Recovering CSI and Data in Dense Network Environments Using IEEE 802.11ax Midamble

There has been considerable amount of research to improve performance for a dense wireless local area network (WLAN) environment. While some studies focus on aggressive channel access, others highlight frequent channel state information (CSI) corruption by excessive transmissions. We pay attention to midamble, adopted in the IEEE 802.11ax standard specification, to overcome CSI corruption. If the transmitter inserts midamble symbols, the receiver can acquire new CSI periodically during a physical layer convergence protocol (PLCP) protocol data unit (PPDU) frame. In this paper, we propose a precise receiver performance model to describe the impact of CSI, and design a standard-compliant algorithm called REMEDY that works with conventional channel access schemes by handling CSI corruption and time-varying channels in high-density WLAN networks. REMEDY determines whether to use midamble considering overhead, estimates on-frame signal-to-interference and noise ratio (SINR) to notice channel environments, and cancels the effects of scrambling and incorrect descrambling. We evaluate the performance of the conventional schemes with and without REMEDY in 11ax task group (TGax) indoor simulation scenarios using the ns-3 simulator, considering time-varying channels and CSI corruption. REMEDY helps the existing channel access schemes to achieve up to $2.20\times $ higher throughput while improving the throughput of the lowest performing group, compared to the existing schemes without REMEDY.


I. INTRODUCTION
Wi-Fi is one of the most representative wireless technologies in our daily lives, based on the IEEE 802.11 wireless local area network (WLAN) standard, by virtue of its easy deployment and convenience for users at low prices. These The associate editor coordinating the review of this manuscript and approving it for publication was Li Zhang. strengths have accelerated the explosion of Wi-Fi devices and infrastructure, making billions of users routinely enjoy handy Internet access, and causing their networks to grow constantly with crowded and diversified environments. In such real network scenarios, however, it is also widely known that Wi-Fi users commonly experience severe performance loss [1], [2]. Looking further into the user-unfavorable scenarios from the viewpoint of link-level Wi-Fi device operation, it should be noted that the performance loss is highly concerned with the quality of channel state information (CSI), acquired and employed at Wi-Fi receiver in an on-frame manner.
Specifically, the CSI obtained from the frame preamble is prone to get outdated in mobile environments or initially corrupted by interference in congested networks bringing the estimated channel vectors that are dispersed from the actual wireless channel. This erroneous CSI is used for data symbol equalization, so the Wi-Fi receiver suffers from a poor error vector magnitude (EVM) and thus a high frame error rate (FER), resulting in loss of network throughput. To clarify CSI-related detrimental factors, we highlight two different aspects of real network scenarios: the time-varying nature of wireless channels and concurrent interference.
The first aspect is the time-varying channel due to user mobility or its surroundings. A Wi-Fi station acquires its CSI at the preamble of a received frame, so the EVM grows as the acquired CSI is outdated, as depicted in Fig. 1 [3], 1 where NI 1 is an initial EVM with noise and channel gain. The second aspect is interference, which is a decisive factor in degrading decoding performance in dense network environments. It's worth noting that the interference primarily originates from a lack of coordination among the network nodes, which appears as excessive collision and hidden terminal relation. Denoting the EVM during interference as NI 2 , the pattern of the EVM with intruding interference is shown in Fig. 1b. It is evident that the EVM suddenly increases from NI 1 to NI 2 due to the distortion in data symbols. However, with preceding interference in Fig. 1c, the EVM does not drop from NI 2 to NI 1 after the interference ends [4].
The consistent EVM is due to distortion in the preamble, called CSI corruption, which affects the whole frame even after the cause disappears. The receiver does not send a response due to the complete frame failure. CSI corruption becomes a major concern due to frame retransmission after missed responses and backoff counter increments. In dense networks, the dynamic relationship between stations causes extensive interference.
Consequently, the phenomenon depicted in Fig. 1c harms network performance more severely, making CSI corruption an urgent issue [5]. There have been numerous studies dealing with mobile network environments, but none have addressed CSI corruption in those environments. Most studies attempt to assume practical environments, but do not consider CSI corruption and channel changes together during frame reception. In this paper, we deal with CSI corruption using the midamble adopted in the IEEE 802.11ax standard specifications for mobile environments [6]. To this end, we first propose a channel model that considers user mobility and CSI corruption together.
We raise three issues when using midamble to address CSI corruption: midamble overhead, on-frame channel estimation, and data recovery. Our proposed algorithm called REMEDY makes decisions on whether to use midamble based on error patterns, estimates on-frame signal-to-interference ratio (SINR) to analyze channel environments, and recovers erroneously descrambled data bits by rescrambling. REM-EDY shows considerable throughput gains and fairness under various 11ax task group (TGax) indoor scenarios and, importantly, is standard-compliant. To the best of our knowledge, this is the first work that fundamentally solves the CSI corruption problem and studies the effects of using midamble in dense network environments.
The rest of this paper is organized as follows. We introduce the background and related work of midamble, timevarying channel, and high-density network in Section II. In Section III, we propose a post-processing SINR model that considers both interference and channel change due to user mobility during frame reception. Then we study the effects of using midamble in Section IV. We propose REMEDY to improve performance in terms of throughput and fairness in a dense network in Section V and evaluate it in Section VI. Finally, Section VII concludes this paper.
what the transmitter has sent. The IEEE 802.11 WLAN standards, including the latest amendment for high efficiency (HE), specify predefined types of preamble sequence to be appended at the beginning of each frame, such that the receiver can utilize it for CSI acquisition purpose [6]. In detail, the transmitter inserts HE long training field (HE-LTF), consisting of known symbols on data subcarriers. The receiver compares the received HE-LTF symbols to the predefined ones to acquire the CSI, and computes the coefficients to estimate and decode the transmitted data symbols.
The midamble introduced in HE WLAN has already been proposed in IEEE 802.11p [7], aiming to overcome rapidly changing channels in wireless access in vehicular environment (WAVE) systems [8], [9]. As shown in Fig. 2, when transmitting frames, the transmitter can insert midamble symbols periodically for every predetermined number of data symbols, midamble periodicity, reusing HE-LTF symbols present in the preamble as they are. Signaling information to indicate the presence of midamble symbols and its periodicity is simply carried in the HE-SIG-A subfield, such that the receiver can check its availability for channel equalization. Afterward, the receiver can update CSI at every midamble symbol location during channel equalization. The use of midamble has been shown to effectively resolve the time-varying channel issues in a mobile environment, as demonstrated in previous studies [8], [9].
Although the benefits of using midamble are evident, the overhead burdens the users to use it in real scenarios. To be specific, when transmitted every 20 data symbols, the midamble occupy approximately 4.8% ( = 1/21) of an entire frame duration given each midamble part consisting of a single LTF symbol with 4x HE-LTF type. 2 If the transmitter uses additional spatial streams, the number of HE-LTF symbols in both the preamble and midamble symbols increases linearly. Besides, as the transmitter inserts midamble symbols more frequently, the number of midamble symbols in a frame increases, resulting in an overhead of up to 29% (= 4/14) of frame transmission when using four spatial streams with a midamble periodicity of 10.

B. TIME-VARYING CHANNEL AND CAUDAL LOSS
In a mobile environment that involves the mobility of stations and surrounding objects, wireless channels typically have time-varying characteristics. Given the nature of the Wi-Fi frame structure, which acquires CSI at the preamble, the receiver equalizes received symbols using the CSI that is different from the channel actually experienced. Since the actual channel effects cannot be properly canceled out using such outdated CSI, the channel equalization process produces additional error vectors bringing inaccurately decoded orthogonal frequency division multiplexing (OFDM) symbols referred to as caudal loss [3]. As the caudal loss problem in mobile environments is one of the well-known obstacles to achieving better Wi-Fi performance, there have been numerous studies to overcome the time-varying channel characteristics.
A common way to track the channel variations is to update CSI using pilot subcarriers [10], [11], [12], [13], [14]. However, the channel estimation via pilots can never be sufficient to renew the CSI for whole data subcarriers, due to the lack of available pilot subcarriers. Instead of using pilots, the authors in [15] renew the CSI via preceding OFDM data symbols that have been already decoded. This approach works effectively as intended in high SNR environments, but errors can be easily propagated if the CSI begins to be mistracked.
On the other hand, adaptive control of transmission parameters can be an effective approach to avoid caudal loss. Lee et al. [16] proposed to use various modulation and coding schemes (MCS) within a single frame, but this approach is not standard-compliant. In [3], the authors calculate the optimal MCS and aggregation size of the aggregate MAC protocol data unit (A-MPDU) based on the error rates of subframes, given a time-varying channel. Nevertheless, their approaches come at the cost of efficient use of time resources as they do not actively utilize transmission opportunities.

C. HIGH-DENSITY NETWORK AND CSI CORRUPTION
The more Wi-Fi users there are, the greater the likelihood of ongoing interference during the preamble, leading to CSI corruption [4]. Since a frame without midamble symbols enables CSI acquisition only at the preamble, the whole frame is affected by the corrupted CSI. That is, each CSI corruption results in one full frame error as depicted in Fig. 1c. Due to the lack of consideration for this error factor, however, previous studies on high-density networks have mainly focused on resolving hidden and exposed terminal problems from a medium access control (MAC) perspective.
Some of the previous works suggest lowering the receiver's sensitivity to ignore ongoing signals in the air [17], [18] or just disregarding beacon frames [19] and start their own transmissions aggressively, but their proposals do not comply with the standard specifications. Others propose to lower the transmission power used for control frames such as acknowledgement (ACK) frame [20] or clear-to-send (CTS) frame [21], to allow neighboring stations to transmit concurrently. However, their evaluation does not take into account dense networks sufficiently [17], [20], or simply relies on unrealistic assumptions on rate control [18]. Thus, as shown in recent studies, aggressive and concurrent transmission only makes performance worse in dense networks [4], [5].
A dense, interference-prone network causes frequent preamble passing problems where two stations that are not in a hidden relation cannot sense each other's preamble [5]. Most of the conventional approaches to improving performance in dense networks rely on the precondition of successful frame reception, or at least preamble reception, to achieve their intended action. However, in dense networks where preamble passing occurs frequently, these approaches are unlikely to work as intended. Moreover, the frequent occurrence of preamble passing causes unexpected interference and blind transmission, resulting in CSI corruption.

III. PROPOSED PPSINR MODEL FOR REALISTIC WI-FI LINK PERFORMANCE
To accurately model the effects of both time-varying channels and CSI corruption, it is important to develop a model that can embrace both effects. However, relying on the nominal SINR, which indicates the traditional SINR value defined by the ratio of the received power to the noise interference level, is not sufficient to model realistic Wi-Fi link performance. In contrast, the post-processing SINR (PPSINR) [22], measured by the ratio of the received power to the error vector power between the intended and equalized symbols, represents more accurate performance at the receiver. For a comprehensive evaluation of network performance, we propose a PPSINR model that considers two additional error vectors, derived by caudal loss and CSI corruption, respectively.

A. PPSINR MODEL DERIVATION
Based on the process of CSI acquisition and equalization, we focus on the difference between the initially acquired channel at the preamble and the later experienced channel during data symbol decoding. We first derive PPSINR for the ideal case using perfect CSI, and subsequently embrace the effects of a time-varying channel and CSI corruption by altering the conditions of imperfectly acquired and experienced channels. Suppose an N × N multiple-input and multipleoutput (MIMO) system with a minimum mean-squared error (MMSE) receiver. During the CSI acquisition, the receiver estimates a channel matrix H LTF ∈ C N ×N based on the received HE-LTF symbols, Y LTF ∈ C N ×N , which can be expressed as where X LTF ∈ C N ×N is the predefined HE-LTF symbols. Then y D ∈ C N , the received data symbol to decode, is while H D ∈ C N ×N denotes the channel matrix that the symbol actually experiences, x D ∈ C N is the transmitted data, and z D ∈ C N is the noise and interference vector. For equalization purpose, the receiver generates MMSE coefficient matrix W (H LTF ) using the acquired H LTF as where E z D z H D = σ 2 z,D I and P rx is the mean received power per spatial stream. Therefore, the baseline equation to derive error vector e ∈ C N from the difference between the transmitted and received symbols after channel equalization is with G ∈ C N ×N representing channel equalization gain as Assuming the use of ideal CSI (i.e., H LTF = H D ), the PPSINR for the i-th spatial stream becomes while W D = W (H D ) and {·} a,b stands for the (a, b)-th element of the matrix. Different from the ideal case above, we introduce an additional error vector e D to consider the impact of imperfect CSI, which comes from the difference between H LTF and H D : where e D ∈ C N . We obtain this error vector from the difference between a generated MMSE coefficient for decoding, W (H LTF ), and a desired MMSE coefficient, W (H D ).

1) CAUDAL LOSS
Acquired CSI without midamble contains channel information only at the time of receiving HE-LTF at the preamble, so it cannot properly help to track wireless channels that change later. The difference between the acquired and experienced channels grows over time, and this gap produces an additional error vector during the channel equalization process. Assume that the channel matrix at HE-LTF is H 0 ∈ C N ×N and the channel matrix becomes H τ ∈ C N ×N at τ . Then with respect to the acquired and experienced channel, i.e., H LTF = H 0 and H D = H τ , we can rewrite Eq. (7) as Then the power of the additional error vector due to the time-varying channel for the i-th spatial stream is VOLUME 11, 2023 with σ 2 caud,i given in [3] as

2) CSI CORRUPTION
If there exists interference during HE-LTF reception, the receiver acquires corrupted CSI rather than perfect CSI. The corrupted CSI propagates the error in HE-LTF over all decoded OFDM symbols and prevents the receiver from achieving a PPSINR higher than the SINR at the header [4].
Considering the CSI acquisition under concurrent interference during HE-LTF, the receiver obtains an corrupted HE-LTF Y LTF as where Z LTF ∈ C N ×N denotes the interference matrix whose n-th column vector is z LTF,n with E z LTF,n z H LTF,n = σ 2 z,LTF I. Subsequently, the imperfect channel matrix H ∈ C N ×N is acquired by the receiver as 3 Then we can rewrite Eq. (7) again for the CSI corruption case with regard to H LTF = H and H D = H 0 , where W stands for W = W ( H) − W (H 0 ). Hence, we get the power of the additional error vector from the corrupted CSI for the i-th spatial stream as with σ 2 corr,i given in [4] as Drawing on the same derivation as found in [4] and [22], we make approximations for each of the two expectation 3 The least squares (LS) estimation is used for CSI acquisition. For simplicity, we assume that the transmitter transmits the same number of LTF symbols as its spatial streams. terms present in Eq. (15) as where µ = σ 2 z,LTF / (NP rx ), K = H H 0 H 0 + µN I −1 , and Tr (·) denotes the trace of a matrix.

3) COMBINED MODEL
Considering the both effects, i.e., caudal loss and CSI corruption, we put H LTF = H and H D = H τ . Fig. 3 depicts each step of extracting the error vectors based on the acquired and experienced channels. We can rewrite Eq. (7) for the error vector of the combined model, e comb , as Therefore, we have the power of the additional error vector for the combined model as while e caud and e corr are independent of each other and the expectation of each vector is zero vector making the term E e caud e H corr + e corr e H caud i,i zero. Consequently, with considerations on two additional error vectors from caudal loss and CSI corruption, we present our proposed PPSINR model for the i-th spatial stream based on Eq. (6) as where ρ = σ 2 z,D /P rx , the inverse of nominal SINR. Eq. (20) represents the ratio of power in the correctly decoded symbol to the power of EVM at the receiver in total, which encompasses the effects of noise plus interference, caudal loss, and CSI corruption. 4

B. PPSINR MODEL VERIFICATION
Our verification has been driven by the elaborate 11ax linklevel simulator. The features of 11ax PHY and lower MAC protocols, including new OFDM numerology and HE physical layer convergence protocol (PLCP) protocol data unit (PPDU) format as well as midamble, are embedded by using IT++ libraries [23] and GNU Radio [24] at the baseband signal processing level. The traced channel we employ in our simulations is derived from TGax channel model [25] which is built upon the TGac and TGn channel models assuming environmental speed of 1.2 km/h under mobile conditions. In addition, we employ 4x HE-LTF that enables a receiver to utilize all the data subcarriers for CSI acquisition. 5 Table 1 shows the other model and simulation parameters used in the link-level simulator.
In our link-level simulation, we choose MCS 7 for data symbol modulation and coding, i.e., the highest mandatory data rate for stations, but it should be noted that the PPSINR level, as a performance metric, is not dependent on the MCS being used. Further, employing such a high data rate, despite the presence of concurrent interference, is a possible scenario in practice due to the unpredictable nature of interference in distributed networks. Sudden interference at the receiver 4 Note that the receiver can update the acquired CSI and MMSE coefficient with the use of midamble. This changes the input of Eq. (20), leading to the re-calculation of on-frame PPSINR using the given CSI. 5 Using either 1x or 2x HE-LTF necessitates subcarrier interpolation at the receiver, causing potential imperfection in CSI depending on the given channel conditions, which is beyond the scope of this work. could not be instantly detected by the transmitter side, challenging the agile rate control [4], [5].
To verify the suggested PPSINR model in Eq. (20), we set up a time-varying channel with preceding interference which makes the nominal SINR 20 dB and disappears at 1 ms making the nominal SINR 40 dB. In Fig. 4, LLS describes the PPSINR values from link-level simulation, induced by the inverse square of EVM measurements between transmitted and received symbols. On the other hand, Caudal loss, CSI corr, and Combined model represent the PPSINR values from the mathematical models, calculated by the formulas in Section III-A, using the same channel traces as in our link-level simulation for fair comparison. Note that in our simulations, we employ a zero-forcing decoder for single-input and single-output (SISO) system and an MMSE decoder for MIMO system.
As shown in Fig. 4, Caudal loss reflects the degradation of PPSINR over time, due to growing channel variation from the initial HE-LTF. But at the same time, PPSINR recovers over 20 dB at 1 ms, as this model simply assumes ideal CSI acquisition which is not the realistic case in LLS. Meanwhile, CSI corr shows that PPSINR cannot exceed the nominal SINR of 20 dB even after the preceding interference disappears at 1 ms, because the model reflects the impact of CSI corruption at the preamble. Without taking into account the impact of time-varying channels, CSI corr becomes incomparable with LLS over time, which implies an unrealistic PPSINR level. Lastly, PPSINR from Combined model reveals both its descending trend over time and the persistent upper-bounded level after the end of preceding interference, which verifies good consistency with the results from link-level simulation for both SISO and 2 × 2 MIMO cases.
In addition, Fig. 5  Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  recovers to 40 dB at 1 ms. With the preamble SINR of 40 dB, where the nominal SINR remains unchanged over time, the PPSINR consistently diminishes spotlighting the caudal loss effect of the time-varying channel. On the other hand, the impact of CSI corruption is more evident with lower preamble SINRs such as 10 dB and 20 dB, showing poor PPSINR levels even after the recovery of nominal SINR at 1 ms. 6 Through this comparison, it can be verified that the Combined model retains good congruence with the results from the simulation, LLS.

IV. CASE STUDY A. MIDAMBLE ON A SINGLE LINK
Using the same simulation settings as in Section III-B, we conduct link-level simulation to see the effects of midamble on a single link performance with midamble periodicity of 20 if inserted. Without using midamble, it can be expected that PPSINR just decreases over time due to the caudal loss in a time-varying channel, as shown by Midamble Off in Fig. 6. The use of midamble then allows for periodic CSI renewal in the middle of a frame reception. Midamble On in Fig. 6 shows a repetitive pattern of sudden increases and gradual decreases in PPSINR. This pattern arises because the CSI acquired from a midamble symbol matches well with the actual channel at the very moment, but becomes outdated again with their gap growing until the next midamble symbol is received. This simple scenario with a time-varying channel 6 The slight fluctuations in LLS come from the effect of noise and inter-stream interference in spatial domain. verifies that the midamble works as intended, i.e., it can help the receiver track the channel by renewing its CSI periodically within a frame reception, thus leading to mitigation of the caudal loss.
On the other hand, the effect of midamble appears a bit different when there is any external interference involved. This time, to exclude the caudal loss effect, we adopt a static channel and generate intruding interference that makes the nominal SINR vary from 40 dB to 20 dB at 1 ms in the middle of a frame reception. Fig. 7 shows that PPSINR drops immediately when the intruding interference starts. In this case, using midamble does not help the receiver recover its PPSINR, as the data symbols to be decoded are being corrupted by the interference. Interestingly, we observe that PPSINR rather deteriorates with the use of midamble. This is because the midamble symbols also being corrupted by the interference after 1 ms are used by the receiver to renew its CSI, which makes the performance even worse.
As a countermeasure to the case of intruding interference above, we consider preceding interference, with the same signal strength levels as those in Fig. 7. While the preceding interference ends at 1 ms in the middle of a frame reception, the receiver's CSI remains corrupted as the preamble had been received under the interference. As a result, even if the rest of the frame reception after 1 ms is not damaged directly by the interference and the receiver can see a high nominal SINR, it still suffers poor PPSINR that is comparable to the PPSINR level at the preamble, as shown by Midamble Off in Fig. 7b. In contrast, with the use of midamble (Midamble On), the PPSINR is recovered to almost a similar level to the nominal SINR after the interference disappears. Fig. 8 depicts a detailed illustration of PPSINR recovery at the receiver using midamble in the presence of CSI corruption and time-varying channels. We pay attention to the periodic CSI re-acquisition via midamble symbols, which helps recover CSI and thus the PPSINR despite its initial corruption at the preamble. The use of midamble provides a new way to address the CSI corruption at the preamble, as it allows the receiver to renew its CSI in more favorable environment, e.g., after the interference disappears.
To see how the on-frame PPSINR recovery via midamble does affect the receiver performance in practice, we further evaluate subframe error rate (SFER) in Fig. 9. SFER  represents the ratio of failed subframes to total transmitted subframes within an A-MPDU. Again, it is assumed that the preceding interference ends at 1 ms, which is in the middle of the 6-th subframe. Since the initial CSI corruption has a persistent effects on data symbols if not using midamble, Midamble Off shows high SFER even after the 6-th subframe. On the other hand, while the use of midamble helps mitigate the errors from CSI corruption, SFER still remains above 20% as shown by Midamble On, which is contrary to the aforementioned PPSINR recovered to almost the nominal SINR level as depicted in Fig. 7b.
The reason for such high SFER remaining despite the use of midamble can be found in the scrambling and descrambling process of Wi-Fi systems. At the beginning of payload part in every Wi-Fi frame, a SERVICE field provides the receiver with scrambler initialization bits for descrambling process on the subsequent payload bits. Unlike the other PLCP headers, the SERVICE field is encoded with the same MCS as that for data symbols, thus being vulnerable to the CSI corruption in interference-prone environments. Unfortunately, once the SERVICE field is received with errors, the following data bits become all messed up as they are descrambled using wrong scrambler initialization bits. The result is a decoding failure of the whole data bits at the receiver, even in the absence of errors in the data part itself. 7 This explains the remaining SFER for Midamble On in Fig. 9, i.e., the SERVICE field is received with errors in 20% cases on average, and thus the following data bits become broken despite the recovery of PPSINR with midamble. It can be verified by Midamble On + No Scramble in Fig. 9, where the desired recovery of zero SFER is accomplished at 1 ms by only skipping the scrambling and descrambling process at 7 From this aspect, the SERVICE field plays a similar role as CSI in that its accurate information is essential for successful data decoding.  the transmitter and receiver. To address this issue and achieve the actual performance gain via midamble, we can conclude that it is necessary to correct the erroneous descrambled bits, called rescramble, to resolve the frame losses from CSI corruption.

B. MIDAMBLE IN DENSE NETWORKS
We evaluate the effects of midamble on network performance using ns-3 simulator [26], taking into account both the caudal loss and CSI corruption. To ensure accurate link performance in practical environments, we apply our proposed PPSINR model as described in Eq. (20) to the ns-3 simulator. The network topology follows TGax indoor simulation scenario [27] with frequency reuse 3, as depicted in Fig. 10, which consists of 19 hexagonal basic service sets (BSS) with a radius of 10 m spaced 30 m apart from each other. Each BSS is composed of 1 access point (AP) and N STA station(s). With the same model and parameters listed in Table 1, we assume that each AP and station employs Minstrel rate control algorithm, and determines A-MPDU aggregation size to maximize the frame duration up to 5.484 ms, as defined by standard specification. Given that an A-MPDU frame contains MPDU subframes with a fixed size of 1500 bytes, the number of data symbols varies from 329 to 342 depending on the chosen MCS. With midamble periodicity of 20, if inserted, the number of midamble symbols falls between 16 and 17 corresponding to additional PHY overhead of approximately 4.7% in the entire frame duration. Every AP generates fully backlogged user datagram protocol (UDP) traffic toward its associated station(s).
We compare the performance of three different scenarios: Legacy (Mobile Ch), Midamble (Mobile Ch), and Legacy (Static Ch) in Fig. 11. In Midamble (Mobile Ch), every transmitting AP or station inserts midamble symbols into each PPDU frame, while the midamble feature is always disabled in Legacy (Mobile Ch). Further Legacy (Static Ch) assumes static channel environments only, where there exists no caudal loss involved when receiving PPDU frames. We set the number of stations N STA to 1, 4, and 7 to investigate the impact of network density on performance. Note that A-MPDU error rate (AER) represents the ratio of entirely failed A-MPDUs, which can be noticed by missed block acknowledgement frame (BA), to the total transmitted A-MPDUs, while SFER is measured by received BA indicating success of at least one subframe within an A-MPDU.
When there is only one station per BSS, the impact of caudal loss appears to be substantial, particularly with the use of request-to-send and clear-to-send (RTS/CTS), which suppresses interference from hidden node and where channel condition matters more. In this case, the aggregated throughput in Legacy (Mobile Ch) is only about 85% of that in Legacy (Static Ch). The rate control algorithm lowers the MCS in response to caudal loss, leading to reduced throughput due to the use of a lower MCS and the errors from time-varying channel. In case of Midamble (Mobile Ch), the stations barely suffer from caudal loss, but only achieves up to 94% of the throughput of Legacy (Static Ch) due to its midamble overhead.
The midamble is beneficial for alleviating caudal loss as shown by Midamble (Mobile Ch) in Fig. 11, but its performance gain diminishes when there are multiple stations in each BSS. Besides, the gap between the scenarios shrinks considerably in the absence of RTS/CTS. This implies that the impact of caudal loss becomes less dominant as the network density grows with more stations, which can supported by observing that the throughput of Legacy (Mobile Ch) even becomes comparable to that of Legacy (Static Ch). In addition, while SFER remains similar, AER becomes much higher with increasing number of stations, which stands for frequent occurrences of the CSI corruption. As the network density increases and interference becomes prevalent, CSI corruption has more dominant impact on the network throughput because it causes entire frame losses at receivers regardless of the caudal loss effect. With no ACK response sent by the receivers for entire frame losses, it can even worsen the network performance.
In all scenarios, Legacy (Mobile Ch) shows the lowest AER and SFER, even though it is unable to prevent the caudal loss. The transmitter's rate control algorithm in Legacy (Mobile Ch) selects lower MCSs in response to the caudal loss, providing robustness against the interference. On the other hand, Midamble (Mobile Ch) does not achieve significant improvement in throughput and rather shows higher error rates in dense scenarios, which is due to the use of higher MCSs. Moreover, Legacy (Static Ch) eliminates the effects of caudal loss, but shows even worse error rates incurred by prevalent interference from hidden node. Therefore, simply resolving the caudal loss is not enough to enhance the network performance in dense scenarios. Elaborate decisions on the use of midamble and MCS selection considering the network environment, as well as recovering incorrectly descrambled data bits, are necessary. In summary, the decision on whether or not to use midamble should be based on network density and mobility.

V. PROPOSED ALGORITHM: REMEDY
In dense networks where the hidden node and preamble passing problems prevail, a receiver is prone to suffering CSI corruption when receiving a frame in the presence of preceding interference. Such CSI corruption then causes persistent degradation in the decoding process of subsequent data symbols at the receiver. Based on the idea depicted in Fig. 8, however, we note that the receiver can renew its CSI via midamble in the middle of a frame, and desirably can utilize the recovered CSI to achieve better decoding performance after the preceding interference vanishes. Our proposed algorithm, REMEDY, aims to recover the CSI and MPDUs in an on-frame manner by utilizing midamble and addressing the following three challenges: 1) Determining whether to use midamble considering its overhead, 2) estimating and tracking the on-frame SINR to understand the channel environment, and 3) correcting the wrongly descrambled bits to recover data bits. Fig. 12 depicts the flowchart of REMEDY. In response to previous data transmission, the transmitter waits for BA from the receiver. The transmitter first checks the midamble request from the receiver via 1 in the Doppler field in the BA. Then if midamble is not requested, it determines whether to insert midamble for its next transmission via error patterns recognized by the BA. On the other hand, the receiver decodes MPDU to confirm the correct reception of the PPDU frame, and estimates on-frame PPSINR using midamble symbols to understand the surrounding environment. Failure of the first MPDU implies high probability of CSI corruption and wrong descrambling. Then, once the receiver observes that the on-frame estimated PPSINR increases, it attempts to cor-rect wrongly descrambled data bits. Additionally, based on the on-frame PPSINR characteristics, the receiver determines and indicates if the use of midamble is needed afterwards, through Doppler field in its BA. It is worth noting that REMEDY does not require any extra functionality beyond the scope of IEEE 802.11 specifications, as it exploits the midamble feature for CSI recovery purpose. In this regard, REMEDY is fully standard-compliant and simply resides in the area of implementation-specific algorithm.

A. MIDAMBLE DECISION USING BLOCK ACK
As the use of midamble incurs a non-negligible overhead, it is crucial to estimate whether CSI corruption has occurred at the receiver and decide whether to insert midamble accordingly. Since the preceding interference that causes CSI corruption cannot be seen by transmitter, however, detecting CSI corruption from the transmitter's perspective is challenging. Therefore, REMEDY decides whether to insert midamble or not by examining the response from the receiver, i.e., BA for a previously transmitted frame. The BA delivers information regarding the transmission results, such as success or failure of each subframe within the previous A-MPDU, which can provide clues about the environment experienced by the receiver. By interpreting the error patterns within previously transmitted A-MPDU, the transmitter can infer that CSI corruption has occurred or not at the reeiver.
In detail, we notice three major error patterns, and REM-EDY decides to insert midamble when any of the error patterns is detected. The first pattern is the failures of N fp successive MPDUs right after the preamble. This indicates the presence of preceding interference or ill-conditioned channel gain around the preamble. Nonetheless, if the BA is received after the PPDU without midamble, CSI corruption is not severe enough that the receiver does not need midamble since reception of BA means success of at least one MPDU. The second one is N fc consecutive subframe errors in any part of a frame, which implies the existence of persistent and critical interference hidden from the transmitter. REMEDY inserts midamble for frames with a probing rate specified by the rate control algorithm. The third pattern is BA missing event. In this case, the transmitter inserts midamble assuming frequent interference or rapidly varying channels.
After receiving the BA, the rate control algorithm usually updates the statistics for the MCS used, but REMEDY only does for successfully transmitted MPDUs with midamble. This approach allows for maintaining the use of high MCSs suitable for the channel between the transmitter and receiver, while the interference-driven loss can be addressed by REMEDY. Hence, the rate control algorithm operates compatibly, with its rate selection principle not being constrained by REMEDY.

B. ON-FRAME PPSINR ESTIMATION
For intended operation of REMEDY, it is essential for the receiver to be aware of circumstances around its transmission link, where the received frames are coming. Thus, REMEDY proposes a novel on-frame PPSINR estimation. By estimating and tracking the PPSINR during a received frame, the receiver can determine whether it is experiencing CSI corruption or caudal loss, by referring to the time variation of on-frame EVM as in Fig. 1. In the case of CSI corruption, the receiver can detect when the interference has ended, enable to update the CSI, and then initiate data recovery. Meanwhile, for caudal loss, the receiver can detect the channel variation, and request the transmitter to use midamble via the BA's HE-SIG-A subfield. 8 Previous studies have attempted to detect and mitigate caudal loss based on SFER [3] or EVM [15]. However, these methods work as intended in small networks, but not in dense networks with frequent interference, which also affects SFER and EVM. Furthermore, there have been no studies focusing on identifying CSI corruption. This motivates us to propose a method to accurately distinguish between caudal loss and CSI corruption based on the on-frame PPSINR estimation mechanism.
By reusing the HE-LTF as a midamble symbol, it is possible to compare a known symbol and a decoded OFDM symbol. Based on the difference between the two symbols, whose magnitude corresponds to EVM, the station calculates the PPSINR. Specifically, REMEDY compares the PPSINR of the first and last midamble symbols decoded by the channel trained with the preamble.
Suppose τ n is the time for the n-th midamble symbol in a PPDU frame, τ 0 is for the HE-LTF symbol in the preamble, and τ l is for the last midamble symbol. The number of midamble symbols in the frame is l. Eq. (21) is the PPSINR calculated by the EVM between the known HE-LTF symbol X LTF and the equalized HE-LTF symbol. Fig. 13 illustrates this process in time-domain and I-Q plane basis. In detail, the equalized HE-LTF symbol is originally received HE-LTF symbol at τ b , but equalized by the MMSE coefficient based on HE-LTF at τ a . H a ∈ C N ×N denotes the acquired CSI at τ a including the effect of CSI corruption. Note again If we consider a in Eq. (21) as 0, the equation represents the PPSINR at τ b without the aid of midamble symbols. When the ratio of PPSINR 0,l to PPSINR 0,1 is lower than PPSINR thre satisfying the condition in Eq. (22), it indicates that on-frame PPSINR has been decreasing due to the presence of interference from hidden node or a time-varying channel. In consequence, the receiver requests midamble insertion through BA to avoid CSI corruption or caudal loss. Moreover, PPSINR k,k+1 represents the PPSINR at τ k+1 using the CSI obtained at τ k . Therefore, we can use PPSINR k,k+1 as an indicator to initiate rescrambling when the interference vanishes, i.e., to rescramble if the PPSINR goes sufficiently high for decoding data symbols correctly, depending on the used MCS.

C. DESCRAMBLE CORRECTION
Wi-Fi stations utilize scrambling to randomize bit transition patterns in transmitting data symbols, while descrambling removes such effects when receiving the data bits. When constructing a PPDU, a SERVICE field involving scrambler initialization bits is prepended to the data payload. Similar to CSI, the scrambler initialization bits are essential for descrambling all the data bits in the following MPDUs, but they can also ruin the entire frame if incorrectly received at the beginning [28], as explained in Section IV-A. Unfortunately, since HE-LTF and the SERVICE field are located in HE preamble and PLCP header, i.e., both at the front part of a frame as depicted in Fig. 2, the CSI corruption at the preamble most likely leads to wrong scrambler initialization bits and subsequent descrambling failures as shown in Fig. 9. This observation implies that as well as the CSI re-acquisition, we also need to rectify the wrong scrambler initialization bits by using the updated CSI, in order to benefit from midamble for the entire data bit decoding process.
To this end, REMEDY leverages the characteristics of scrambling process 9 and the A-MPDU frame structure. Our proposed procedure is detailed in Algorithm 1. REMEDY performs XOR between its 48-bit MAC address and the incorrectly descrambled data bits, as illustrated in line 4 of Algorithm 1. Since the MAC address of receiver itself is a known sequence at the known position 10 for intended transmission, we can expect the XOR between incorrectly descrambled MAC address bits and the actual MAC address to cancel out the MAC address component. The outcome is a 48-bit segment representing the result of XOR operation between two sequences: the sequence used for scrambling, and the incorrectly initialized descrambling sequence. 11 Since this 48-bit segment is also a part of the repetitive 127-bit unique sequence, 12 we can pinpoint the segment position and construct rest of the entire 127-bit sequence in order, which is the desired rescrambling sequence, R. By XORing the rescrambling sequence with wrongly descrambled data bits again in the unit of 127-bit segment, REMEDY can cancel out the effects of both scrambling and wrong descrambling simultaneously, which we refer to as rescrambling process.
The remaining issues in rescrambling are that it requires an exhaustive search to find the incorrectly descrambled MAC address every 32 bits, and the search process itself can be meaningless if the CSI corruption is not yet resolved via midamble. By estimating on-frame PPSINR at τ k+1 , PPSINR k,k+1 , the receiver knows when it can ignore the effect of CSI corruption. If the MPDU still fails after the recovery of estimated on-frame PPSINR, REMEDY assumes descramble failure and starts searching for the MAC header. Then REMEDY can rescramble to restore correctly descrambled data bits. In this way, with conditional application, REMEDY can reduce the computation overhead from rescrambling. As the rescrambling mechanism does not involve quite intensive computations, its processing time also can be expected to be within the timing margin for the receiver to prepare BA response. 9 Scrambling and descrambling processs are exactly the same operation of calculating exclusive OR (XOR) between the bit sequence produced by X 7 + X 4 and data payload bits. Due to the 7-th order binary equation, the scrambling sequence repeats every 127 bits. This scrambling effect is canceled out by descrambling where the same sequence is XORed again. 10 Every subframe within A-MPDU consists of multiples of 32 bits, and includes a MAC header containing the receiver's MAC address. 11 Since both sequences are produced by X 7 + X 4 , the XOR outcome also satisfies X 7 + X 4 . 12 If the position of MAC address is wrong, the XOR of incorrectly descrambled bits and MAC address is not XOR of the sequences used for scrambling and descrambling since MAC address cannot be canceled out. Thus, the XORed value can never correspond to any part of the 127-bit sequence. The search for correct position and sequence corresponds to line 3 and 5 in Algorithm 1.

VI. EVALUATION
We implement the proposed algorithm, REMEDY, on three comparison schemes for channel access in ns-3 to evaluate its performance in the indoor dense network topology of Fig. 10 suggested by TGax with time-varying channels. The model and parameters used in the evaluation are the same as those used in Section IV-B. We apply the PPSINR model in Eq. (20) for a realistic link performance based on channel environment. We set the parameters N fp , N fc , and PPSINR thre for REMEDY to 2, 5, and 2, respectively with midamble periodicity of 20, if inserted. The considered three schemes are Legacy, OBSS PD [6], and REFRAIN [5]. Stations in Legacy use typical Wi-Fi MAC and PHY, and stations in OBSS PD start concurrent transmission based on overlapping basic service set preamble detection (OBSS PD) in HE WLAN. We choose REFRAIN proposed to improve performance in dense network scenarios. We compare these three schemes with and without REMEDY. Traffic scenarios used for evaluation are uplink and downlink fully piggy-backed UDP traffic, and we evaluate performance with and without RTS/CTS. HE WLAN adopts OBSS PD to alleviate throughput degradation in dense networks. When receiving a frame, a station with OBSS PD first checks the BSS Color field in HE-SIG-A to determine whether the frame is from OBSS, is BSS specific. If it is verified that the OBSS transmission is not OBSS PD prohibited 13 and the received power is below energy detection threshold, the station drops the receive process to restart distributed coordination function (DCF) procedure. Then the OBSS PD transmission, i.e., transmission after dropping the OBSS frame, may use maximum transmission power lowered by the difference between the received power and carrier sense threshold.
REFRAIN senses other transmissions by detecting OFDM symbols and finds adequate MCS by sending a probing packet. Unlike other approaches, even if REFRAIN can start a new transmission, it does not attempt to send a PPDU packet aggressively to avoid imprudent transmission in dense networks. Since REFRAIN selects an MCS based on null data packet (NDP) handshake when attempting concurrent transmission, it can pick an MCS suitable for an environment with 13 The OBSS PD prohibited conditions according to HE WLAN specification are Spatial Reuse subfield in HE-SIG-A of OBSS frame prohibits OBSS PD, associated AP disallows OBSS PD, or OBSS frame is a response frame. frequent interference or just refrain from starting concurrent transmissions.
The proposed algorithm, REMEDY, shows an improvement in aggregated throughput for both uplink and downlink scenarios compared to the comparison schemes as described in Fig. 14. The highest gain is 120% in the case of N STA = 7 and UL without RTS/CTS. The cases with REM-EDY always show higher throughput than those without it.
In the case of downlink scenarios, the aggregated throughput decreases with increasing number of stations per BSS, and the throughput gain also decreases. For the case with a small number of stations per BSS, the midamble works well due to the influence of time-varying channel, but the impact of caudal loss decreases with large number of stations per BSS as explained in IV-B. In addition, since the transmitters in downlink scenarios are access points only, there are less diversity of position and relation between transmitters and receivers, which leads to less chance of simultaneous transmissions and CSI corruption, resulting in lower throughput gain.
In the case of uplink traffic, the aggregated throughput differs significantly depending on the simulation settings. Unlike downlink scenarios, the transmitters (non-AP stations) are randomly placed, bringing the diverse relation between transmitters, receivers, and interferers according to their positions. This produces more frequent concurrent transmissions, which in fact causes interference. Hence, the use of RTS/CTS results in an increase in the aggregated throughput as the number of stations increases. Conversely, the aggregated throughput in the uplink without RTS/CTS is significantly lower than that observed with RTS/CTS. This is because preamble passing disturbs other stations from sensing ongoing transmission and causes them to start new transmission even if the transmission is from a station in the same BSS. Therefore, RTS/CTS cannot prevent all interference from hidden node due to preamble passing, which makes RTS/CTS useless. Accordingly, REMEDY helps recover MPDUs from CSI corruption and achieve performance gain while tracking channel changes.
The cases with OBSS PD do not show remarkable differences since receiving the preamble from other stations is not possible during preamble passing [5], which is necessary for OBSS PD operation. REFRAIN shows much greater aggregated throughput compared to Legacy for uplink traffic. REFRAIN finds a reasonable MCS, thanks to its ability to  find ongoing transmission and validate the link. 14 However, REFRAIN uses a short null data frame to validate the link, so the following transmission is vulnerable to caudal loss. Therefore, REFRAIN with REMEDY can overcome caudal loss and recover CSI if corrupted. Fig. 15a and Fig. 15b depict the error rates for the cases with N STA = 7. MPDU error rate (MER) is the ratio of failed MPDUs including failed MPDUs in failed A-MPDUs to total transmitted MPDUs. REMEDY lowers both AER and MER by recovering CSI and MPDUs. Fig. 15c displays the scrambler error rate (SER) which indicates wrong descrambling due to an error in the scrambler initialization bit. Fig. 15d shows the rescramble success rate (SRR) which means recovering original data bits via rescrambling among incorrectly descrambled frames. Note that the error rates of the cases with Legacy and OBSS PD are overlapped in Fig. 15. In addition, we verify the effect of rescrambling on a single link in Fig. 9, showing alleviated SFER after updating CSI. We observe that the SER is not ignorable, and REMEDY can successfully rescramble the incorrectly descrambled frames from a minimum of 15.7% to a maximum of 43.4%.
The cumulative distribution function (CDF) of individual station's throughput, for both downlink and uplink cases when N STA = 7, is illustrated in Fig. 16. Interestingly, despite the use of RTS/CTS, stations with lower throughput still suffer from starvation, revealing an inherent defect in the RTS/CTS handshake mechanism. REFRAIN tends to prioritize enhancing aggregated throughput at the expense of performance fairness among stations. In contrast, REMEDY 14 The null data packet for validation acts like RTS/CTS handshake abstaining the transmitter from starting a concurrent transmission while reducing critical interference. takes a more balanced approach, effectively mitigating the throughput starvation experienced by these stations in unfavorable conditions.

VII. CONCLUSION
This paper presented an algorithm termed REMEDY that helps conventional channel access schemes to improve throughput and error rate performance in high-density WLAN environments by utilizing midamble. The insertion of midamble symbols between OFDM data symbols generates overhead, so it is effective to use midamble only when CSI corruption is currently occurring. Assuming a time-varying channel, the receiver estimates PPSINR during frame reception and requests midamble insertion to the transmitter.
Additionally, rescrambling is essential to restore data bits if the scrambler initialization bits are received incorrectly. We applied our PPSINR model to ns-3 under time-varying channels and CSI corruption. Through extensive simulation, we confirmed that REMEDY helps the conventional channel access schemes to improve the aggregated throughput and the throughput of the lowest performing group by lowering the error rate in high-density WLAN environments.