Adaptive Feedback Compression for MIMO Networks

Xiufeng Xie and Xinyu ZhangUniversity of Wisconsin-Madison{xiufeng,xyzhang}@ece.wisc.edu

Karthikeyan SundaresanNEC Laboratories Americakarthiks@nec-labs.com

ABSTRACTMIMO beamforming technology can scale wireless data rateproportionally with the number of antennas. However, theoverhead induced by receivers’ CSI (channel state informa-tion) feedback scales at a higher rate. In this paper, weaddress this fundamental tradeoff with Adaptive FeedbackCompression (AFC). AFC quantizes or compresses CSI from3 dimensions — time, frequency and numerical values, andadapts the intensity of compression according to channelprofile. This simple principle faces many practical chal-lenges, e.g., a huge search space for adaption, estimation orprediction of the impact of compression on network through-put, and the coupling of different users in multi-user MIMOnetworks. AFC meets these challenges using a novel cross-layer adaptation metric, a metric extracted from 802.11 packetpreambles, and uses it to guide the selection of compres-sion intensity, so as to balance the tradeoff between over-head reduction and capacity loss (due to compression). Wehave implemented AFC on a software radio testbed. Ourexperiments show that AFC can outperform alternative ap-proaches in a variety of radio environments.

Categories and Subject DescriptorsC.2.1 [Computer-Communication Networks]: NetworkArchitecture and Design—Wireless Communications; C.2.2[Computer-Communication Networks]: Network Pro-tocols

General TermsAlgorithms, Design, Theory, Performance

KeywordsMulti-user MIMO networks, limited feedback, feedback com-pression

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1. INTRODUCTIONMIMO beamforming, also referred to as closed-loop MIMO

technology, has the potential to scale wireless data rate pro-portionally with the number of transmit antennas. In fact,it has become a hallmark of recent high-throughput 802.11standards. In particular, 802.11n adopted single-user MIMO(SU-MIMO) beamforming, where multiple transmit anten-nas precode one packet, so that the precoded signals coher-ently combine at a receiver to enhance SNR. The ongoing802.11ac further incorporates multi-user beamforming (MU-MIMO), which precodes different receivers’ packets, so thatthey can be transmitted simultaneously without interfer-ence. The precoding operations in SU- and MU-MIMO areessentially a weighted combination of outgoing packets, andthe weights must be carefully designed based on the channelstate information (CSI), i.e., the channel matrix from trans-mit antennas to all receive antennas. Hence, a transmittermust obtain timely CSI feedback from all receivers. As CSIis needed for different transmit antennas, frequency bandsand receivers, the resulting information grows with a mul-tiplication of all these parameters, which causes formidableoverhead and may even nullify the MIMO capacity gain.Therefore, managing feedback overhead is critical to the per-formance of MIMO beamforming.

The 802.11n/ac standards propose to compress the CSIalong three dimensions: time — sending CSI less frequently;frequency— allowing adjacent spectrum units (called sub-carriers) to share the same CSI; and numerical values —quantizing CSI values into a small number of bits. Thoughpromising for reducing feedback overhead, such compressioncomes with a loss in CSI accuracy and may adversely af-fect the MIMO network throughput. Therefore, it is criticalto strike a balance between overhead reduction and capac-ity loss. But finding such a sweet spot is non-trivial as itinvolves sophisticated coupling of all three dimensions. Sim-ilar to the bit-rate options, the choice of compression optionsand levels remains vendor-specific in 802.11, and to the bestof our knowledge has not been explored before.

This paper attempts to fill the gap in this space through:a comprehensive measurement study of the impact of com-pression on network performance, and the design of Adap-tive Feedback Compression (AFC) - a feedback managementmechanism for SU-/MU-MIMO networks. Our measure-ment study is based on a comprehensive software-radio im-plementation of the 802.11n SU-MIMO and 802.11ac MU-MIMO OFDM PHY layer. The results reveal that althoughCSI compression can save substantial overhead, it may sig-nificantly degrade link capacity if too aggressive. More im-

portantly, a link’s tolerance to CSI compression depends notonly on its channel stability, but also on SNR, spectrum lo-cation, and user pairing (for MU-MIMO) — a number offactors unreported in previous works. This calls for an au-tomatic configuration scheme that maximizes compressionintensity without losing too much capacity.

AFC is designed to meet this goal with a simple principle.It quantizes or compresses CSI from 3 dimensions: time,frequency and numerical values, and adapts the intensityof compression according to channel profile. Realizing thisprinciple involves non-trivial challenges: (1) The 3 dimen-sions together constitute a huge parameter space. Hence acomprehensive search algorithm is inefficient and may neverconverge. In fact, when searching over one dimension, thechannel profile w.r.t. the other two dimensions may have al-ready changed. (2) Compression intensity can be configuredaccording to a certain metric that reflects channel stabilityover time or frequency. Coherence time/frequency is widelyused for this purpose. But through experimental study, wefind that there does not exist a fixed mapping between sucha metric and the optimal compression intensity. (3) An ef-ficient adaptation algorithm must be able to estimate thelink capacity change due to CSI compression over a certaindimension. However, the effects of different dimensions oncapacity loss are coupled.

AFC meets these challenges using CNo, a novel cross-layeradaptation metric that can model the information loss (orerrors) due to compression. Upon each packet arrival, AFCcan instantaneously extract the CNo metric from the CSI of802.11 packet preambles, and evaluate the errors and SNRreduction caused by each dimension of compression respec-tively. As CNo decouples the 3 dimensions of adaptation,it substantially reduces the search space. It also helps iso-late the effects of compression from channel fading, whichcan both result in changes in link capacity. Based on CNo,AFC can easily identify the appropriate compression levelthat optimizes the overall network throughput, taking intoaccount both capacity loss and overhead reduction.

We have implemented AFC on top of the SU-/MU-MIMOOFDM module that we built on WARP. This PHY mod-ule closely follows the 802.11n/ac specifications, and real-izes linear precoding based beamforming, OFDM modula-tion/demodulation, CSI estimation as well as symbol-leveldecoding. Experiments on a WARP testbed show that AFC’sadaptation metric leads to fast and effective selection of com-pression levels along all 3 dimensions. In contrast, no singlestatic configuration of compression intensity can fit all chan-nel/network profiles. Overall, by balancing the capacity-overhead tradeoff, AFC’s throughput performance is compa-rable with the best fixed compression scheme for any givenchannel profiles, and 40% to 120% higher than the non-adaptive scheme in 802.11n/ac.

In summary, we make the following contributions in thispaper.

• We present the first comprehensive measurement studyof the effects of feedback compression in 802.11 SU-/MU-MIMO networks.

• We propose AFC, which introduces effective cross-layermetrics to trigger the adaptation of compression lev-els along 3 dimensions, and strike a balance betweenoverhead reduction and capacity loss.

To our knowledge, AFC represents the first algorithm thatprovides guidelines to address this tradeoff for SU-/MU-MIMO beamforming in wireless networks.

2. BACKGROUND

2.1 SU-/MU-MIMO networksMU-MIMO systems are commonly realized use Zero-Forcing

Beamforming (ZFBF), a low-complexity linear precoding sch-eme that is amenable for practical transceivers. Consider anetwork with a n-antenna AP and n single-antenna receivers.Let X be a n × 1 vector, representing the data symbols tobe sent to n receivers, then the vector of received symbolscorresponding to the n receivers is:

Y = HWX + V (1)

where H is the n × n channel matrix, and V the n × 1noise vector. W is the precoding matrix, with each row W∗kcorresponding to the precoding vector of transmit antenna k.In ZFBF, W is obtained via a pseudo-inverse of the channelmatrix:

W = H∗ · (H ·H∗)−1 (2)

where (·)∗ is the complex conjugate operator.With precoding, it is straightforward that the received

symbols become Y = X +V , i.e., data symbols of differentreceivers are decoupled — each receiver only obtains its ownsymbol plus some noise. In practical MIMO transceivers,each antenna is accompanied by one radio back-end and hasa maximum power constraint Pm. To satisfy this constraint,the precoding vector of each transmit antenna k should bescaled by: arg maxj

√Pm/||W∗j || [1].

SU-MIMO can be considered as a MU-MIMO networkwith one receiver but n transmit antennas. The pseudo-inverse precoding will result in n copies of the receiver’ssymbols added up, boosting the signal power to n2.

To perform precoding, however, both SU- and MU-MIMOtransmitters need to know the CSI, i.e., the channel matrixH, which can only be obtained from receivers’ feedback. Inthis paper, we only consider precoding for single-antenna re-ceivers, but multi-antenna precoding is also feasible throughblock-diagonalization [2]. The adaptation algorithm pro-posed in this paper is not limited to any precoding schemeas it only leverages vanilla 802.11 preambles.

2.2 CSI feedback and compression in 802.11SU-/MU-MIMO

In 802.11n/ac, before beamforming a data packet, a SU-/MU-MIMO transmitter follows a polling procedure to ob-tain CSI from the receiver(s). Fig. 1 illustrates an examplefor a MU-MIMO network with 2 transmit antennas and 2receivers. The transmitter first sends an NDP announce-ment to initiate the procedure, and then polls the intendedreceivers one by one and obtains CSI feedback from them.Afterwards it precodes the data packets based on the CSI.CSI feedback for SU-MIMO follows the same procedure.

The accuracy of CSI determines how effectively the interdata-symbol interference can be cancelled for MU-MIMO,and whether copies of a symbol can align their phases toenhance received SNR in SU-MIMO. Hence, it is critical tothe SNR and consequently network capacity.

However, accuracy comes at the cost of overhead. Tobound the CSI overhead, 802.11 allows CSI to be compressed,

MU-MIMO TXNDP

time

CSIClient1

Client2

APPoll Poll

CSI

Figure 1: CSI feedback and MU-MIMO beamform-ing in 802.11ac.

with multiple levels of intensity, along three dimensions: i)Time, i.e., instead of per-packet feedback, allowing CSI tobe shared among multiple subsequent packets. ii) Frequency,i.e., instead of collecting CSI for each subcarrier (the small-est spectrum unit in an 802.11 OFDM band), group neigh-boring subcarriers and use one subcarrier’s CSI to representits neighbors’. iii) Numerical values, i.e., instead of send-ing float-point complex numbers directly, quantizing the CSIinto a small number of bits.

To compress CSI in frequency-domain, 802.11 allows 1, 2,or 4 subcarriers to be grouped and share the same CSI1. Inaddition, for each CSI value, its real and imaginary com-ponents can be quantized into 4, 5, 6 or 8 bits [3]. Aschannel stability and inter-packet time are hard to charac-terize, 802.11n/ac employs per-packet CSI feedback, leavingthe time-domain compression as an open option.

3. MOTIVATIONIn this section, we use simulation and testbed measure-

ment to evaluate the MAC-layer overhead reduction andPHY-layer capacity loss due to compression, which moti-vates the need for an mechanism that automatically config-ures compression intensity to address this tradeoff.

3.1 How much can compression save?We provide an account of all factors that contribute to the

CSI feedback overhead – defined to be the ratio between thetime spent in obtaining CSI (including the NDP and pollingpackets) and that in data transmission. To this end, we ex-tend the ns-2 simulator with a SU-/MU-MIMO MAC mod-ule, following the 802.11n/ac MAC specifications. We thenevaluate the CSI overhead for UDP transmissions in a MIMOWLAN. By default, the simulation is configured to 20MHzbandwidth (with 52 data subcarriers), 1.5KB packet size, 4transmit antennas and 1 receiver, 32-bit float-point CSI (forboth real and imaginary components), and per-packet CSIfeedback. We first isolate the PHY layer effect by config-uring an intermediate data rate of 18Mbps for all receivers.Note that CSI feedback is always sent with 6Mbps data ratein 802.11. Fig. 2 plots the CSI overhead when varying eachfactor while keeping others to the default values.Bandwidth (number of subcarriers). CSI overhead

increases linearly with the spectrum width, which in turndepends on the number of subcarriers. For a typical 20MHzspectrum, the CSI feedback overhead can be 3.4× comparedto data transmission, and increases linearly with bandwidth(Fig. 2(a)). Note that the NDP, polling packets, and theirinter-frame spacing also contribute to the overhead. How-ever, these are fixed, resulting in the CSI overhead dominat-ing. By compressing CSI in frequency domain, the feedbackoverhead decreases sharply, on the same order as the numberof subcarriers grouped together to share CSI.

1A 20MHz band in 802.11 contains 52 data subcarriers. Thenumber of subcarriers increases linearly with bandwidth.

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CSI bits. Representing CSI with full-resolution float-point numbers is clearly inefficient (Fig. 2(b)) — it inducesan overhead of 0.96 under the default network setting. Quan-tization of the numerical values can reduce the overhead al-most linearly, to 0.33 with the most aggressive 4-bit quanti-zation defined in 802.11.Feedback period. Similar to the above two factors, by

compressing the CSI over time, i.e., increasing the feedbackperiod, an inverse-linear reduction in overhead is achieved,as shown in Fig. 2(c). CSI feedback overhead is only 0.096with an 8ms feedback period and 0.019 with 40ms. Note thatour simulation isolates the compression along these three di-mensions. As they can be done independently, a combina-tion would achieve a multiplicative reduction.Number of TX antennas and receivers. These two

factors independently account for an almost linear increaseof overhead (Fig. 2(d) and (e)), as the channel from eachtransmit antenna to each receiver needs to be estimatedand fed back. Unfortunately, no CSI compression is feasiblew.r.t. these two factors.Data rate. For small packet sizes, CSI induces formidable

overhead, e.g., 2.46× for a 200B and 0.48 for a 1KB packetsent at 6Mbps (Fig. 2(f)). Increase of data rate amplifies therelative overhead, to 2.88× for a 1KB packet at 36Mbps.

From the above simulation results, we can infer that therelative overhead of CSI feedback is roughly linear w.r.t.:

#SubcGroups×#CSIbits×#TXantennas ×#Receivers×DataRate

Feedback period × Pkt size

Among these factors, the number of subcarrier groups,CSI bits and feedback period can be compressed. 802.11’sstandard linear compression over the three dimensions cancontribute to a multiplicative reduction in feedback over-head. With more sophisticated compression schemes, suchas a Givens rotation [4, Section 20.3.12] of channel matrix,

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Figure 3: Effects of time-domain compression onSNR for (a) SU-MIMO and (b) MU-MIMO. Errorbars show the max and min SNR among 10 experi-mental runs, unless noted otherwise.

feedback overhead can be further reduced. Besides compres-sion, frame aggregation can also reduce the relative overheadof CSI by amortizing it over concatenated data frames. Butlarge frames may incur unacceptably long buffering delay,which compromises the performance of real-time applica-tions such as VoIP and interactive web sessions. Such effectslimit the practical usage of frame aggregation.

We will now study the associated impact of feedback com-pression on the link capacity of MIMO networks.

3.2 Why adaptive compression?Feedback compression, if too aggressive, can severely de-

grade the accuracy of CSI and lower the achievable SNR orbit-rate. The extent to which compression affects networkperformance varies with the radio environment (channel pro-file), which we will study through comprehensive experi-ments below. Our experiments are conducted on a testbed of5 WARP MIMO software radios, located in an office build-ing. We have implemented a full-fledged MIMO-OFDMcommunication module on WARP, following the 802.11n/acspecification for SU- and MU-MIMO networks (Sec. 5 pro-vides a detailed description of our implementation). Withthis testbed implementation, we perform a quantitative studyto identify the channel characteristics that lead to the posi-tive and negative effects of CSI compression. These in turncontribute to the factors that AFC should monitor and reactappropraitely.Effects of time domain compression. The time-domain

accuracy of compressed CSI depends on how frequently it isrefreshed, relative to the channel variation over time. InFig. 3, we allow a transmitter to periodically initiate CSIpolling, obtain feedback from receiver(s), and send one beam-forming packet. We then compute the SNR2 by varying thefeedback period.

We consider two scenarios: i) static environment: a re-search lab with negligible human movement. ii) mobile nodes:receiver(s) are moving around the transmitter (along a cir-cle) at walking speed. From the results in Fig. 3(a), wesee that in static environment, SU-MIMO link SNR is vir-tually unaffected by time-domain compression, even with a2-second feedback period. This implies substantial space forCSI overhead saving: for each link, packets separated bywithin 2 seconds can share the same CSI.

2Our testbed implementation allows us to obtain SNR fromdecoded symbols. This leads to an accurate estimation,which accounts for not only ambient noise, but also receiver-induced noise due to, e.g., imperfect channel estimation.

The impact of stale CSI becomes pronounced as the ra-dio environment becomes more dynamic, as reflected in thelarge variation of SINR. When nodes are moving at walk-ing speed, we observed that average SINR may reduce by 1to 2 dB when feedback period is below 300ms. But the re-duction may vary significantly across different experiments.We have observed in certain experiments that even a 20msfeedback period can reduce SNR by up to 5.3dB comparedwith an oracle scheme with zero feedback delay.3 Clearly,an aggressive time-domain compression will hurt the MIMObeamforming performance for mobile nodes. However, dueto packet transmission delay (e.g., caused by contention),inter-packet arrival time can easily reach 20ms. Hence, per-packet feedback becomes inevitable for mobile nodes, whichnecessitates compression from alternative dimensions.

Fig. 3(b) shows the performance of a MU-MIMO networkwith a 2-antenna AP and two receivers (one mobile, theother static). MU-MIMO is more sensitive to CSI than SU-MIMO, since the channel variation of multiple receivers areindependent, and therefore their CSI errors add up and ex-acerbate the impact of stale CSI. Remarkably, mobility onlyaffects the mobile receiver itself. This is because when run-ning linear precoding, the transmitter only needs to ensuresignals from all its antennas combine coherently at each in-tended receiver, which is only related with the channel gainsbetween transmit antennas and that receiver. This also im-plies that in MU-MIMO networks, different receivers canperform time-domain compression and adaptation indepen-dent of each other, which is critical for a scalable solution.Effects of frequency domain compression. Theoret-

ical wireless channel models [5] have shown that neighboringsubcarriers of a wide spectrum may be highly correlated witheach other, hence it is sufficient to use one subcarrier’s CSI torepresent that of a group. Subcarrier correlation is roughlyinversely proportional to multi-path delay spread, i.e., themaximum separation between multiple reflected copies of asignal. In environment with rich reflections and obstacles,delay spread is small and channel may be correlated over awide spectrum with many subcarriers, making it possible tocompress CSI aggressively in frequency domain. Our experi-ments in Fig. 4 indeed verify this effect. In a small laboratoryenvironment, compressing neighboring 4 subcarriers resultsin negligible SNR loss. A lobby – a relatively open-spaceenvironment, experiences a larger delay spread (consistentwith theoretical channel models [5]) and is hence more sen-sitive to compression. Compressing 4 subcarriers degradesSNR by 3 dB on average and up to 3.3dB in certain cases(MU-MIMO in Fig. 4 (b)).

Interestingly, our experiments reveal several other factorsgoverning the effectiveness of frequency-domain compres-sion. First, different spectrum bands (with different carrierfrequencies) reveal different levels of sensitivity to subcarriergrouping. A typical 2.4GHz band exhibits high sensitivity,since it may experience different level of leakage noise (in-terference) from neighbors across its spectrum. Even acrossthe 5GHz bands, which are unused around our testbed, thesensitivity varies. We suspect this to be the result of imper-fect radio hardware, which causes unequal RF/antenna gainsacross the spectrum. Finally, mobility does not affect theimpact of frequency-domain compression, implying it can

3We create the oracle case by collecting CSI and then replay-ing the channel distortion effect (Sec. 5). The transmitter isan oracle which knows the CSI without polling and feedback.

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be decoupled from time-domain compression. MU-MIMO ismore sensitive to subcarrier grouping than SU-MIMO, forthe same reason as in time-domain compression.Effects of numerical quantization. Fig. 5 plots the

MIMO network capacity as a function of the number ofquantization bits used to represent CSI4. It reveals a sub-linear relation: capacity grows sharply as quantization bitsincreases from 2 to 3, but shows marginal improvement be-yond that. In addition, low SNR links are less sensitive toquantization, as channel noise dominates the quantizationerrors. Again, MU-MIMO is more sensitive to quantizationdue to the additive quantization noise of multiple receivers.

To summarize, although compression can save substantialoverhead, it may come at the cost of capacity loss. Thistradeoff manifests differently depending on the radio envi-ronment and network dynamics. Clearly, an autonomousalgorithm is needed to guide the 3-D compression and hencebalance the overhead reduction and capacity loss, therebyresulting in maximium network throughput.

4. ADAPTIVE FEEDBACKCOMPRESSION

4.1 OverviewAFC is a systematic approach to balancing CSI compres-

sion intensity with SU-/MU-MIMO network capacity, therebyhelping achieve optimized network throughput under variousnetwork (channel) conditions. The core component of AFCis a cross-layer adaptation algorithm that extracts the chan-nel dynamics from 802.11 packet preambles, and approxi-mates a throughput-optimal point by choosing an appro-priate compression configuration over 3 dimensions: time,frequency and numerical values.Cross-layer adaptation. Fig. 6 showcases AFC’s adap-

tation procedure for a SU-MIMO network. CSI feedback isreactive in AFC. By default, the transmitter uses the previ-ous (most recent) CSI feedback for beamforming precoding.

4802.11 defines three algorithms for quantizing CSI values.Without loss of generality, we adopt the direct quantizationapproach [4, Section 20.3.12.2.1] which compresses the realand imaginary components into a few number (4, 5, 6 or 8)of bits.

CSI stale?

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Notify senderto start CSI poll

Send ACKReceive ACK

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Figure 6: Cross-layer adaptation protocol in AFC.

It initiates the CSI polling only if the receiver indicates aneed to do so. The receiver is able to refresh its channelestimation whenever it receives a new packet. It evaluatesthe CSI therein in comparison with its last CSI feedback tothe transmitter, and, upon identifying a trend of severe CSIstaleness, requests the transmitter to initiate a polling fornext beamforming transmission. It conveys this request tothe transmitter by setting the “Protected Frame” bit in theACK for current data packet. The Protected Frame bit isan unused field in legacy 802.11 ACK packets.

For frequency-domain compression, AFC extracts per-sub-carrier CSI from the 802.11 Long-Training-Field (LTF) pream-ble, which precedes the data portion of each packet, and issent by each transmit antenna sequentially without beam-forming. Based on the LTF, AFC designs an estimationalgorithm to quantify the expected compression error andresulting capacity loss when several subcarriers are groupedto share the same CSI. The estimation of compression er-ror induced by numerical quantization follows a similar pro-cedure. With such estimations, AFC can select the com-bination of subcarrier grouping and quantization with thehighest expected throughput, taking into account overhead,capacity loss as well as the time-domain feedback period. Ifthis combination differs from the current grouping, the re-ceiver again dictates the transmitter to reinitiate the pollingfor next beamforming packet. As in 802.11n/ac, informa-tion about the subcarrier group size or quantization bits areembedded in the receivers’ CSI feedback packet.

For a MU-MIMO network, each receiver performs adapta-tion as if it forms a SU-MIMO link with the multi-antennatransmitter. Decoupling of their operations enables decen-tralized AFC and precludes complicated message exchangesbetween clients, which can be costly especially in large net-works. We note, however, that the adaptation of quantiza-tion bits may be coupled among MU-MIMO receivers, andcan lead to unfair power allocation. This problem will beelaborated in Sec. 4.3.2.A unified metric for compression. The above adap-

tation mechanism entails a key question: How does a certainlevel of compression affect throughput? AFC proposes a uni-fied metric, called CNo (compression noise), to evaluate theerror introduced by each dimension of compression. CNois obtained by inspecting the per-subcarrier CSI from the802.11 LTF preamble. With CNo, AFC can instantaneouslyestimate the expected data-rate and weigh it against feed-back overhead, to determine the optimal compression in-tensity. This evades the complexity of an intuitive searchalgorithm that attempts all combinations of compression in-tensities and leads to a huge search space, especially along

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the time dimension. In addition, CNo can be estimated sep-arately for time, frequency and numerical values. Such isola-tion is important as it guarantees the total compression noiseintroduced by all dimensions is simply the sum of their CNometrics.

In what follows, we detail AFC’s adaptation mechanismsalong three-dimensions, based on the CNo metric.

4.2 Time-domain adaptation

4.2.1 Is coherence time a good adaptation metric?A channel’s tolerance to time-domain compression strongly

depends on channel stability. A widely used stability met-ric is coherence time, defined as the interval within whichchannel gain remains highly correlated. According to the802.11ac recommendation [6], correlation between two in-stances of channel estimations, separated by T , is definedas:

K(T ) =L

L− T· |

�L−T−1t=0 h(t)h∗(t + T )|�L−1

t=0 |h(t)||h∗(t)|(3)

where L is the total length of the sequence of sampled chan-nel gains. Coherence time is defined as an instance T0.5 whencorrelation drops to 0.5, i.e., T0.5 = K−1(0.5). Occasionally,T0.9 is also used as a coherence time definition.

It is tempting to use coherence time as an update intervalfor CSI — CSI feedback can be initiated periodically, witha period equal to coherence time. All packets can shareone CSI obtained in the beginning of each period. However,through extensive experiments, we found coherence time tobe a poor gauge for predicting the effect of such CSI com-pression. In particular, the experiment in Fig. 7 shows that,even though channel correlation remains above 0.5 within a400ms interval (corresponding to the T0.5 definition for co-herence time), SNR is already severely degraded before that(at around 260ms). On the other hand, the T0.9 definitionof coherence time is too conservative. Channel correlation isabove 0.9 within 100ms, but SNR remains relatively stablewithin 200ms. Thus sending CSI at a peroid of 100ms incursunnecessary overhead.

In addition, we found that this tradeoff manifests differ-ently for different channel profiles (static, human movingaround, or node mobility). Hence, no single definition ofcoherence time can be used as the period for time-domaincompression.

An additional limitation of the coherence time metric isthat the statistical correlation (3) is relevant only with alarge number of channel gain samples, each correspondingto one packet. To adapt compression intensity, however, aresponsive metric is needed that can be obtained from oneor two packets. The CNo metric is designed to satisfy thisrequirement.

4.2.2 CNo metric for the time domainCompression noise. In AFC, a receiver uses a Com-

pression Noise (CNo) metric to overcome the limitations ofconventional channel stability metric. CNo gauges how cur-rent CSI (at time t) differs from the last CSI feedback (attime t0). Suppose there are K subcarriers whose CSI needsfeedback and Hk(t) is the channel gain for subcarrier k attime t. Due to channel variation, Hk(t) can be consideredas a noisy version of Hk(t0):

Hk(t) = Hk(t0) + Nk(t) (4)

We model the noise Nk, (k ∈ K) as complex Gaussianrandom variables with a similar level of variance (i.e., noisepower). This is reasonable as the staleness of CSI appliesequally to all subcarriers. Consequently, we can model thetime-domain compression-induced noise power as:

NT (t) =K�

k=1

����Hk(t)−Hk(t0)

��Hk(t)−Hk(t0)

�∗���

This is exactly the CNo metric we use in time-domain.The receiver stores Hk(t0), and directly obtains Hk(t), theper-subcarrier channel gain, from the 802.11 LTF preamblefor each packet. Therefore, NT (t) becomes an instantaneousgauge for time-domain compression error. Taking into ac-count the signal power Pr(t) and channel noise power Nr(t),the expected SNR after compression becomes:

SNR(t) =Pr(t)

Nr(t) +NT (t)(5)

An AFC receiver compares SNR(t) with SNR(t0). If forany channel between a transmit antenna and a receive an-tenna, the difference is sufficient to cause data rate to dropfrom the current level to a lower level, then the receiver willrequest for CSI polling. Note, however, that channel fad-ing may cause unpredictable SNR decrease/increase, whichmust be isolated in order to evaluate the true effect of time-domain compression.Isolating fading effects. To solve this problem, the re-

ceiver also stores the nominal expected SNR (without com-pression noise) at t0: SNR

�(t0) = Pr(t0)/Nr(t0). It com-pares SNR�(t0) with SNR�(t). If the difference exceeds theSNR threshold for boosting data rate to a higher level (thresh-old SNRth

h ), or degrading it to a lower level (threshold SNRthl ),

then the receiver will also request for a CSI polling. Thishelps the transmitter to select the bit-rate that fits the chan-nel condition5. The SNR threshold for each data rate canbe readily obtained from WiFi chip specifications (e.g., [7]).

Note that a link may become idle for a long time. Withoutdata transmission, the transmitter cannot receive any ACKor CSI update indication from the receiver, and is unawareof CSI staleness. AFC overcomes this problem by setting amaximum update interval Tm, which equals the average in-terval of the past 5 CSI update indication from the receiver.If the link becomes idle for more than Tm, the transmitterwill initiate CSI polling without a request from the receiver.Signal and noise power. So, how does AFC estimate

the signal power Pr(t) and noise power Nr(t)? We remarkthat such estimation should be isolated from the beamformeddata portion of a packet, which mixes the channel gains frommultiple transmit antennas to the receive antenna. Towardsthis end, we again leverage the LTF preamble which is sentby each transmit antenna sequentially. Fig. 8 illustrates the

5AFC’s adaptation algorithm does not depend on the bit-rate adaptation mechanism.

64 samplesduplicate

32 samplesduplicate

cyclicprefix

Figure 8: Time-domain structure of the LTF pream-ble in an 802.11 packet.

structure of an LTF preamble, which comprises two dupli-cated sequences (each containing 64 samples) and an OFDMcyclic prefix (32 samples). At the receiver side, it runs FFTover each sequence to estimate the frequency-domain chan-nel distortion:

Y 1k = HkXk + N1

k ; Y 2k = HkXk + N2

k

Xk is a known symbol carried by subcarrier k. AlthoughN1

k and N2k are instances of two random Gaussian variables,

they can be considered to have the same variance, whichequals the noise power per-subcarrier. Thus the channelnoise power over an entire bandwidth can be estimated as:

Nr(t) =

K�

k=1

|(Y 2k − Y 1

k ) · (Y 2k − Y 1

k )∗| (6)

Subtracting noise power from total received power, we ob-tain:

Pr(t) =

K�

k=1

|Y 1k |2 −Nr(t) (7)

Combating random phase offset. Ideally, if channel isstable, the receiver should experience a similar Hk for eachpacket. Due to the CSMA-based MAC layer, however, eachtransmitted packet has a random starting time and whenmodulated, will result in a random initial phase offset rela-tive to the receiver. This causes a large NT (t) even thoughthe CSI does not change. We observe that transmit anten-nas on a MIMO radio share the same clock, and thus we usethe phase of the differential channel HA

k /HBk between trans-

mit antenna A and B, instead of that of Hk directly whencomputing NT (t), which removes the random phase offset.

4.3 Adaptive frequency-domain compressionand numerical quantization

4.3.1 Is coherence bandwidth a good adaptation met-ric?

Coherence bandwidth is a classical metric for evaluatingchannel stability over frequency. Specific to 802.11 OFDMsystems, it is defined as the range within which subcarri-ers’ channel gain correlation is larger than 0.5 (B0.5) or 0.9(B0.9). The correlation can be obtained in the same way astime correlation as in (3), except the separation is in fre-quency (number of subcarriers).

As channel gains of the subcarriers within B0.5 or B0.9 arehighly correlated, one may wonder if they can be compressedand represented by a single subcarrier’s CSI. The testbed ex-periments in Fig. 9 invalidate this perception. While B0.9 istoo conservative, B0.5 is over-optimistic, incorporating moresubcarriers than should be compressed, thus degrading ca-pacity. Consistent with the experiments in Fig. 4, we foundsuch effects to differ among different carrier frequencies andlocations. In addition, correlation does not always decreasemonotonically with subcarrier separation. Clearly, no sin-gle, static definition of coherence bandwidth can be used asa threshold for frequency-domain compression.

0

4

8

12

16

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

SIN

R(d

B)

Cha

nnel

corr

elat

ion

Subcarrier index

correlation

SINR

Figure 9: Channel correlation over frequency (in alab environment), and SU-MIMO link capacity whenK� subcarriers share the same CSI. PHY param-eters are configured following 802.11 specification:20MHz bandwidth, 52 data subcarriers (each occu-pying 312.5KHz).

4.3.2 CNo metric for subcarrier grouping and nu-merical quantization

We generalize the time-domain CNo metric to predict thelink throughput for a certain level of frequency-domain com-pression and numerical quantization. Suppose Hk(f0, q0) isthe true CSI for subcarrier k without compression, which isobtained from the receiver’s LTF preamble. Hk(f, q) is thecompressed CSI for subcarrier k with subcarrier group sizef and q-bit quantization. All subcarriers inside each groupshare the CSI of the group’s first subcarrier, following the802.11 specification. Then, given a fixed quantization levelq, the frequency domain CNo metric is:

NF (f) =K�

k=1

���Hk(f, q)−Hk(f0, q)��Hk(f, q)−Hk(f0, q)

�∗��

Similarly, given a subcarrier group size f , the quantizationnoise with q-bit quantization is:

NQ(q) =K�

k=1

|(Hk(f, q)−Hk(f, q0))(Hk(f, q)−Hk(f, q0))∗|

Then, the receiver estimates the effective SNR with com-pression intensity f as SNR�(f, q) = Pr

Nr+NF (f)+NQ(q). As

Pr and Nr are obtained from packet preambles, they can-not reflect the power increase due to beamforming or noiseincrease due to multi-user cross-talk interference. Neverthe-less, the receiver can estimate the true SNR based on thedecoded SNR of the current packet, accounting for the SNRloss due to compression, i.e.,

SNRdB(f, q) = decodedSNRdB + SNR�dB(f, q) − 10 log10

Pr

Nr

This can be mapped to data rate typically provided byWiFi vendors [7]. Then, we can estimate the increase ofdata packet transmission time, compared with the currentcompression intensity, say (f1, q1), as:

ΔTd(f, q) = D/Rate(SNR(f, q)) −D/Rate(SNR(f1, q1))

where D is the average data packet size (estimated by aver-aging over past 10 packets in AFC).

Owing to compression, the decrease of time in transmit-ting CSI, amortized over each packet, is:

ΔTo(f, q) = Kq1Mt(f1R0Tp)−1 −KqMt(fR0Tp)

−1

where Mt is the number of transmit antennas, and R0 thedata rate of feedback packet (default to 6Mbps in 802.11).Tp is the number of recent packets that shared one CSI overtime, which reflects the current time-domain compressionintensity.

AFC compares ΔTo(f, q) with ΔTd(f, q). A positive dif-ference implies benefit for changing the compression inten-sity. This comparison is made for each possible combina-tion of subcarrier group size and quantization level (in totalthere are only 12 such combinations in 802.11 as introducedin Sec. 2), and the receiver will select the combination withlargest ΔTo(f, q)−ΔTd(f, q). If it is positive and differs fromthe current one, the receiver switches to this new compres-sion level and notifies the transmitter. Again, the above es-timation is performed for each transmit antenna separately.CSI feedback will be triggered whenever one antenna passesthe test.Isolating different users’ CSI quantization. A unique

problem in MU-MIMO is that different users’ CSI quantiza-tion may affect each other’s performance. When users choosedifferent quantization levels, their CSI will be scaled dispro-portionally. Suppose user A and B have a similar level ofchannel gain. If user A adopts 8-bit quantization whereasuser B adopts 4-bit, then A’s CSI feedback will have 24 = 16times as high magnitude as B’s, causing the transmitter tothink A has much better channel quality. Since zero-forcingprecoding implicitly projects the same received power to-wards both receivers (Sec. 2), the transmitter will allocateonly 1√

16= 1

4as high power to user A as the case without

quantization, resulting in unfair capacity loss for A.In AFC, the transmitter solves this problem by normaliz-

ing the real and imaginary components with the maximumpossible value (2q−1−1 for q-bit quantization), for each userrespectively. This prevents the unfair CSI scaling and thusisolates the quantization choices of different users. Note thatAFC’s adaptation algorithm is immune to such an effect, asit only leverages the non-beamformed LTF preamble.

4.4 3-D joint adaptationAlgorithm 1 summaries AFC’s adaptation over all three

dimensions. Note that the CNo metric serves as a unifiedfunction for estimating compression noise for each dimen-sion. It naturally isolates the effects of each dimension, andreduces the search space for throughput-optimal compres-sion. It is also decentralized with respect to each user, whoonly needs to evaluate CNo between itself and the transmitantennas. In addition, unlike traditional metrics (e.g., coher-ence time), it can be obtained instantaneously after receivingeach packet. The complexity of AFC’s adaptation dependson the number of subcarriers and transmit antennas, all ofwhich are limited in 802.11n/ac. Thus AFC involves a con-stant computation time and is amenable for implementationin real WiFi drivers.

5. IMPLEMENTATION

5.1 Testbed implementationWe have implemented a full-fledged 802.11ac-compatible

MU-MIMO OFDM system on the WARP [8] platform, basedon the WARPLab driver which provides interfaces to theWARP software radio. Fig. 10 illustrates the main compo-nents in our system. The transmitter uses linear precoding(ZFBF, Sec. 2) to pre-cancel inter-user interference. Pre-coded data symbols are divided into Mt streams (equal tothe number of transmit antennas), each subject to OFDMmodulation. The modulated data symbols are prependedwith the 802.11 LTF, and STF (a preamble for synchroniza-

Algorithm 1 3-D cross-layer adaptation in AFC.

1. Transmitter module:2. if “Protected Frame” bit in ACK equals 1 or link idle

time exceeds Tm

3. Initiate CSI polling and request for next packet4. Run SU-/MU-MIMO beamforming with latest CSI5. endif6.7. Receiver module:8. /* Time-domain adaptation */9. Compute CNo metric NT (t) and SNR(t)

10. if SNR(t)−SNR(t0) > SNRthl or SNR�(t)−SNR�(t0) >

SNRthh or SNR�(t0) − SNR�(t) > SNRth

l

11. Request CSI update; update Tp

12. endif13. /* Adaptive subcarrier grouping and CSI quantization*/14. Compute CNo metric NF (f) and NQ(q)15. Compute expected TX time increase ΔTd(f, q) and over-

head time decrease ΔTo(f, q)16. Search for (f∗, q∗) = arg maxf,q ΔTo(f, q) − ΔTd(f, q)17. if ΔTo(f

∗, q∗) − ΔTd(f∗, q∗) > 0

18. Switch to new subcarrier group size f∗ and quantiza-tion level q∗

19. Request CSI update; continue to next transmission.20. endif

tion). Note the SU-MIMO is a special case of MU-MIMOimplementation, as introduced in Sec. 2.

The receiver uses an auto-correlation algorithm to detectthe STF and identify exact starting time of each packet.It then leverages the LTF to estimate the channel matrixbetween itself and each transmit antenna. This channel ma-trix (CSI) will be compressed by the receiver using AFC andthen fed back to the transmitter when needed. As inter-userinterference is pre-cancelled, the receiver is able to decodethe data portion of the packet using a standard OFDM de-modulator.

The 3-D cross-layer adaptation algorithm is implementedat the receiver side following the description in Sec. 4. Itextensively leverages the LTF to compute CNo along threedimensions, and decides if an adjustment of compression in-tensity is needed and in which dimensions. As the round-triptime between the PC (the central MAC/PHY processor run-ning AFC and MU-MIMO OFDM modulation/demodulation)is several orders of magnitude longer than real WiFi hard-ware, we do not directly implement real-time control mes-sages such as ACK, NDP and CSI feedback. Instead, as allWARP nodes in our testbed share the same central proces-sor, control messages are directly realized as function calls.The exact transmission duration and inter-packet spacing(defined in 802.11) are implemented using a virtual timer.In addition, all MIMO data packets are sent through realchannels by the WARP radios, and polling packets are ini-tiated if AFC dictates a CSI refresh.

5.2 Trace-driven emulationThrough benchmark tests, we found it takes 127ms for a

pair of WARP radios to finish an entire SU-MIMO transmis-sion involving CSI polling, precoding, data transmission anddata decoding. The latency is mainly caused by the hard-ware interface between WARP and its PC host. Such hard-ware latency is incompatible with real WiFi radios, and can-

Bit-to-symbol

Receiverradio(s)

mappingZFBF

precodingOFDM

ModulationPrepend

STF, LTF preambles

TX/RX syncbased on STF

Channel est.based on LTF

AFCadaptation

OFDMDemodulation

Symbol-to-bitDemapping

Compressed CSI

Transmitterradio

Figure 10: Implementation of an 802.11-compatibleMU-/SU-MIMO OFDM system.

not faithfully reproduce AFC’s behavior in dynamic/mobilescenarios. To overcome this limitation, we adopt a trace-driven emulation approach, which is inspired by [9] but har-nesses WARP’s flexibility to collect raw channel traces.

We fill a WARP transmitter’s transmit buffer with an802.11 MIMO preamble (containing STF and LTF sequences),and configure it to repeatedly send the preamble over the air.The receivers log the raw digital samples to a file, and per-forms packet detection and channel estimation offline to ob-tain a sequence of channel traces. With this setting, we areable to obtain fine-grained sampling of the MIMO channelevery 8.7ms, which is sufficient for evaluating mobile chan-nels with walking speed [10].

To evaluate the feedback compression algorithms, we re-place the WARPLab interface to the WARP radios with aninterface to an emulated channel, whose time variation fol-lows the collected traces. The MU-/SU-MIMO OFDM andAFC module that we implemented can run directly over thisemulated channel. When a packet’s arriving time does notexactly match any instances of the channel trace, the closestinstance is used to represent its channel distortion. We willshow in Sec. 6 that the trace-driven emulator can faithfullyreproduce the results from realtime experiments.

6. EVALUATIONIn this section, we first evaluation AFC’s adaptation mod-

ules through micro-benchmark experiments. Then we inte-grate all the modules and validate the system-level perfor-mance under various channel conditions.

6.1 Micro-benchmark evaluation

6.1.1 Validation of trace-driven emulation.Part of our experiments are conducted under mobile/dynamic

channel profiles, and rely on trace-driven emulation. Thus,we first validate the accuracy of such trace-driven emulation,using real-time runs as a benchmark.

T1 Tc Freq 1 Freq 52 Qbits 2 Qbits 8

Trace 20.206 20.041 20.262 16.131 18.662 20.315

Real 20.142 20.074 19.825 15.148 17.599 20.066

Error 0.32% 0.16% 2.20% 6.49% 6.04% 1.24%

Table 1: Trace-driven emulation can faithfully repro-duce the SINR results from realtime experiments.T1 and Tc denote per-packet and per-coherence-timeCSI feedback, respectively. Freq denotes subcarriergroup size 1 and 52. Qbits denote quantization bits.

Following the steps in Sec. 5.2, we first run SU-MIMOtransmission between a 2-antenna WARP transmitter andsingle antenna receiver, while logging the per-packet channelmatrices between them. Then we replay the transmissions

Static0

10

20

30

40

Throu

ghpu

t(Mbp

s) Per pktPer TcAFC

MobileAmbientmobility

Figure 11: Time-domain adaptation: SU-MIMO.

in the emulator based on the traces. Table 1 compares theresults from real-time runs and trace-driven emulation. Wecreate 6 traces, each lasting 1 minute and representing thecase with or without compression (or with minimum com-pression) along three dimensions. For the majority of cases,relative error of emulation is well below 3%. When SINR islow, the relative error tends to be magnified (to around 6%).However, the absolute error remains below 1.1dB. Therefore,the trace-driven emulator can reproduce real-time experi-ments with a sufficient level of accuracy.

6.1.2 Time-domain adaptationThe effectiveness of AFC’s time-domain compression and

adaptation depends on channel stability. Thus we evaluatethis component under three representative channel profiles:static, ambient mobility (human moving around the nodes)and node mobility (node moving at walking speed). All ex-periments run over the 2.4GHz WiFi channel 14, which isunused by nearby wireless devices. The static case runs di-rectly on the WARP testbed. The other two cases are basedon trace-driven emulation, since WARP’s latency may ex-ceed the time-resolution needed for real-time CSI feedback.

We compare AFC against two alternative CSI feedbackschemes: per-packet feedback and Per-Tc feedback. Theformer is the default scheme in 802.11n/ac. In the latterscheme, we first collect channel traces, compute the coher-ence time T0.5, and then use T0.5 as the feedback periodwhen replaying the traces.SU-MIMO network. In a typical small or medium

sized network, contention overhead is much smaller com-pared with data transmission. Thus, without loss of gener-ality, we first consider a single receiver SU-MIMO network6,where the transmitter has 2 antennas and receiver 1 antenna.Fig. 11 plots the resulting network throughput.

In static case, channel variation is negligible, and thus per-packet CSI feedback incurs huge overhead. AFC only needsto opportunistically feed back CSI without affecting link ca-pacity noticeably. Its mean throughput is 25.4% higher thanthat of per-packet feedback. Per-Tc feedback results in asimilar level of throughput as AFC.

With ambient mobility, per-packet feedback degrades evenwith per-Tc feedback in terms of throughput, as the formermaintains link capacity whereas the latter attempts to re-duce feedback overhead. In contrast, AFC strikes a balancebetween these two objectives, improving average throughputby 17% over the other two schemes.

When receiver is mobile, Per-Tc feedback underestimateschannel variations, leading to even lower throughput thanper-packet feedback. On the other hand, per-packet feed-back incurs more overhead. AFC’s time-domain adapta-

6Even for a single-link WLAN, contention backoff is requiredafter each transmission attempt [4].

0

5

10

15

20

25

Thr

ough

put(

Mbp

s)

0

10

20

30

40

Thr

ough

put(

Mbp

s)

0

5

10

15

20

25

30

35

Thr

ough

put(

Mbp

s)

Rx1

Rx1 Rx2(b) Ambient mobility

Rx1 Rx2(c) Mobile

(a) StaticRx2

Per-packetPer-Tc

AFC

Figure 12: Time-domain adaptation: MU-MIMO.

tion mechanism can effectively estimate the instances whenCSI feedback is needed. Its throughput is 18.2% and 38.5%higher than per-Tc and per-packet, respectively.MU-MIMO network. We further evaluate AFC in a

MU-MIMO network with a 2-antenna AP and 2 single-antennareceivers. Fig. 12 plots the receiver’s throughput under dif-ferent channel profiles and feedback schemes. Similar to SU-MIMO, per-Tc achieves a comparable level of throughputwith AFC. However, for per-packet feedback, since the over-head doubles compared with SU-MIMO, the throughput lossis substantial. In particular, AFC can achieve 39.7% higherthroughput over per-packet — a much higher gain comparedwith SU-MIMO case.

Under channel dynamics, MU-MIMO is expected to bemore sensitive to CSI feedback errors. Fig. 12 testifies thisintuition. With ambient mobility, per-Tc induces long feed-back delay and large CSI error, resulting in significant through-put loss. AFC can achieve 61.5% and 123% higher through-put, for receiver 1 and 2, respectively.

AFC’s performance gain is most remarkable in mobile case(Fig. 12(c)). It achieves 69.1% and 269% higher throughputfor the two receivers, compared with per-Tc; and a 13.2%and 71.3% gain compared with per-packet feedback.

In summary, none of the static CSI feedback mechanismsare appropriate for all channel profiles. On the other hand,by triggering CSI updates only when needed, AFC can achieveup to multi-folds of throughput gain over static schemes.

6.1.3 Frequency-domain adaptationWe proceed to evaluate whether AFC can effectively adapt

to an appropriate level of compression for the frequency do-main, i.e., the subcarrier group size. Our investigation ofchannel traces in a lab environment reveals that even forthe same spectrum band, coherence bandwidth may change,e.g., due to minor change of location or antenna orientation.Thus we create frequency domain dynamics by running mul-tiple experiments with minor adjustment of transmitter’s lo-cations. We isolate the effect of the other two adaptationdimensions by assuming default configuration in 802.11n/ac(per-packet CSI feedback and 8-bit quantization).

Fig. 13 plots the throughput of AFC compared with twoalternative schemes with fixed subcarrier group size 1 and52, respectively. For SU-MIMO, AFC’s throughput is 19.8%higher than Size1, implying that a fixed subcarrier group sizeof 1 underutilizes the channel correlation between subcarri-

0

5

10

15

20

25

30

Rx1 Rx2Throughput(Mbps)

Size1Size52AFC

01020304050607080

Throughput(Mbps)

Size1Size52AFC

(b)MU-MIMO(a)SU-MIMO

Figure 13: Frequency-domain adaptation for (a) SU-MIMO and (b) MU-MIMO. Error bars denote max-imum and minimum among 5 consecutive experi-ments, unless noted otherwise.

0

10

20

30

40

50

60

High SINR Low SINRThr

ough

put(

Mbp

s)

3bits32bits

AFC

Figure 14: Adaptive quantization: SU-MIMO.

ers, which could have been harnessed to compress the CSI.In our lab environment, Size52 achieves a similar level ofthroughput with AFC.

However, a MU-MIMO network is more sensitive to CSIcompression errors, since severe inter-receiver interferencecan occur when CSI is noisy. In particular, Fig. 13(b) showsthat for one receiver (Rx2), AFC’s throughput can be 5.2×that of Size52, and 1.36× for Rx1. In this case, a fixedsubcarrier group size of 1 outperforms Size52.

Therefore, from frequency domain perspective, static sub-carrier grouping can be either very conservative or aggres-sive. AFC can effectively strike a balance, selecting the bestcompression level to optimize the network throughput.

6.1.4 Adaptive quantizationTo evaluate AFC’s adaptive quantization mechanism, we

compare it against static quantization algorithms with ag-gressive (3-bit) and conservative (32-bit, essentially no com-pression) quantization algorithms. Accordingly, we allowAFC to choose from these two quantization levels along withthe default options in 802.11n/ac (4, 5 6 and 8 bits). Fig. 14shows the experimental results for a SU-MIMO network. Itcan be seen that for both high and low SINR7 cases, the sav-ing of feedback overhead dominates the capacity loss, evenwith a very aggressive 3-bit quantization. However, thereis still sufficient space for AFC to optimize the choice ofquantization levels. An examination of experimental resultsreveals that AFC tends to choose the quantization level of 6bits, which is close to 3-bit but avoids the capacity loss dueto excessive compression.

In addition, as we noted above, in high SINR case, closed-loop MIMO transmission is more sensitive to compression,hence aggressive compression tends to suffer more from ca-pacity loss. Indeed, Fig. 14 shows that AFC improves through-put by 15.1% over 3-bit compression in high-SNR region, and

7We adjust link distance to ensure the receivers’ SINR levelsatisfy the requirement of the minimum level of modulationin 802.11, which is 9dB for BPSK modulation [7].

0

5

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15

20

25

30

Rx1 Rx2Thr

ough

put(

Mbp

s)3bits

32bitsAFC

0

5

10

15

20

25

30

Rx1 Rx2Thr

ough

put(

Mbp

s)

3bits32bits

AFC

High SINR Low SINR

Figure 15: Adaptive quantization: MU-MIMO.

4.5% in low-SINR region. Owing to its intelligent overheadreduction, performance gain over fixed 32-bit reduction ismore prominent (52.2% and 28.3% for high and low-SINRcase, respectively).

Experimental results from a MU-MIMO network (Fig. 15)show a similar trend. In particular, for low-SINR case, chan-nel noise dominates CSI error, and thus 3-bit quantizationachieves comparable throughput as AFC. But in high SINRregion, AFC achieves 18.5% higher throughput. The gain iseven higher than in SU-MIMO, because aggressive quanti-zation amplifies the effects of inter-receiver interference.

6.2 Field test of AFCIn this section, we integrate all three components of AFC

and evaluate its network performance on our WARP radiotestbed.

6.2.1 AFC in actionWe first check whether AFC can react to changes in a

real wireless link with unpredictable dynamics. To this end,we evaluate a 2-receiver MU-MIMO network, and vary thetransmitter’s location and link distance, such that a varietyof channel profiles can be generated for both receivers. Wecollect the per-packet channel traces during this process andthen replay them in our emulator.

Fig. 16 plots the throughput variation of AFC over time,in contrast with the legacy configuration in 802.11ac (per-packet feedback, subcarrier group size 1, 8-bit quantization).Throughput is calculated for each inter-packet arrival inter-val. The results show that AFC can react instantaneously tothe change of channel state, and effectively adapt its com-pression levels accordingly. It consistently achieves higherthroughput than 802.11ac under any channel dynamics. Thethroughput gain ranges from 1.4× to 2.2× in general, andvaries depending on the channel profile and users. Occasion-ally, the fixed configuration in 802.11ac may work as well asAFC when it is appropriate for the channel state.

6.2.2 Other factorsAs mentioned in Sec. 3, besides time, frequency and quan-

tization, there are a number of other factors that determinethe CSI overhead, which may in turn affect AFC’s choiceof compression. Below we use testbed experiments to verifysuch effects.

We first evaluate packet length, which affects relative over-head of CSI feedback and hence throughput. To isolate theeffects of bit-rate change, we vary packet duration insteadof size. Experiments in a SU-MIMO network (Fig. 17) showthat for shorter packet durations, AFC achieves higher gain(e.g., 2.14 × for 100 µs). In such cases, balance betweenoverhead and capacity becomes more important, which can-not be handled by the legacy scheme.

010203040506070

0 2 4 6 8 10 12Throughput(Mbps)

Time(s)

LegacyAFC

010203040506070

0 2 4 6 8 10 12Throughput(Mbps)

Time(s)

LegacyAFC

(a) (b)

static staticmove1

move2newCHL-SNR

H-SNR move1move2

newCH L-SNR

H-SNR

Figure 16: Field test of AFC in a MU-MIMO net-work. “newCH” indicates a change of spectrumband. “L-SNR” and “H-SNR” denote low-SNR andhigh-SNR scenarios created by adjusting transmitpower.

0

2

4

6

0.1 0.5 1 1.5 2

Thr

ough

put (

Mbp

s)

Packet Length(ms)

AFCLegacy

Figure 17: Effects ofpacket length on MIMOnetwork throughput.

0

10

20

30

2 4

Thr

ough

put(

Mbp

s)

Number of antennas

LegacyAFCPer-Tc

Figure 18: SU-MIMOnetwork throughput with2 and 4 transmit anten-nas.

Fig. 18 further shows how this balance manifests underdifferent number of antennas. The experiment is done ina lab environment with receiver moving at walking speed.AFC’s throughput gain is around 47% higher than legacyfor both 2 and 4 antenna cases. Under 2 antenna case, Per-Tc feedback underestimates channel variation, resulting in72% lower throughput compared with AFC. With 4 anten-nas, feedback overhead plays a greater role, and thus Per-Tc feedback enjoys throughput improvement due to its ag-gressive time-domain compression, but its throughput is still45% lower than AFC.

7. RELATEDWORKCSI feedback has been a critical issue in broadband cellu-

lar networks such as LTE [11]. For CSI quantization, earlygenerations of LTE adopt codebook based approach, whichprescribes a set of precoding vectors, such that the receiveronly needs to feed back an index of the best precoding vec-tor [12]. Latest generation of LTE (Release-10) proposesquantized CSI feedback, which is shown (via simulation)to achieve comparable performance with the same numberof CSI bits [13]. But even for LTE, the adaptive selectionof quantization levels or feedback delay remains an openproblem. There exists a vast literature of work on limitedfeedback MIMO communications (see [11] for a comprehen-sive survey), which focuses on the design of effective CSIquantization mechanisms to restrict the feedback overhead.In [14], Huang et al. analyzed the effect of time-domaincompression, based on a theoretical model of channel cor-relation over time. Pohl et al. [15] simulated the SNR andBER of MIMO communication systems under Rayleigh fad-ing model. However, a systematic approach is still lackingthat adapts various quantization and compression mecha-nisms in realistic LTE channel conditions.

Relatively less work has been devoted to the CSI feed-back mechanism in wireless LANs. In [16], Sun et al. sim-ulated the 802.11n SU-MIMO performance in time-varying

and frequency-selective channel conditions. Crepaldi et al.[17] proposed a sampling algorithm that can efficiently esti-mate the channel matrix of a MIMO link. To our knowledge,there does not exist any experimental work that addressesthe tradeoff between CSI compression and capacity loss forWLANs.

Recently, there has been a number of software-radio basedprototypes of multi-user MIMO [18] or distributed MIMOnetworks [19], which verified the practicality of theoreti-cal MIMO communication algorithms, but ignored the CSIfeedback overhead. In [20], Shepard et al. built a massivemulti-user MIMO system, based on implicit CSI feedback— an alternative feedback mechanism defined in 802.11n,which leverages channel reciprocity of uplink/downlink toreduce CSI overhead. Implicit beamforming involves sophis-ticated calibration that is not amenable for handheld WiFidevices [21, 22]. In addition, it cannot be used in manypractical wireless transceivers that have more receive an-tennas than transmit antennas [21,23]. The new generationof 802.11ac has discarded implicit beamforming, leaving ex-plicit CSI as the only option for CSI feedback.

8. CONCLUSIONIn this paper, we have conducted a comprehensive mea-

surement study that characterizes the tradeoff between feed-back compression and capacity loss in SU-/MU-MIMO wire-less networks. We then address this tradeoff by proposingAFC, a simple mechanism that adapts compression inten-sity to optimize network throughput. AFC’s adaptation issteered by CNo, a unified metric that can be extracted from802.11 packets’ preambles, and used to estimate the noiseeffects due to compression in time, frequency and numericalvalues. We implemented AFC on the WARP software radiotestbed and validated its performance under various channeldynamics and network scenarios. We believe AFC can be ageneral mechanism for other non-802.11 MIMO networks,such as those based on interference alignment [24]. Suchextension is left for our future exploration.

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