MAPS: MU-MIMO-Aware AP Selection for 802.11acNetworks

Yunze Zeng1, Ioannis Pefkianakis2, Kyu-Han Kim2, Prasant Mohapatra1

1Department of Computer Science, 2Hewlett-Packard Labs,University of California, Davis, CA, USA Palo Alto, CA, USA

{zeng, pmohapatra}@ucdavis.edu {ioannis.pefkianakis, kyu-han.kim}@hpe.com

ABSTRACTMajor Wi-Fi Access Point (AP) vendors worldwide seek toprovide gigabit wireless connectivity, by densely deployingMU-MIMO capable APs, which can support multiple, con-current data streams to a group of clients, connected tothem. However, MU-MIMO gains can only be achievedif an AP can identify groups of clients with homogenousconfigurations and orthogonal wireless channels, where con-current transmissions will not cause inter-client interference.Hence, MU-MIMO performance is fundamentally dependingon how the clients are assigned to APs. Our experimentswith 802.11ac commodity testbeds show that state-of-the-art client assignment algorithms are MU-MIMO obliviousand limit the MU-MIMO grouping opportunities in realisticsettings. In this paper, we design and implement MAPS, anMU-MIMO-Aware AP Selection algorithm that is 802.11-compliant and can boost network’s MU-MIMO throughputgains. We verified MAPS’ gains over legacy designs via ex-tensive experiments with 802.11ac commodity testbeds.

1. INTRODUCTIONThe major Wi-Fi Access Point (AP) vendors worldwide

seek to provide ubiquitous, gigabit wireless connectivity, bydeploying high-density networks [1,4,20], where a large num-ber of clients and APs operate in the same RF coveragezone. A key feature for such deployments is MU-MIMO,which uses beamforming to support multiple, concurrentdata streams from an AP to a group of client devices. MU-MIMO feature has already been adopted by the IEEE 802.11acnetworks, to realize gigabit downlink speeds. It has beenalso widely perceived among the primary means to meet thespeed requirements of the next generation Wi-Fi 802.11ax [10]and 5G networks [3]. However, MU-MIMO gains can beachieved only if an AP can identify groups of clients with ho-mogenous configurations and orthogonal wireless channels,where concurrent transmissions will not cause inter-client in-terference. Consequently, MU-MIMO performance is funda-

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DOI: 10.475/123 4

mentally depending on how clients will be assigned to APs,which operate in the same coverage zone.Limitations of legacy AP selection: State-of-the-art APselection designs proposed by industry [2,13] and academia [7,22,38] typically assign clients to the strongest signal (RSSI)AP. Interestingly, our experiments with commodity MU-MIMO 802.11ac testbeds show that such approaches yieldup to 230 Mbps lower throughput compared to the optimalclient assignment, even for small-scale, 2-AP topologies. Wehave identified three root causes for such poor performance.

(a) Legacy designs are MU-MIMO oblivious and may as-sign clients with correlated channels to the same AP. Group-ing clients with correlated channels results in high inter-client interference, which forces the AP to operate in SU-MIMO mode (serving one client at a time). (b) Even whenclients communicate over orthogonal channels thanks to richmultipath environment, legacy designs may still limit MU-MIMO grouping opportunities, by assigning clients with het-erogeneous bandwidth configurations to the same AP. Specif-ically, clients which operate on different 802.11ac bandwidthoptions cannot be grouped together. This constraint is at-tributed to AP’s capability, which can only transmit on asingle center frequency and bandwidth at a time. Moreover,the AP cannot always use the highest bandwidth option fortransmitting to all the clients in a group, due to clients’ dif-ferent interference profiles. (c) Finally, the widely adoptedapproach to assign clients to the least “loaded” AP, can limitMU-MIMO gains, even for clients which operate on orthog-onal channels and homogenous bandwidths. This is becausemore loaded APs may offer more grouping opportunities.Design challenges: The design of MU-MIMO-aware APselection, which addresses the above limitations, poses sig-nificant challenges. First, a key design challenge is to iden-tify clients with orthogonal channels and assign them to thesame AP. A simple approach would be to associate eachclient to all APs in its range, and use explicit beamformingfeedback [28, 30, 37] to estimate channel correlation. How-ever, such an approach requires excessive handoffs in high-density Wi-Fi deployments, and leads to poor performance.Hence, a new, low-overhead approach is required for profilingthe multipath environment and estimating channel correla-tions. Moreover, MU-MIMO-aware AP selection should beable to capture clients’ (and APs’) bandwidth profiles, whichdynamically change in time, due to interferences. Then, itneeds to estimate how clients’ bandwidth profiles will affecttheir grouping opportunities at an AP. Finally, AP selectionmust balance the load among APs, without limiting theirMU-MIMO gains, which are often conflicting objectives.

MAPS design: In this paper, we propose a new Mu-mimo-Aware AP Selection (MAPS) design for 802.11ac networks,which addresses the aforementioned challenges. MAPS lever-ages a NULL frame probing scheme to collect CSI (ChannelState Information) feedback from clients, without requiringthem to associate with APs. CSI samples measured at theAP-side can capture the multipath characteristics of the en-vironment, and can be used as a proxy for clients’ channelcorrelation, as shown by our experiments. MAPS first san-itizes CSI samples by removing the RF-hardware triggeredamplitude deviations, using local regression smoothing fil-ters. It then constructs a CSI profile that differentiates be-tween persistent and transient multipath. The CSI profilerapplies a correlation metric among back-to-back CSIs, whichcaptures dominant multipath changes, and at the same timeremains robust to RF hardware-triggered CSI phase shifts.Using the CSI profile, MAPS can estimate the SINR (Signal-to-Interference-plus-Noise Ratio) and hence the PHY rate ofa client as a part of an MU-MIMO group. MAPS’ SINR ap-proximation error is typically small (<2 dB) compared toSINR estimation using explicit client’s channel feedback.

MAPS introduces a novel client assignment model, whichleverages clients’ SINR, traffic and interference profiles toinfer the effective MU-MIMO throughput performance of aclient, at each AP. Our proposed model is able to balancebetween MU-MIMO gains and AP load, by considering theWi-Fi channel busy time, and the airtime to be allocatedto a client, at each AP. MAPS then assigns a client to theAP which maximizes its throughput. Since optimal clientassignment is an NP-Hard problem, we propose a low over-head heuristic algorithm, which performs close to optimal,as shown by our experiments.

We evaluate MAPS’ performance gains over legacy designsusing testbed experiments with 802.11ac commodity APsand MU-MIMO-capable smartphones. Our results show thatMAPS outperforms legacy designs in 90% of the settings,with network throughput gains greater than 50%, even insmall 3-AP topologies. In the majority (∼85%) of our ex-periments, MAPS performs the same as the optimal, best-throughput client assignment. Finally, our results show thatMAPS can also improve throughput fairness among clients.Contributions: In summary, our main contributions are:(1) We conduct a measurement study with commodity 802.11acMU-MIMO testbeds, and identify the limitations of legacyAP selection designs (Sec. 3). To the best of our knowledge,this is the first work that studies AP selection in MU-MUMOnetworks, using commodity 802.11ac testbeds.(2) We design MAPS, a practical, 802.11-compliant system,which can boost MU-MIMO gains by appropriately assign-ing clients to APs. (Sec. 4).(3) We implement MAPS in 802.11ac commodity hardware(Sec. 5), and evaluate its performance in multiple networksettings, using 802.11ac APs and smartphone devices (Sec. 6).

2. BACKGROUND

2.1 IEEE 802.11ac BackgroundIEEE 802.11ac operates on 5 GHz band, and supports

denser modulation (up to 256-QAM) and faster MIMO (upto 8 streams and 6.9 Gbps rates) compared to its predeces-sor 802.11n. However, its key differentiator over 802.11n isthe MU-MIMO feature, which uses beamforming to supportconcurrent downlink data streams from an AP to a group

controller

AP1 AP2ethernet

(2) client feedback client feedback

(1) probe request

(3) probe response

(4) authentication association

Figure 1: Client association in enterprise Wi-Fi.

of clients. Specifically, an 802.11ac AP can support MU-MIMO beamforming, by using a sounding protocol [15] tocollect a VHT Compressed Beamforming Feedback (CBF)from wireless clients. The CBF is represented by V, whichis a steering matrix that specifies how AP should decorre-late transmitted data to multiple clients. A client calcu-lates V by applying Singular Value Decomposition (SVD)on H as H = UDV H . Here, H (or CSI) is the channelmatrix measured at the client’s side from sounding packet.An AP uses V to precode the transmission data, followingthe Eigen-subspace beamforming [31]. Apart from CBF,802.11ac clients provide an MU Exclusive Beamforming re-port to AP, which is only available in MU-MIMO mode, andcarries per-subcarrier SNR (Signal to Noise Ratio) feedback.

An 802.11ac AP selects a set of clients to transmit dataconcurrently through a client selection algorithm that pre-cedes sounding and beamforming. Client selection algorithmis vendor-specific and unspecified by the 802.11ac standard.

802.11ac supports 20, 40, 80 MHz channel bandwidths,and an optional 160 MHz bandwidth. An 802.11ac devicecan use a 20 MHz sub-channel only if it is not occupied byanother transmission in its vicinity. An 802.11ac AP cannegotiate communication at higher channel widths throughan RTS/CTS handshake protocol [15]. Interestingly, onlyclients with the same channel bandwidth configuration canbe grouped together in the same MU-MIMO group. Thisis because an AP can only transmit using a single centerfrequency and bandwidth at a time. Moreover, clients ofdifferent channel bandwidth may have different interferenceprofiles, and hence the AP cannot transmit data to all ofthem using the highest channel bandwidth.

2.2 Enterprise Wi-Fi NetworksIn this paper, we focus on enterprise Wi-Fi networks where

multiple APs operating in infrastructure mode, provide wire-less connectivity in large buildings. APs are typically con-nected through Ethernet to controllers, as shown in Figure 1.Controllers support network-wide optimizations (e.g., chan-nel selection), network management, and enterprise appli-cations’ security. They also assign clients to APs (i.e., APselection) and initiate clients’ handoffs. Specifically, prior toassociation, a client C scans Wi-Fi channels for APs. In pas-sive scanning mode, C listens for beacons. In active mode,C broadcasts probe requests. The APs which receive theserequests send information about C (such as RSSI) to thecontroller, which assigns C to an AP. The selected AP sendsa probe response to C, which initiates the authenticationand association process (Fig. 1). If the controller decides tohandoff C from AP1 to AP2, then AP1 sends a disassociate

C1-C2(AP1)

C1-C3(AP1)

C2-C3(AP1)

C3-C4(AP2)

0.30.350.40.450.50.550.60.650.7

Correlation

(a) V correlation of different pairs ofclients.

0.0 20.0 40.0 60.0 80.0 100.0PER(%)

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(b) C3 and C4 connected to AP2.

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CDF

Client-1Client-2Client-3

(c) C1,C2 and C3 connected to AP1.

Figure 2: V correlation and Packet-Error-Rate statistics for clients in MU-MIMO mode, for our case study setting.

C3C4

C2

C1

AP1

AP2

?RSSI: -47

RSSI: -48

RSSI: -50

RSSI: -46

RSSI: -46

16 meters

10 m

eter

s

Figure 3: Network topology for the case study setting.

frame to C, and C follows the process shown in Figure 1.After connecting to AP2, C does not need to send a DHCPrequest if APs are on the same subnet.

3. A MEASUREMENT STUDYIn this section, we show the limitations of legacy AP se-

lection approaches in MU-MIMO networks, by conductingexperiments with 802.11ac commodity wireless testbeds.

3.1 Platform and MethodologyOur experiments use commodity 802.11ac AP boards, equipped

with a Qualcomm Beeliner 4×4 MU-MIMO-capable 802.11ac5 GHz radio. The 802.11ac radio supports up to 80 MHzchannel bandwidth and up to 256-QAM modulation level,with 1733.3 Mbps peak PHY rate. It has 4 antennas, butsupports up to 3 data streams (clients) in MU-MIMO mode.MU-MIMO client selection along with other core MAC-layerfunctionalities (e.g., PHY rate and bandwidth adaptation)are implemented in the AP’s firmware, and the source codeis available for our implementation. Our experiments useXiaomi Mi 4i smartphones [33] as clients. Mi 4i has an802.11ac wave-2 chipset, with one receiving antenna.

For our experiments, we have modified the firmware of ourAPs to collect per-client wireless feedback such as: a) PHYrates (i.e., MCS, spatial stream, channel bandwidth), b)sounding feedback statistics (i.e., V matrix, per-subcarrierSNR - cf. Sec. 2.2), c) frame error rate, and d) CSI mea-sured at the AP side, from the received frames. We conductexperiments at enterprise and university campus settings.

3.2 Correlated Wireless ChannelsWe next show the limitations of legacy AP selection al-

gorithms in typical 802.11ac deployments, with testbed ex-periments. In our case study setting, clients C1 and C2 areconnected to the strongest signal (RSSI) AP1 and C4 toAP2, as shown in Figure 3. All clients operate at 80 MHz.C1 and C2 form an MU-MIMO group and achieve 378 Mbpsaggregate downlink UDP throughput compared to only 296Mbps, when they operate at Single-User MIMO (SU-MIMO)(where one client is served at a time). When a new client C3wants to join the network, legacy (e.g., RSSI-based) designswill assign C3 to the highest RSSI AP2. However, is thisthe best-throughput client assignment?

Our results show that clients C3 and C4 perform poorly inMU-MIMO mode, at AP2. Specifically, the aggregate down-link throughput at AP2 is 178.8% higher when C3 and C4operate in SU-MIMO, compared to forming an MU-MIMOgroup. Hence, C3 cannot leverage MU-MIMO gains by con-necting to the highest RSSI AP2. Interestingly, the aggre-gate (over AP1 and AP2) network throughput is from 50 to230 Mbps higher when C3 connects to the lower RSSI AP1(assuming AP1, AP2 operate on orthogonal channels). Par-ticularly, the best-throughput setting is observed when C1,C2 and C3 form an MU-MIMO group at AP1, and C4 op-erates in SU-MIMO at AP2. The aggregate and per-clientthroughput for the above settings is summarized in Table 1.

Client C3 cannot leverage MU-MIMO gains when it con-nects to AP2, because its wireless channel is highly corre-lated with C4, leading to inter-client interference. Chan-nel correlation (and hence interference) between clients i, jat subcarrier s, can be estimated by the V matrix correla-tion [30] as:

ρ(i, j) =

∑s||Vi(s)V

Hj (s)||√∑

s||Vi(s)||2√∑

s||Vj(s)||2(1)

Figure 2a shows that the V correlation between C3 and C4(ρ(C3, C4)) is 64% higher than that of clients C1 and C2,which gives the best MU-MIMO performance. Highly corre-lated channels result in inter-client interference and conse-quently to high Packet-Error-Rate (PER). Figure 2b showsthat the median PER for C3 when grouped with C4 is ap-proximately 70%, and the maximum PER exceeds 90%. Onthe other hand, the channel correlation among the clients ofthe MU-MIMO group {C1, C2, C3} at AP1, is lower than{C3,C4}, as shown in Figure 2a. Due to lower inter-clientinterference, the PER for C3 at AP1 is lower than 10% for

Setting C1 C2 C3 C4 Aggregate

AP1(MU), AP2(MU), C3-AP2 186.0± 5.2 192.3± 5.8 8.8± 2 91.9± 21 479.0AP1(MU), AP2(SU), C3-AP2 186.0± 5.2 192.3± 5.8 146.7± 5.9 134.1± 4.7 659.1AP1(MU), AP2(SU), C3-AP1 146.4± 1.7 147.9± 1.9 145.3± 2 269.4± 4.7 709.1

Table 1: Per-client and aggregate (across APs) downlink UDP throughput (Mbps), when C3 connects to AP1, AP2.

Setting C1 C2 C3 Aggregate Jain Index

AP1(SU), AP2(SU), C3-AP2(80MHz) 269.4± 4.7 79.8± 3.5 150.6± 4.8 499.8 0.82AP1(SU), AP2(MU), C3-AP2(40MHz) 269.4± 4.7 127.3± 9.7 125.3± 9.8 522.0 0.87AP1(MU), AP2(SU), C3-AP1(80MHz) 186.0± 5.2 161.2± 3.1 192.3± 5.8 539.5 0.99

Table 2: Per-client and aggregate downlink UDP throughput (Mbps) and fairness, for heterogeneous width clients.

90% of the samples, as shown in Figure 2c. Hence, the best-throughput AP selection algorithm needs to assign C3 to thelower RSSI AP1, in order to leverage the MU-MIMO gains.Summary: RSSI-based AP selection designs are obliviousto MU-MIMO feature, and assign clients to APs, withoutconsidering the channel correlation among clients connectedto the same AP. Correlated channels lead to high inter-clientinterference and low throughput performance, in MU-MIMO802.11ac settings.

3.3 Heterogeneous Bandwidth ClientsWe next evaluate a two-AP topology setting (similar to

Fig. 3), where C1 and C2 are connected to AP1 and AP2respectively. C1 operates at 80 MHz and C2 at 40 MHz (dueto the interference from neighboring networks). Let’s con-sider a new client C3 operating at 80 MHz, whose RSSI is -50dbm and -46 dbm from AP1 and AP2, respectively. RSSI-based designs will assign C3 to AP2, without consideringthat different bandwidth clients cannot be grouped together(cf. Sec. 2.2). Consequently, C2 and C3 will operate at SU-MIMO. On the other hand, C3 could form an MU-MIMOgroup with C1 at AP1, increasing by 40 Mbps the aggregatenetwork throughput (cf. rows 1, 3 of Tab. 2). Even whenAP’s bandwidth adaptation algorithm allows for C2 and C3to form an MU-MIMO group at 40MHz, at AP21, assign-ing C3 to the lower RSSI AP1 still gives better networkthroughput, as shown in rows 2, 3 of Table 2.

Assigning clients to APs with high MU-MIMO gains canalso improve fairness. For example the Jain Fairness Index[17] of the network when C3 operates in SU-MIMO at AP2is 0.82 (1 implies perfect fairness), while it increases to 0.99,when C3 connects to AP1.Summary: RSSI-based AP selection designs can limit MU-MIMO grouping opportunities in 802.11ac networks, by as-signing clients with heterogeneous channel bandwidths to thesame AP.

3.4 Load BalancingWe finally evaluate a topology of two APs in the same

vicinity, which operate on the same wireless channel. Thisis a realistic setting in dense AP deployments, where theremay not be enough non-overlapping channels for adjacentAPs. Moreover, the approach of assigning the same channelto adjacent APs has been used by industry [1] for betterinterference management and faster inter-AP handoff. Inour setting, client C1 operating at 80 MHz is connected to

1Commodity 802.11ac APs do not adjust channel band-width, to increase MU-MIMO grouping opportunities.

C1 C2

Thro

ughp

ut (M

bps)

0

50

100

150

200

250

300C1, C2 at AP1C1 at AP1, C2 at AP2

Figure 4: Performance of legacy load balancing designs inMU-MIMO setting.

AP1, while AP2 does not serve any client. We assume thatAP1 fully utilizes the wireless channel capacity to serve C1’straffic. Let’s now consider a new client C2 operating at 80MHz, whose RSSI from AP1 and AP2 is exactly the same.Existing designs [22, 38] will assign C2 to AP2, to balancethe load among APs. However, such assignment is subopti-mal in terms of throughput, as shown in Figure 4. ClientsC1 and C2 can operate on MU-MIMO when both are con-nected to AP1, and achieve 515 Mbps aggregate throughput.However, when they are assigned to different APs, they haveto share the wireless medium, and hence achieve 162 Mbpslower aggregate throughput.Summary: Legacy load balancing designs can reduce MU-MIMO grouping opportunities and hence throughput perfor-mance, by assigning clients to the least loaded AP.

4. DESIGNIn this section we present MAPS (Mu-mimo-Aware AP

Selection), an 802.11-compliant system, which can boostMU-MIMO gains by appropriately assigning clients to APs.MAPS seeks to increase MU-MIMO grouping opportunitiesby setting three key design goals: (a) to accurately identifyclients with uncorrelated channels at low overhead, and as-sign them to the same AP, (b) to assign clients with homoge-nous bandwidth settings to the same AP, by monitoringtheir interference profiles, (c) to allow for client assignmentto more “loaded” APs, if they can form high-throughputMU-MIMO groups. MAPS is a practical, lightweight design,which can be implemented in commodity 802.11ac APs andcontrollers, without client-side modifications. It can workin concert with existing core MAC-layer AP and controllerfunctionalities (rate adaptation, MU-MIMO grouping etc.).MAPS architecture: An overview of MAPS’ architectureis shown in Figure 5. MAPS takes an implicit feedback ap-proach to identify clients with uncorrelated channels, with-

CSI Collector

Probing Module

Bandwidth Profiler

Traffic Profiler

MLME

AP 1

Client

NULL Packet

ACK

RTS/CTS

Asso./Disasso.Packets

CSI Decompression

CSI Sanitization (RLOWESS Filter)

CSI Profiler

CSI Processor

Throughput Estimation(Thrk,1)

Profile for AP 1

Profile for AP N

Throughput Estimation (Thrk,N)

…

Handoff Trigger AP Selection

Controller

csi

Sampdu

bw

Asso. Decision

Channel Monitoru

Figure 5: MAPS architecture.

out requiring them to be associated to an AP. It leverages aNULL data probing scheme to collect CSI samples at APsfor each client in their vicinity. The compressed CSI sam-ples are sent to the controller, which upon sanitizing them,it constructs the dominant multipath profile of a client, ateach AP. The controller uses a client’s CSI profile to esti-mate its performance (i.e., PHY rate) as a member of anMU-MIMO group. A MAPS’ AP further maintains client’sbandwidth and traffic profiles, which along with AP’s Wi-Fi channel busy time and load, are used to estimate thethroughput of a client connected to an AP. When a newclient wants to join the network, or a client’s handoff is re-quired, MAPS’ controller identifies the APs in client’s range,and assigns it to the AP which maximizes its throughput.Then, it communicates its decision to the selected AP, whichuses the Medium Access Control (MAC) Sublayer Manage-ment Entity (MLME), to associate the client to itself. Wenext elaborate on MAPS’ building blocks.

4.1 MU-MIMO Performance InferenceA key challenge for MAPS is to identify clients with uncor-

related channels, and map them to the same AP. A simpleapproach would be to periodically associate each client toall APs in its range, and collect explicit beamforming feed-back (CBF) to estimate clients’ channel correlation. How-ever, such approach requires frequent handoffs and long as-sociation with low-throughput APs, which can significantlydegrade clients’ performance. Specifically, our experimentsshow that handoff time can be in the order of seconds. Uponassociating to an AP, a client can only provide CBF feedbackwhen sounding is triggered. Given the dense Wi-Fi deploy-ments with multiple APs in a client’s vicinity, we considerthe overhead of collecting explicit CBF from all APs, to beprohibitive. To this end, MAPS takes an implicit feedbackapproach to overcome this challenge, as we discuss next.

4.1.1 Leveraging Implicit FeedbackMAPS adopts an implicit CSI feedback approach to iden-

tify MU-MIMO groups of clients with uncorrelated chan-

0

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Figure 6: Robust LOWESS filter on CSI samples.

nels, without requiring them to be associated to an AP. In-tuitively, since the “physical” wireless channel (i.e., multi-path characteristics) can be considered reciprocal [29], AP-side CSI can capture the correlation among clients’ wirelesschannels. However, leveraging implicit CSI feedback for APselection poses several challenges. How can an AP collectCSI samples from clients not associated with it? Is it possi-ble to filter Wi-Fi RF-hardware triggered noises of the col-lected CSI samples? How to construct a CSI profile thatcan capture both the persistent and the transient multipathcharacteristics of the environment? We next describe MAPSapproach to such challenges.CSI collection: MAPS leverages an 802.11-compliant NULLdata probing scheme to collect CSIs from all the clients inAP’s vicinity. Specifically, an AP transmits a NULL dataframe, and estimates the CSI from the ACK frame sent bythe client. A client will respond to a NULL frame receivedby an AP, even if it is not connected to this AP, as verified byour experiments. NULL data probing is a low overhead CSIcollection scheme. Particularly, a NULL data frame is onlytens of bytes (depending on the 802.11 family), and can betransmitted at higher PHY rates than the basic. Its trans-mission time is only 0.85 microseconds, for the smartphonesused in our testbed. This overhead is negligible consideringthat MAPS only periodically (every 100ms in our implemen-tation) transmits NULL frames to collect CSI.CSI sanitization: MAPS collects CSI samples at the AP-side from the received frames. A CSI is a Nt × Nr matrixof complex numbers, where Nt and Nr are the number ofantennas at the AP and client, respectively. Our AP de-vice reports one CSI per OFDM subcarrier. Hence, a CSIsample estimated from an ACK frame (transmitted at 20MHz, using 57 subcarriers) is a 4 × 57 matrix (for our 4-antenna AP and 1-antenna client). However, our measure-ments show that the CSIs reported by commodity Wi-Fi de-vices can be very noisy. Such noise is attributed to transmis-sion power changes, rate adaptation, internal CSI referencelevel changes [32]. For example, Figure 6 shows that noisespikes can exceed 10 dB (cf. antenna 4). MAPS applies arobust LOWESS (Locally Weighted Scatterplot Smoothing)filter [8], which performs local regression with weighted leastsquares to smoothen outliers. Non-parametric smootherslike LOWESS are appropriate for CSIs, since they do notassume that the data fit some distribution shape. Figure 6shows that such filter can remove noise from CSIs.

0 2 4 60

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Figure 7: MAPS’ CSI profiling: a) SINR accuracy, b) back-to-back CSI phase shifts, c) CSI correlation distribution.

The smoothed CSI is then used to estimate the SINR ofa client k operating in an MU-MIMO group of K clients as:

SINR =

1

K||Dk||2︸ ︷︷ ︸

signal power

N︸︷︷︸noise floor

+1

K||Dk||2

∑j 6=k||V

Hk Vj ||2︸ ︷︷ ︸

interference

(2)

The above metric has been proposed in [30], and has beenshown to accurately estimate SINR in 802.11ac devices. Tothis end, MAPS first estimates V and D by applying SVD onCSI (cf. Sec. 2.2). Then, it captures inter-client interferencein an MU-MIMO group, by estimating clients’ V correla-tion. It further computes the noise N using EVM (ErrorVector Magnitude) feedback, provided by AP’s firmware,for every received frame across all subcarriers. Finally, itcalibrates Dk to account for the transmit power differencebetween the client and AP. Specifically, it multiplies the fac-

tor ||Dk||2 with 10PAP−Pclient

10 , which is the transmit powerdifference (dBm) at AP and client sides. Pclient is availableat the AP through 802.11 Event Report frames. Notice thatthe SINR metric can be estimated per OFDM subcarrier.MAPS computes an effective SINR across all subcarriersusing the approach proposed in [12], which has been shownto be robust in frequency-selective fading environment.SINR accuracy: We evaluate our SINR metric’s accuracy,by comparing it with muSINR metric [30], which uses ex-plicit, receiver-side V andD feedback, communicated throughCBF. Figure 7a shows the distribution of the absolute dif-ference between the two SINR metrics, from multiple MU-MIMO experimental settings. We observe that for 70% ofthe cases, the SINR estimation error is less than 2 dB. Thiserror will not lead to erroneous PHY rate estimation mostof the times (cf. Tab. 22-25 in [15]), and hence it doesnot affect MAPS’ ability to infer client’s throughput. SinceMAPS’ SINR estimation is not used for core functionalitiessuch as MU-MIMO client selection and beamforming, es-timation error outliers will not significantly impact MAPS’performance, as shown by our evaluation results (cf. Sec. 6).

4.1.2 Identifying Dominant MultipathsMAPS’ operations are triggered at coarser time scales

(second scale) compared to other CSI-based algorithms, suchas MU-MIMO grouping and rate adaptation (millisecondscale), to avoid excessive handoffs. Hence, instead of onlymaintaining the latest CSI sample, MAPS needs to construct

a CSI profile which is able to differentiate between persistentand transient multipath characteristics of the environment.

Constructing such a CSI profile is a challenging process.First, storing and processing all the measured CSIs is a bigoverhead even for a powerful Wi-Fi controller, since CSIscan be collected at microsecond granularity. Hence, MAPSneeds to consider only CSIs that capture changes in themultipath environment. However, capturing such dynam-ics is not trivial. Even if the multipath characteristics of theenvironment remain the same, the phase of back-to-backCSI samples may vary. Such phase variations have been at-tributed to RF hardware characteristics [29, 32].A CSI pro-filer should be robust to such variations and capture onlysignificant multipath changes.

Interestingly, different from related studies [29], our ex-periments show that phase variations caused by 802.11ac RFhardware are not random. For example, Figure 7b shows thephase curves of two back-to-back frames, in a controlled en-vironment with no human or object movement. We observean almost constant phase shift for all subcarriers (y-axis),and a small shift in phase curve across frequency domain(x-axis), for antennas 1, 2. However, we observe similarshapes of phase curves. Since the hardware-triggered phaseshifts do not change the shape of the phase curves of back-to-back frames, we expect that their correlation will be high.Figure 7c shows the distribution of the correlation factor ρ(eq. (1)) for CSI samples, collected from multiple controlledsettings in a time window of 0.5 msecs, of stable multipathenvironment2. We observe that for 80% of the cases, ρ isequal or greater than 0.85 (ρ = 1 for same CSI samples).

While CSI correlation metric is robust to hardware-triggeredphase shifts, it can also capture changes in multipath envi-ronment. We illustrate our point by studying the spatialdistribution of CSIs (in polar coordinate system) in casesof stable (Fig. 8) and dynamic (Fig. 9) multipath environ-ments. For stable multipath, back-to-back CSIs overlap inspace, which is reflected in their CSI correlation. For dy-namic multipath, the CSIs’ main lobes do not overlap (cf.Fig. 9), as indicated by their lower correlation. We con-clude that CSI correlation ρ is a robust metric for capturingdominant multipath.

MAPS leverages the CSI correlation metric to maintainL dominant multipaths (i.e., CSIs). For each new CSI i,MAPS estimates its correlation ρ(i, j) with each CSI j, ofcurrent CSI profile. If the maximum correlation with a CSI j

2We compute ρ by using CSI H instead of V in eq. (1).

0.5

1

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2

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180 0CSI Corr = 0.97

Figure 8: CSIs for stablemultipath.

0.5 1

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6090

120

150

180 0CSI Corr = 0.67

Figure 9: CSIs for dynamicenvironment.

is greater than a threshold (maxj∈L{ρ(i, j)} > R), then MAPS

replaces CSI j, with i and increases a counter csij (j isan index of the CSI profile)3. Otherwise, the new CSI isstored in a new entry of the profile. If the CSI profile is full(with |L| CSIs), MAPS will either replace an existing CSIj entry with the new CSI, if csij = 1, or it will discard i.MAPS periodically clears a client’s CSI profile to allow fornew dominant multipaths.

MAPS needs to estimate clients’ SINRs for all the MU-MIMO group assignments, to select the best AP (cf. Sec. 4.3).However, a client’s SINR will change for each CSI in its pro-file. Processing all the CSIs in a client’s profile, for all thepossible MU-MIMO groups, results in significant process-ing overhead. MAPS amortizes such overhead, using thecounter csii, which reflects the “dominance” of a multipath.It selects as client’s dominant multipath, its CSI i with aprobability Pcsii = csii∑|L|

j=1 csij. Then, it uses the dominant

CSI for computing the SINR metric. Client’s SINR alongwith its bandwidth and traffic profiles are used for estimat-ing client’s throughput at an AP, as we discuss next.

4.2 Client and AP ProfilingMAPS leverages the SINR metric calculated by AP-side

CSI samples, to estimate a client’s MU-MIMO throughputperformance, when assigned to an AP. Hence, it can pre-vent clients with correlated channels from being connectedto the same AP. However, apart from channel correlation,MU-MIMO grouping opportunities also depend on clients’bandwidth settings and their traffic dynamics.Bandwidth profile: Heterogenous clients’ bandwidth pro-files can limit MU-MIMO groups opportunities, as we dis-cussed in Section 3.3. MAPS monitors the interference pro-file of each device (AP and client), to allow for homogenousbandwidth clients to be assigned to the same AP. Partic-ularly, it maintains for each device, the number of trans-missions or receptions that could use the bandwidth optionbw ∈ {20, 40, 80, 160}. MAPS estimates bw, by monitor-ing which 20 MHz sub-channels are occupied through theRTS/CTS handshake process (cf. Sec. 2.2). Since, a de-vice’s interference profile (and hence bandwidth configura-tion) may change at runtime, MAPS selects bwk for a devicek, to be the bandwidth option with the highest probability.The probability of a bandwidth option i is estimated as:

Pbwi =#Packets bwi∑

j∈{20,40,80,160}#Packets bwj(3)

MAPS maintains different bandwidth profiles for differentchannels that APs may operate on. It periodically resetsbandwidth profiles, to account for new interference dynam-ics. Finally, it computes the bandwidth configuration of aclient k at an AP α as: bwk,α = min{bwk, bwα}.3R can be set to 0.85, from our experiments in Fig. 7c.

Traffic profile: MAPS monitors the size of 802.11ac aggre-gated frames (i.e., A-MPDU) to capture traffic dynamics. Itmaintains a moving average of a client’s A-MPDU size as:

Sampdu = (1− β) · Sampdu + β · Sampdu (4)

where β = 18

in our implementation. It periodically ages a

client’s traffic profile as: Sampdu = (1− β) · Sampdu, to con-sider the client’s idle time. Typically, small Sampdu valuesimply low traffic activity.AP profile: Apart from client profiling, MAPS furthermaintains the wireless channel utilization uα and the num-ber of client devices connected to each AP α. It capturesthe AP’s Wi-Fi channel busy time due to transmissions fromneighboring devices, with the factor uα ∈ [0, 1], which is thefraction of free transmission cycle opportunities within thelast 10 beacon intervals. In the following section, we showhow client and AP profiles are used to estimate a client’sthroughput at an AP.

4.3 AP Selection ModelMAPS introduces a novel client assignment model, which

can boost grouping opportunities at MU-MIMO APs. Itfirst leverages the CSI, traffic and interference profiles toestimate the effective throughput performance of a client,at each AP. Then, it selects the AP which can maximize aclient’s throughput. We next elaborate on our model. Wesummarize the notations used in this section, in Table 3.

Parameters DefinitionsA set of APsK set of clientsKα set of clients associated to AP α ∈ Ag MU-MIMO group of clients, subject to |g| ≥ 1Gα set of all MU-MIMO groups

that can be formed at AP αuα channel busy time at AP αbwk,α bandwidth of client k associated to AP αrk,α PHY rate of client k associated to AP αwk,α allocated time for client k associated to AP αThrk,α throughput of client k associated to AP α

Table 3: Definition of notations.

4.3.1 Throughput ModelMAPS estimates the throughput of a client k when it as-

sociates to an AP α, considering: (1) client’s PHY rate rk,α,when it operates in an MU-MIMO group at α, (2) client’straffic Sampdu,k, (3) 802.11 protocol overheads (to), (4) chan-nel busy time uα, and (5) airtime allocated to client wk,α.Specifically, it is:

Thrk,α = wk,α · uα ·Sampdu,k

td + to(5)

The factor uα ∈ [0, 1] captures the WiFi channel busy time,and is maintained by the AP profile. The amount of client’sdata Sampdu,k is computed based on equation 4. The timeconsumed by the various 802.11 protocol overheads (e.g.,sounding, ACK) is to. Finally, the data transmission timeis modeled as td = tplcp + Sampdu,k/rk,α, where tplcp is thePLCP preamble transmission time, and Sampdu,k/rk,α is theframe transmission time, where rk,α is the PHY rate.

PHY rate rk,α: MAPS leverages client’s CSI and bandwidth

profiles to identify its best-throughput PHY rate rk,α (i.e.,

MCS, spatial streams), when it is part of an MU-MIMOgroup. Specifically, for a given MU-MIMO group, it esti-mates client’s SINR from equation (2). Then, it uses the802.11ac rate tables [15], which provide SINR-PHY ratemappings, for each bandwidth option. However, a clientcan form multiple different groups with other clients at anAP. These groups may change in time, depending on clients’channel correlation characteristics, bandwidth and trafficprofiles. Hence, it remains an open question, which are likelygoing to be k’s MU-MIMO groups at AP α?

In practice, only the highest throughput MU-MIMO groupsof active (in terms of traffic) clients are typically used fortransmission. To this end, MAPS considers only the ac-tive clients (i.e., Sampdu > 0) as candidates for MU-MIMOgrouping. Then, it computes the set of MU-MIMO groupsGα that can be formed by the active clients associated toan AP α, subject to the bandwidth constraint. Here, wedefine as group g ∈ Gα, a set of clients of cardinality of atleast one (|g| ≥ 1). From all the possible MU-MIMO groupcombinations Gα, an AP typically forms and serves only thehighest-throughput MU-MIMO groups, while ensuring thatall clients will be fairly served. Given a set of clients Kα atAP α, a fair allocation will assign k at least 1/|Kα| of the air-time. To this end, MAPS seeks to identify such groups, byfirst ordering the set Gα, in decreasing MU-MIMO groupthroughput performance4 order. Then, starting from thehighest throughput group g ∈ Gα, MAPS adds g to a newset G′α, subject to two constraints:(a) Group g cannot be a proper subset (or superset) of ex-isting groups in G′α: ∀gi, gj ∈ G′α then gi 6⊂ gj .(b) Every client associated to the AP α must belong to atleast one group in G′α: ∀k ∈ Kα then k ∈ g for g ∈ G′α.

The algorithm above selects the best-throughput sets, whileensuring all clients will be served at least once. Hence, theset G′α ⊂ Gα includes the MU-MIMO groups which will belikely served by the AP, as verified by our experiments withcommodity APs. Note that MAPS can leverage any of thetechniques proposed in the literature [28,30] to identify G′α,at low computational cost.

Now, let’s assume that G′k,α ⊆ G′α is the subset of groupswhich include client k. Then, we estimate rk,α as the averageclient’s PHY rate when it is part of the groups g ∈ G′k,α:

rk,α = 1|G′k,α| ·

∑g∈G′

k,αrgk,α.

Allocated airtime wk,α: MAPS uses a weight wk,α to cap-ture the airtime to be allocated to client k, at AP α. Factorwk,α depends on number of groups which are likely to beserved by AP α (i.e., |G′α|), or by other APs in α’s vicinity,operating on the same channel. Specifically, the airtime tobe allocated to a client k at α is the cardinality of subset ofgroups that include k (G′k,α ⊂ G′α), to the total number ofgroups. Hence, we set wk,α to be equal to |G′k,α|/|G′α|. Forexample, in the case study scenario of Figure 3, G′AP1 ={{C1, C2, C3}}, G′AP2 = {{C4}} when C3 connects to AP1,and G′AP1 = {{C1, C2}}, G′AP2 = {{C3}, {C4}} when C3connects to AP2. Hence, C3 will get more airtime at AP1(wC3,AP1 = 1), compared to AP2 (wC3,AP2 = 1/2). Notethat, if a set of APs A in the same vicinity with α operateon the same channel, then wk,α = |G′k,α|/

∑a′∈A |G

′a′ |.

4MU-MIMO group throughput is estimated from eq. (5), byconsidering the group’s total transmitted data and its totaltransmission time.

In conclusion, MAPS’ throughput model is able to cap-ture inter-client interference and client’s bandwidth profilewith the rate factor rk. Hence, it can be used by MAPS toboost grouping opportunities. It also considers the Wi-Fichannel utilization uα, and can prevent client assignmentto APs with highly congested channels. Finally, it capturesthe “load”wα at each AP (or APs in range, operating on thesame channel), which is required for load balancing. Our APplatform maintains all the per-client state, which is requiredfor throughput estimation.

4.3.2 Client Assignment ModelMAPS’ objective is to associate each client with an AP,

i.e., determining the proper association set Kα, ∀α ∈ A,by considering downlink MU-MIMO performance, such thatthe sum-rate of all clients can be maximized. This optimiza-tion problem can be formulated as follows:

I∗ = argmaxI

∑k∈K

∑α∈A

Ik,αThrk,α

subject to∑α∈A

Ik,α ≤ 1, ∀k ∈ K

Ik,α ∈ {0, 1}, ∀k ∈ K,∀α ∈ A

(6)

where the binary variable Ik,α indicates whether a client kassociates with an AP α,∀α ∈ A. Specifically, Ik,α equals 1 ifclient k is served by AP α, and 0, otherwise. Such constraintensures that each client associates with at most one AP.

We prove that our AP selection problem is NP-Hard, byreducing a simple instance of it, to the maximum indepen-dent set problem. We describe the reduction in Appendix A.Hence, we propose a heuristic algorithm that seeks to maxi-mize the aggregate clients’ throughput (eq. (6)), while satis-fying all the constraints. The algorithm operates as follows.Profiling: MAPS periodically updates each client’s andAP’s profile. Clients’ CSI profiles are updated every 100 ms,upon NULL frame transmission. Their bandwidth profilesare updated upon RTS/CTS handshake, while their trafficactivity is updated on per A-MPDU transmission basis. Fi-nally, AP’s channel busy time gets updated every 10 beaconintervals. MAPS maintains a timer for each client to triggerhandoff, as we discuss next.Handoff trigger: MAPS associates a timer with each clientk ∈ K. It triggers AP selection for k, when its timer expires,or when a special event occurs. Since handoff process lastsapproximately for 1.5 seconds in our testbed, MAPS setsclient’s timer in the order of tens of seconds. It freezes thetimer for idle or very low traffic clients (i.e., Sampdu ≈ 0),to prevent frequent handoffs. It also defers handoff process,when delay-sensitive traffic (e.g., VoIP) is in progress.

Client assignment is also triggered upon client’s mobil-ity. Mobility can be detected through RSSI variations. Forexample, RSSI drops when a client moves away from itsassociated AP. MAPS leverages RSSI-PHY rate mappingsfrom 802.11ac rate tables [15], and triggers client assignmentwhen the measured RSSI corresponds to low MCS values(i.e., <MCS4 in our implementation). MAPS can also useWi-Fi localization solutions already deployed in existing en-terprise Wi-Fi networks [27] to identify a client’s mobility,and trigger client assignment. By using both timers andevents for handoff trigger, MAPS remains adaptive to chan-nel dynamics, without triggering excessive handoffs.

HighCorr.

Hetero.Bandwidth

LoadBalance

ClientMobility

0100200300400500600700800

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ughput

(Mbps)

MAPSDenseAP

(a) Aggregated UDP throughput (acrossall clients) for MAPS and DenseAP.

29.3 351 3900.0

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(b) Rate distribution for clients atAP1 and AP2, in MU-MIMO.

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C4C3

(c) Dominant multipaths for the mobileclient C3, and static C4, at AP2.

Figure 10: MAPS performance over DenseAP in four representative settings. MAPS performs the same as Oracle.

Group formation: Upon triggering handoff for client k,MAPS will identify the set of APs in its range. To re-duce the MU-MIMO group formation computational over-heads, MAPS excludes in advance APs with very low RSSI,since they will likely be sub-optimal in terms of through-put. Then, it calculates the set of groups G′α (and G′k,α)for APs in k’s range, using the greedy search approach pro-posed in [30]. In summary, it first sorts in descending order,the clients based on their SU-MIMO throughput, and itera-tively goes through the list, to group the clients that providethe highest aggregate throughput with the already selectedclients. The search terminates when the group is complete(the maximum number of clients has been reached), or whenadding more clients to a group results in lower throughputthan serving them in SU-MIMO mode. Finally, MAPS com-putes k’s throughput at an AP α based on equation 5. Itassigns k to the AP which maximizes its throughput.

Our experimental results show that MAPS heuristic algo-rithm performs very close to the optimal AP selection.

4.4 DiscussionDownlink throughput: MAPS seeks to improve downlinknetwork throughput (from AP to clients). This is becauseMU-MIMO feature is only supported in downlink direction,in 802.11ac networks. Moreover, the downlink traffic domi-nates the uplink in Wi-Fi networks [11, 24]. However, sinceMAPS can improve downlink throughput, we are expect-ing more airtime (and hence better throughput) for uplinktransmissions as well.Co-existence with existing AP functions: MAPS canwork in concert with existing core functionalities implementedat the AP, such as MU-MIMO client group selection andPHY rate adaptation (RA). However, MAPS’ SINR estima-tion could be also used for MU-MIMO grouping and RA. Weleave such extensions for future work. Finally, MAPS canwork in concert with any network optimization algorithms(e.g., channel selection or bandwidth adaptation [25,26]) im-plemented at the controller side.Legacy clients: MAPS seeks to optimize the assignment ofIEEE 802.11ac MU-MIMO-capable clients to APs. Legacy802.11a/b/g/n clients are assigned to APs, based on legacy(e.g., RSSI-based) algorithms. However, MAPS’ throughputmodel will still consider the load offered by legacy clientsconnected to an AP, when it assigns 802.11ac clients to APs.

5. IMPLEMENTATIONA challenging question for MAPS’ implementation is which

functionality should be implemented at AP and controller

sides. First, since CSI, bandwidth and traffic information isavailable at AP’s firmware, client’s profile could be imple-mented in the firmware, to reduce the amount of feedbackto be sent to the controller. However, our AP’s firmware hasaccess to only 960 KB on chip memory, whose 98% is alreadybeing used by various functions (e.g., MU-MIMO client se-lection and rate adaptation). Given that one decompressedCSI sample from ACKs requires 3.6 KB memory space,storing multiple CSIs for all the connected clients at AP’sfirmware, is not feasible. Another option is to construct theCSI profile to the more powerful AP’s “host” board, whichruns a variant of Linux kernel on a dual core Qualcomm1.4 GHz CPU with a 512 MB DDR3 memory, and commu-nicates with the AP’s 802.11ac chip through a 32-bit PCIebus. However, to avoid overloading the AP, MAPS pushesthe CSIs and constructs clients’ profiles, at the controller.CSI communication overhead is small, considering that alldata packets are going through the controller. The rest ofMAPS’ core functionality is implemented (using MATLAB)at the controller side as well, as shown in Figure 5. Forour experiments, our controller is a laptop with 8GB DDR3memory and 4 Intel core i7-3520M CPU.

Due to their low memory requirements, we implementclients’ bandwidth and traffic profiles, and we maintain theWi-Fi channel busy time statistics, in AP’s firmware. Then,we periodically communicate this information to the con-troller. Note that our implementation does not include theMLME module and hence does not support real time hand-off. To this end, upon estimating the best AP (using MAPS),we manually assign clients to the best APs, and then evalu-ate the network’s performance.

6. EVALUATIONIn this section, we evaluate MAPS’ performance in mul-

tiple settings, using testbed experiments and trace-drivensimulations. We compare MAPS with DenseAP [22], whichis representative of legacy AP selection designs proposedby research studies, and deployed by 802.11 AP vendors.DenseAP leverages an available capacity metric, which es-timates the throughput as a function of PHY-rate (calcu-lated from RSSI) and Wi-Fi channel busy time. It seeks tobalance the load by assigning clients to less loaded APs5.We further compare MAPS with an “Oracle”, which is thebest-throughput (optimal) client assignment. We identify

5DenseAP performs transmit power control, which is out ofthe scope of this work.

the best-throughput setting, by evaluating all the differentclient-AP assignment combinations.

Our experimental setup consists of the 802.11ac APs andphones described in Section 3.1, and one laptop which actsas the controller. We evaluate multiple different networktopologies, under various traffic scenarios (UDP, TCP, VoIP).

6.1 Performance in Representative SettingsWe first evaluate MAPS’ performance in four represen-

tative settings, which capture different aspects of dynamicsin 802.11ac networks. We consider that APs generate satu-rated downlink UDP traffic to clients, and that they operateon orthogonal channels, unless it is explicitely mentioned.

Setting C1-C2 C1-C3 C2-C3 C3-C4

CSI Corr 0.42 0.51 0.48 0.72

Table 4: CSI correlation for case study setting.

Correlated channels: We first evaluate MAPS in our casestudy setting of Figure 3. Similar to Oracle, MAPS can iden-tify the best-throughput client assignment, and achieves 153Mbps (or 27.5%) aggregated throughput gain compared toDenseAP, as shown in Figure 10a. Specifically, MAPS canidentify the high correlation of C3, C4’s wireless channelsat AP2, by computing their CSI correlation and SINR val-ues. The correlation factor ρ(C3, C4) is 41% and 50% highercompared to ρ(C1, C3) and ρ(C2, C3), as shown in Table 4.Such high correlation does not allow for MU-MIMO opera-tion at AP2. Hence, MAPS will assign C3 to AP1.

On the other hand, DenseAP will falsely assign C3 tothe highest RSSI AP2. Although the SU-MIMO is the bestoperation mode for such assignment (cf. Tab. 1), we ob-served that the AP’s MU-MIMO client grouping algorithmwill periodically try to evaluate the performance of MU-MIMO group {C3, C4}. However, this will result in highinter-client interference and hence high PER, as we showedin Figure 2c. When C3, C4 operate as an MU-MIMO group,PHY rate adaptation has to switch to very low PHY ratesto cope with such interference. This is shown in the ratedistribution of Figure 10b, where the AP2 often uses thelowest available 802.11ac PHY rate (29.3 Mbps) to transmitto C3, when C3 is grouped with C4. However, when MAPSassigns C3 to the lower RSSI AP1, the selected PHY rate ismostly 390 Mbps, which results in higher throughputs.Heterogeneous bandwidths: We next evaluate MAPS ina setting of clients with heterogeneous bandwidth configu-rations. We deploy two APs and five clients. C1 and C2 areassociated with AP1 operating at 80 MHz. C4 and C5 areassociated with AP2. Due to interferences, C4 and C5 canonly operate at 40 MHz. A new client C3 has a strongerRSSI with AP2, than AP1. Hence, DenseAP will assign C3to AP2 without considering the fact that, C3 cannot forman 80 MHz MU-MIMO group at AP2. C3’s throughputis 79 Mbps at AP2, while the total network throughput is608 Mbps (cf. Fig. 10a). However, MAPS can identify theopportunity of a high throughput MU-MIMO group {C1,C2, C3} at 80 MHz, and assigns C3 to AP1. Associatingwith AP1, C3 achieves 156 Mbps throughput, with a totalnetwork throughput of 720 Mbps. Leveraging client’s band-width profile, MAPS can almost double C3’s throughput. Italso boosts total network throughput by 112 Mbps (18.4%)compared to DenseAP. MAPS performs the same as Oracle.

0 5 10 15 20 25 30

Time (s)0

20

40

60

80

100

Del

ay (m

s)

DenseAPMAPS

Figure 11: MAPS vs. DenseAP over VoIP.

Mobility: We further evaluate MAPS’ responsiveness tomobility. We deploy two APs, three static and one mo-bile client. Specifically, static clients C1, C2 are associatedwith AP1, and static client C4 with AP2. C3 is movingwith pedestrian speed around AP2. From our traces, weobserve that the highest RSSI AP for C3 is always AP2.Hence, DenseAP assigns C3 to AP2. This results in 65 Mbpsthroughput for C3, and a network throughput of 552 Mbps.

MAPS monitors the channel dynamics of the mobile clientC3, and constructs a CSI profile for AP2 with three domi-nant multipaths, as shown in Figure 10c. The most domi-nant path among the three is represented with the solid line.Interestingly, C3 and C4 channels overlap in space at AP2(cf. Fig. 10c), which implies correlated channels and highinter-client interference. To avoid client groups with corre-lated channels, MAPS will assign C3 to AP1. C3 achieves91 Mbps throughput at AP1, and the aggregated networkthroughput is 663 Mbps (cf. Fig. 10a). This correspondsto a throughput gain of 40% for C3, compared to DenseAP.Network throughput is also increased by 20.1%.Unbalanced traffic: Different from the previous experi-ments, we next evaluate a setting where two APs operatingon the same channel, have unbalanced loads. Specifically,clients C1 and C2 are connected to AP1, while AP2 doesnot serve any client. Let’s now consider a new client C3 inthe network, with similar RSSI from AP1 and AP2. LegacyAP selection (such as DenseAP) will assign C3 to AP2, tobalance the load across APs. Such assignment results in 75Mbps and 389 Mbps throughput for C3 and for the wholenetwork, respectively. On the other hand, MAPS will esti-mate factor wC3,AP1 to be equal to 1, and wC3,AP2 to be 1/2.Hence, given a negligible inter-client interference among C1,C2, C3 at AP1, MAPS will assign C3 to AP1. Such assign-ment almost doubles C3’s throughput. It also increases theaggregated network throughput by 50 Mbps.Delay-sensitive traffic: We finally compare MAPS withDenseAP over delay-sensitive traffic, such as VoIP. In oursetting, clients C1, C2 are connected to AP1, and C4, C5to AP2. Both APs generate saturated downlink UDP traf-fic to their clients. DenseAP will assign a new client C3 tothe highest-RSSI AP1. On the other hand, MAPS connectsC3 to AP2, which can maximize MU-MIMO gains. Uponassociating to an AP, C3 initiates a VoIP call to anotherdevice connected to the AP through Ethernet. In Figure 11,we show the one-way network delay for VoIP traffic overa 30-second time window, for C3 at AP1 (DenseAP), andC3 at AP2 (MAPS). We observe that the average and peakdelays are only 1.1 ms and 8.4 ms, when C3 connects toAP2. This is because MAPS’ assignment allows for C3, C4

−200 0 200 4000

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(a) Aggregated throughput gains (Mbps)of MAPS over DenseAP.

0 50 100 1500

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(b) Aggregated throughput gains (Mbps)of Oracle over MAPS.

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CD

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MAPS−DenseAP(UDP)

Oracle−MAPS(UDP)

MAPS−DenseAP(TCP)

Oracle−MAPS(TCP)

(c) Jain fairness index difference ofMAPS over DenseAP, and Oracle.

Figure 12: Throughput and fairness comparison of MAPS, Oracle and DenseAP, in multiple TCP/UDP settings.

and C5 to form an low interference MU-MIMO group. How-ever, DenseAP assignment results in 11.4× higher averagedelay (12.4 ms) compared to MAPS. We further observethat for 7% of the samples, the delay for DenseAP exceeds30ms, which is above the delay requirements of VoIP ap-plications [21]. This is because C3 mainly operates in SU-MIMO mode at AP1, due to high inter-client interferencewith C1 and C2. Interestingly, Figure 11 shows high delayvariations for DenseAP assignment, with delay peaks up to94ms. We observe that such peaks (between [2.7, 8.8] sec.and [23.8, 27.2] sec.) appear, when the MU-MIMO groupingalgorithm tries to group C1, C2, C3 together. Such group-ing creates high PER (and low throughput). Then it breakssuch group, and C3 operates on SU-MIMO mode.

6.2 Larger Scale Field TrialsIn this section, we seek to get further insights about MAPS’

gains and limitations, by evaluating multiple topologies with6 APs and 20 clients. We conduct our experiments on a cam-pus setting. We present our experimental floorplan in Ap-pendix B. Apart from our APs, we detect 22 more BSSIDs at5 GHz, to operate in various channels, in the same RF cover-age zone. We run each experiment for 5 minutes at differenttimes of day considering both static and mobile client scenar-ios, and we report experiments from multiple runs. For eachrun, we compare MAPS, DenseAP and Oracle, for saturateddownlink UDP and single-flow TCP traffic. In Figure 12a,we present the aggregated (over all APs and clients) net-work throughput gains of MAPS over DenseAP. Each pointof the distribution reflects a different setting. We observethat MAPS performs similar or better than DenseAP inmore than 90% of the settings. For UDP, the gain is atleast 149 Mbps in 50% of the settings, and it can go up to365 Mbps (which corresponds to a 52.3% gain). Through-put gains for TCP are slightly smaller, and can go up to170 Mbps (23.6% gain). MAPS’ gains are higher over UDPsince traffic is always saturated compared to TCP.

The highest gains for MAPS are observed in static (with-out clients’ mobility or physical environment dynamics) set-tings, when clients’ channels are highly correlated. However,in some highly dynamic environments, MAPS’ throughputestimation can be inaccurate, and hence DenseAP may out-perform MAPS by up to 95 Mbps (cf. Fig. 12a). In suchsettings, MAPS’ CSI profile may not capture the channel

dynamics, and may assign clients to lower RSSI APs, whichhappen to be the lower throughput APs.

MAPS mostly performs similar to Oracle. Specifically,Figure 12b shows that MAPS throughput is the same withOracle in 94% of the settings for UDP, and 75% of the set-tings for TCP. Oracle outperforms MAPS in a few scenariosof highly dynamic environments, as we discussed above.

Interestingly, MAPS can also improve the throughput fair-ness among clients connected to APs in the same vicinity.To illustrate our finding, we compute the Jain Fairness Indexof the clients’ throughput, for all of our settings. We plotin Figure 12c the difference of Jain Fairness Index betweenMAPS and DenseAP, and between Oracle and MAPS, forUDP and TCP. We observe that MAPS has always equal orlarger Jain index compared to DenseAP. The difference ex-ceeds 0.2, which is a significant improvement, if we considerthat an index of 1 implies perfect fairness. Since MAPS lim-its inter-client interferences (and hence PER), it does notnegatively affects certain clients’ TCP windows. This re-sults in better TCP fairness gains (compared to UDP) overDenseAP (cf. Fig. 12c). MAPS achieves the same fairnessas Oracle in the vast majority of the settings.

6.3 Trace Driven SimulationsWe next conduct trace-driven simulations to evaluate MAPS

in larger scale network topologies. For our simulation, wehave collected wireless link performance traces (e.g., CSI,throughput, PER) from multiple settings. We have also col-lected per-client traffic load statistics from 82 APs of an En-terprise Wi-Fi network, to simulate realistic traffic scenarios.We then combine these traces to simulate larger networks.We simulate scenarios where 20 APs and 108 (static andmobile) clients are placed in a building floor. The numberof clients per AP varies from 1 to 54.

In Figure 13a, we present the aggregated (over all APs andclients) network throughput gains of MAPS over DenseAP.We observe that MAPS always performs similar or betterthan DenseAP. Specifically, it achieves up to 1.2 Gbps (or28.6%) and 663.8 Mbps (or 17.5%) throughput gain overUDP and TCP, respectively. Figure 13b, further shows thatMAPS performs the same as Oracle, for 85% and 60% of thesettings, for UDP and TCP, respectively.

Interestingly, our results show that MAPS’ gains overDenseAP do not necessarily drop when the number of clientsconnected to an AP increases. For example, Table 5 shows

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Figure 13: Throughput and fairness comparison of MAPS, Oracle and DenseAP, in trace-driven simulations.

the average throughput for MAPS, DenseAP and Oracle,when the number of clients in two APs’ vicinity varies from12 to 108. We observe MAPS’ gains over DenseAP rangefrom 33% to 45%, with the maximum gain to be achievedfor 108 clients. This is because, the higher number of clientsconnected to an AP does not necessarily increase the MU-MIMO grouping opportunities. Specifically, we observe thatthe number of candidate clients for grouping at each trans-mit opportunity (TXOP) is limited by: a) the active clients,b) the fair scheduler implemented in our AP, which willnot reschedule the clients served in the previous TXOPs, c)the clients’ correlated channels and channel bandwidth con-figurations. Particularly, we observe that the MU-MIMOgroups’ size for DenseAP is typically less than maximumsupported size of 3 clients, or it often operates in SU-MIMO.

Finally, our simulations verify that MAPS can improve thethroughput fairness among clients, as shown in Figure 13c.In conclusion, our experiments show that MAPS can signif-icantly boost the performance for large Wi-Fi networks.

Total clients 12 36 60 84 108

MAPS Thr. (Mbps) 313 ± 5 314 ± 2 333 ± 1 341 ± 1 346 ± 1MAPS clients AP1/AP2 6/6 19/17 31/29 40/44 52/56

DenseAP Thr. (Mbps) 223 ± 5 223 ± 2 250 ± 1 242 ± 2 237 ± 1DenseAP clients AP1/AP2 6/6 18/18 32/32 42/42 54/54

Oracle Thr. (Mbps) 360 ± 3 361 ± 2 360 ± 2 362 ± 1 362 ± 1Oracle clients AP1/AP2 6/6 19/17 31/29 40/44 52/56

Table 5: Average throughput for varying number of clients.

7. RELATED WORKThere are several studies related to our work. We briefly

discuss them and position our contributions.AP selection: AP selection approaches can be classified incentralized [7,22,38] and distributed [5,9,16,18,23,36]. Sim-ilar to MAPS, in centralized solutions, APs exchange infor-mation (such as RSSI, traffic load, interference, client’s capa-bility) with a central controller, which seeks to optimize net-work’s performance. In distributed AP selection algorithms,it is the client which selects an AP to associate with. The de-signs proposed in [9,18,36], estimate the available bandwidthat the client side, and select the highest bandwidth AP. Theabove metrics have been further refined [16, 23] to consideruser utility, traffic characteristics and round trip time, toimprove AP selection. However, all the above systems havebeen designed for legacy 802.11a/b/g/n networks and areoblivious to MU-MIMO feature. Hence, they can limit the

MU-MIMO grouping opportunities, as shown by our exper-iments. AP selection designs [2,13], proposed by 802.11 APvendors, are also RSSI-based, and show the same limitationsin MU-MIMO settings. Our experiments with APs and con-trollers from one of the largest AP vendors worldwide, verifythat the deployed MU-MIMO 802.11ac networks are still us-ing legacy AP selection algorithms.

The theoretical study in [14] jointly solves the problemsof AP selection and client grouping in MU-MIMO networks.It seeks to assign clients with uncorrelated channels to thesame AP, to boost MU-MIMO gains. However, such pro-posal has two key limitations. First, it is oblivious to clients’bandwidth configurations, and it does not consider the im-pact of AP load and channel utilization to throughput per-formance. Hence, it performs poorly in the scenarios de-scribed in Sections 3.3, 3.4. Second, our results have shownthat MU-MIMO grouping and AP selection happen at differ-ent time scales (msec. and sec. scales, respectively). Specif-ically, triggering AP selection at millisecond granularity cancause excessive handoff overheads. Different from [14], MAPSdecouples these two design modules, and considers clients’heterogeneity and AP load, when assigning clients to APs.MU-MIMO grouping and scheduling: There have beenseveral MU-MIMO client grouping and scheduling propos-als [28, 30, 34, 39]. Such designs can only achieve high MU-MIMO gains, if clients with uncorrelated channels have beenassigned to an AP. Thus, they can realize their full potential,only by working in concert with designs like MAPS. More-over, MU-MIMO grouping designs leverage explicit beam-forming feedback to identify uncorrelated channels. Suchapproach requires excessive clients’ handoffs (cf. Sec. 4.1),and it is not efficient for AP selection. Hence, MAPS usesimplicit CSI feedback to assign clients to APs.Network MU-MIMO: MAPS assigns clients with orthog-onal channels to APs, to allow for MU-MIMO groups withno inter-client interference. For a given client assignment,recent designs [6, 19, 35, 37] enable APs and clients in inter-fering cells to coordinately cancel the inter-cell interference,using their antennas for beamforming and interference can-cellation. Such solutions typically require client-side modi-fications and are not 802.11-compliant. On the other hand,we implement MAPS in 802.11ac-compliant commodity APsand controllers. Note that, MAPS could also work in concertwith network MU-MIMO, to further improve performance.

8. CONCLUSIONIn this paper, we have studied the AP selection problem

in MU-MIMO Wi-Fi networks, using commodity 802.11actestbeds. Our experimental results show that legacy APselection designs assign clients with correlated channels andheterogeneous bandwidths to the same AP, limiting the MU-MIMO grouping opportunities. Their approach to load bal-ancing is also MU-MIMO oblivious and can decrease theMU-MIMO gains. Based on our findings, we have proposeda new Mu-mimo-Aware AP Selection (MAPS) design, whichcan identify the best-throughput client assignment, withoutrequiring a client device to be associated to an AP. Our re-sults show that MAPS significantly outperforms legacy de-signs in 90% of the settings. We believe that MAPS canbe a key building block for designing the future MU-MIMO802.11ax and 5G wireless networks.

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Figure 14: Correlation graph H at AP1 and AP2, for thescenario of Figure 3.

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Figure 15: Floorplan setting for field trial experiments.

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APPENDIXA. PROOF OF PROBLEM HARDNESS

To prove that the client assignment problem is NP-Hard,we consider a smaller instance of the problem. Given a setK of clients which are in the range of an AP α, MAPS needsto compute the set of all MU-MIMO groups Gα that can beformed by K clients at AP α, where Gα is a totally orderedset in decreasing MU-MIMO group throughput performance

order (cf. Sec. 4.3). The problem of finding Gα can bemodeled as a graph H with vertex set VH and edge set EH ,where each vertex of the graph is a client k ∈ K. We drawan edge ei,j ∈ EH between two vertices (or clients) i, j, onlyif the clients’ channels are correlated. We consider the ratesof clients i, j equal to 0 if there is an edge between them(ri,α = 0, rj,α = 0 if ei,j ∈ EH), and equal to r, otherwise.

Given the graph H, an independent set, is a set of verticessuch that there is no edge between any two of the vertices.The independence number of graph H is the cardinality ofthe maximum independent set in H. It is easy to see thatfinding the best-throughput MU-MIMO group g ∈ Gα isequivalent to finding the independence number of graph H,which is known to be a hard problem.

As an example, in Figure 14, we show the channel corre-lation graph H for our case study setting of Figure 3, whenclient C3 connects to AP1 and to AP2. For the first case,the independence number of H is 3. However, when C3associates to AP2, the independence number of H is 1.

B. FIELD TRIAL FLOORPLANIn Figure 15, we present the floorplan of the building floor,

where we conduct our field trial experiments. We place ourAPs in 6 locations, while we evaluate different client loca-tions. We conduct experiments with both static and mobileclients.