}$ denotes the probability of AP contending the channel right use, then the throughput can be expressed as

$$\begin{array}{cc}& S\left(m,N,r_{\gamma }\right)=P_{\text{AP}}·\frac{\stackrel{-}{X}\left(m,N,r_{\gamma }\right)}{{\stackrel{-}{T}}_{m,N,r_{\gamma }}},\end{array}$$

(12)

where $\stackrel{-}{X}(m,N,r_{\gamma })$ is the average transmission frame length for N users under m time slots with transmission threshold $r_{\gamma }$ and $\stackrel{-}{T}(m,N,r_{\gamma })$ is the average transmission time for N users under m time slots with transmission threshold $r_{\gamma }$ , which can be expressed as

$$\begin{array}{l}\stackrel{-}{X}\left(m,N,r_{\gamma }\right)={\displaystyle \sum }_{i=\mathrm{1}}^{n_t}i·l·\left(\stackrel{R}{\underset{\omega =\gamma }{{\displaystyle \sum }‍}}{P}_f\left(i,m,N,r_{\gamma },r_{\omega }\right)\right),\\ \stackrel{-}{T}\left(m,N,r_{\gamma }\right)=T\left(i=\mathrm{0},m\right)·P_f\left(i=\mathrm{0},m,N,r_{\gamma }\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}+\stackrel{n_t}{\underset{i=\mathrm{0}}{{\displaystyle \sum }‍}}\stackrel{R}{\underset{\omega }{{\displaystyle \sum }‍}}T\left(i,m,r_{\omega }\right)·P_f\left(i,m,N,r_{\gamma },r_{\omega }\right),\end{array}$$

(13)

where index i represents the different frame types; $i=\mathrm{0}$ represents the null frame without transmission; $i=\mathrm{1}$ represents the frame involving one beam and length is l bits; $i=\mathrm{2}$ represents the frame involving two beams and length is $\mathrm{2}·l$ ; $i=\mathrm{3}$ represents the frame involving three beams and length is $\mathrm{3}·l$ ; $i=\mathrm{4}$ represents the frame involving four beams and length is $\mathrm{4}·l$ . Then the average frame length can be calculated through different frame types with probability. Let $P_f(i,m,N,r_{\gamma },r_{\omega })$ denote the transmission probability of i frame for N users under m time slots with threshold $r_{\gamma }$ and transmission rate $r_{\omega }$ .

If the probability $P_{\text{AP}}$ of AP contending the channel right use can be expressed as [22]

$$\begin{array}{cc}& P_{\text{AP}}=\frac{m!n!}{m^n}\stackrel{\min \left(m,n\right)}{\underset{j=\mathrm{1}}{{\displaystyle \sum }‍}}\frac{{\left(-\mathrm{1}\right)}^{j+\mathrm{1}}{\left(m-j\right)}^{n-j}}{\left(j-\mathrm{1}\right)!\left(m-j\right)!\left(n-j\right)!}.\end{array}$$

(14)

Due to the users in MU-MIMO group needing not to contend the channel, then one user can be located in different groups; therefore, the AP needs to select users in downlink MU-MIMO. If the SINR threshold is $r_{\gamma }$ , then the probability for selecting n users from N and $\text{SNR}>r_{\gamma }$ can be given by

$$\begin{array}{cc}& P_{\text{select}}\left(n,r_{\gamma }\right)=C_N^n{\left(\mathrm{1}-F\left(\gamma \right)\right)}^n{\left(F\left(\gamma \right)\right)}^{N-n}.\end{array}$$

(15)

Then the $P_f(i,m,N,r_{\gamma },r_{\omega })$ can be written as

$$\begin{array}{cc}& P_f\left(i,m,N,r_{\gamma },r_{\omega }\right)=\stackrel{N}{\underset{n=\mathrm{1}}{{\displaystyle \sum }‍}}\left(P_{\text{select}}\left(n,r_{\gamma }\right)·P_{ri}\left(r_{\omega },i\right)\right),\end{array}$$

(16)

where $P_{ri}(r_{\omega ,i})$ is the probability for users with i beams with available rate $r_{\omega }$ , which is owing to all the beams and where one user can have only one MCS in IEEE 802.11ac and can be given by

$$\begin{array}{l}{P}_{ri}(r_{\omega },i)\\ \hspace{0.17em}=P_r\left\{\left(\text{at}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{least}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{1}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{beam}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{with}\mathrm{\hspace{0.17em}\hspace{0.17em}}{r}_{\omega }\right)\cap \left(\text{no}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{beam}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{with}\mathrm{\hspace{0.17em}\hspace{0.17em}}r>r_{\omega }\right)\right\}\\ \hspace{0.17em}=P_r\left\{\left(\text{at}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{least}\mathrm{\hspace{0.17em}\hspace{0.17em}}\mathrm{1}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{beam}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{with}\mathrm{\hspace{0.17em}\hspace{0.17em}}{r}_{\omega }\right)\hspace{0.17em}|\hspace{0.17em}\left(\text{no}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{beam}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{with}\mathrm{\hspace{0.17em}\hspace{0.17em}}r>r_{\omega }\right)\right\}\\ \hspace{0.17em}\hspace{1em}·P_r\left\{\text{no}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{beam}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{with}\mathrm{\hspace{0.17em}\hspace{0.17em}}r>r_{\omega }\right\}\\ \hspace{0.17em}=\left(\mathrm{1}-P_r\left\{\mathrm{1}-P_r\left\{\text{all}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{beams}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{with}\mathrm{\hspace{0.17em}\hspace{0.17em}}r<r_{\omega }\right\}\right\}\right)\\ \hspace{0.17em}\hspace{1em}·P_r\left\{\text{all}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{beams}\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{with}\mathrm{\hspace{0.17em}\hspace{0.17em}}r<r_{\omega }\right\}\\ \hspace{0.17em}=\left(\left(\mathrm{1}-{\left[\frac{{{\displaystyle \sum }}_{v=\gamma }^{\omega -\mathrm{1}}{P}_r\left(r_v\right)}{{{\displaystyle \sum }}_{v=\gamma }^{\omega }{P}_r\left(r_v\right)}\right]}^i\right){\left[\frac{{{\displaystyle \sum }}_{v=\gamma }^{\omega }{P}_r\left(r_v\right)}{{{\displaystyle \sum }}_{v=\gamma }^R{P}_r\left(r_v\right)}\right]}^i\right),\end{array}$$

(17)

where $P_r(r_v)$ is the probability with transmission rate less than $r_{\omega }$ .

Then, we can obtain the $\stackrel{-}{X}(m,N,r_{\gamma })$ and the $T(i,m,r_{\omega })$ can be calculated as

$$\begin{array}{cc}& T\left(i,m,r_{\omega }\right)=T_{\text{data}}\left(i,r_{\omega }\right)+T_{\text{overhead}}\left(i,m\right),\end{array}$$

(18)

where $T_{\text{data}(i,r_{\omega })}$ denotes the transmission time for i frame with transmission rate $r_{\omega }$ and $T_{\text{overhead}}(i,m)$ is the frame control overhead (such as RTS, CTS) for i frame under m time slots.

5. Simulation

In this section, we will verify the performance gains and analysis of the scheme proposed through simulations.

We first show the probability density function (PDF) of the redundant time in SU mode compared with simulation and analysis in different service frame numbers in Figure 5; then it can be observed that the measurement shows good agreement between the theoretical analysis and experimental results. Meanwhile, it is also illustrated that the redundant time in TXOP reduces gradually with the transmission frames increasing.

Figure 5

The PDF of the redundant time in SU mode.

We then compare the theoretical analysis and experimental results of the redundant time PDF in MU mode with different MU-MIMO transmission station number and service frame number in Figure 6; it can be observed that the redundant time in TXOP will reduce with the service frame number increasing as well as SU mode. Furthermore, the station number in group also has greater effect on the redundant time in TXOP. The reason is that the more the station number in group, the longer the transmission time; then the redundant time in TXOP may decrease more obviously.

Figure 6

The PDF of the redundant time in MU mode.

As we can see from the theoretical and numerical results of throughput gains in SU mode in Figure 7, we can know that the measurement shows good agreement between the theoretical analysis and experimental results with different released station number and frame number variation. The results further illustrate that the throughput gains will boost considerably especially with the released station number increasing and no matter how many antennas, the calculation of the released station number can be carried out by Campel theorem [19].

Figure 7

The PDF of the throughput gains in SU mode.

Figure 8 demonstrates that the proposed two-level network allocation vector scheme can be vastly superior to the conventional mechanism with the redundant time increasing, which verifies the superiority and correctness of the proposed scheme. The growing gap in throughput outcomes is due to more stations which can win over more time for data transmission; then the throughput can be enhanced greatly with the redundant time in TXOP increasing.

Figure 8

The tendency comparison with the redundant time increasing.

Figure 9 gives the performance analysis of MU-MIMO in IEEE 802.11ac with parameters as Table 1. From this figure, we can observe that the smaller the threshold is, the larger the throughput will be; the reason is that the user number may reduce gradually if the threshold increases. Furthermore, as expected, the correctness of theory analysis is verified through simulation results.

Table 1

The threshold $r_{\mathrm{\gamma }}$ and available rates $r_{\mathrm{\omega }}$ .

Index	Available rates (Mbps)	Threshold $\mathrm{\gamma }$ (dB)
1	0	$\mathrm{\gamma }\le \mathrm{8}$
2	6	$8<\mathrm{\gamma }\le \mathit{12.5}$
3	9	$\mathit{12.5}<\mathrm{\gamma }\le \mathrm{14}$
4	12	$\mathrm{14}<\mathrm{\gamma }\le \mathit{16.5}$
5	18	$\mathit{16.5}<\mathrm{\gamma }\le \mathrm{19}$
6	24	$\mathrm{19}<\mathrm{\gamma }\le \mathit{22.5}$
7	36	$\mathit{22.5}<\mathrm{\gamma }\le \mathrm{26}$
8	48	$\mathrm{26}<\mathrm{\gamma }\le \mathrm{28}$
9	54	$\mathrm{\gamma }>\mathrm{28}$

Figure 9

Performance analysis of the MU-MIMO in IEEE 802.11ac.

System goodput is a critical assessment consideration for wireless networks and can be generalized to evaluate the performance of the practical network; it is defined as the amount of network data it receives correctly and can be expressed as (1 − Per) * throughput, where the Per is the packet error ratio. As can be seen from Figure 10, we can observe that the proposed scheme is superior to the conventional mechanism; the reason is that the performance gains come from the limited feedback, which can bring AP more accurate channel state information. Furthermore, the BA frame in traditional mechanism also needs to transmit; what we have done is to take advantage of the reserved bits effectively.

Figure 10

The performance comparison of the proposed feedback mechanism with conventional scheme.

In Figure 11, the throughput performance of the secondary AC users polling is compared to the traditional IEEE 802.11ac draft. It can be seen that the throughput of AP is larger than the traditional mechanism, which is resulting from that the polling of the secondary AC users can extend the downlink transmission time of AP. On the contrary, the AP just polls the primary AC user in traditional mechanism may result in unfairness for other STAs in group. Meanwhile, the proposed scheme has little effect on the downlink transmission time of STAs in group because MU-MIMO transmission is only executed by AP in IEEE 802.11ac. Therefore, we can observe that the proposed secondary AC users polling in TXOP can not only increase the system throughput but also enhance the success probability of TXOP initialization.

Figure 11

Secondary AC user polling based on TXOP fairness.

6. Conclusion

In this paper, we propose the enhanced NAV mechanism based on IEEE 802.11ac draft, which only needs subtle frame structure modifications and can bring large improvement of system throughput. Both performance analysis and numerical simulations are also provided for the proposed enhanced NAV scheme. The results showed that the proposed enhanced NAV scheme can obtain noticeable performance gains than the conventional mechanism. From the results, we can know that the performance of conventional mechanism varies with what parameters and also obtain how to adjust parameters related to the proposed scheme to improve the system throughput. Using the scheme we proposed, one can solve the drawbacks of conventional mechanism easily and conveniently and also can evaluate the performance of VHT WLANs fast and obviously. On this basis, in order to solve the SINR inaccuracy calculated based on null data packet in the actual MU-MIMO transmission, the SINR feedback mechanism is proposed and the frame structure modifications are displayed in detail. Furthermore, theoretical analysis is also performed on the proposed mechanism and the formulas of the achieved gains are also derived. Numerical results confirm the validation of our theoretical analysis and further substantiate that the proposed scheme obtains obvious throughput gain over the conventional mechanism. Additionally, the throughput performance of the secondary AC users polling is compared to the traditional IEEE 802.11ac draft. It can be concluded that the throughput of AP is larger than the traditional mechanism, which is resulting from the fact that the polling of the secondary AC users can extend the downlink transmission time of AP. Finally, we can observe that the proposed secondary AC users polling in TXOP can not only increase the system throughput but also enhance the success probability of TXOP initialization.