Adaptive Rate Control with Quality of Service

Guarantees in Wireless Broadband Networks

Shirish Nagaraj

Technology & Innovation - Research

Nokia Solutions and Networks, Arlington Heights, IL 60004

shirish.nagaraj@nsn.com

Abstract— In this paper, we develop a framework for adaptivelearning algorithms for rate prediction with Quality of Service(QoS) guarantees in broadband wireless communications sys-tems such as LTE and LTE-Advanced. These approaches aremotivated by real-world requirements for online rate adaptationfor scheduling packet data transmissions and ensuring a goodtrade-off between maximizing rate and delay constraints. Wepose the problem of temporal learning of the achievable rateas a function of a vector of noisy observations available fromthe receiver in terms of channel quality information (CQI). Weshow that a requirement to maintain a certain target frame errorrate (FER) for a packet transmission translates to a problemof rate estimation using the notion of quantile regression withan asymmetric `1 norm error criterion. The algorithm uses theexisting feedback from the receiver in the form of Ack/Nack bitsof packet decoding, which provide a natural measure of errorgradient in the proposed formulation. This framework of rateprediction is shown to have many applications within the wirelessnetworks, including rate prediction for MIMO rank switching,adapting to noisy CQI data for frequency selective scheduling(FSS) or inter-cell interference co-ordination (ICIC). Simulationresults are shown for a couple of such applications that establishthe efficacy of the proposed framework and algorithms.

I. INTRODUCTION

Fourth generation broadband wireless system such as LTE

have been designed to provide high network spectral effi-

ciency and a rich multimedia data user experience [1]. These

wireless broadband networks are characterized by complex

interactions between multiple distributed cells with users in

the different channel conditions within the network. A key

tenet of providing fast data access over fading channels is

the use of opportunistic scheduling using channel quality

information (CQI), which is a quantized periodic feedback,

in order to keep feedback overhead under control. This CQI

information is expected to capture variations in the users’

achievable spectral efficiency, given fast fading channels and

fluctuating interference levels. However, due to the time-lag

of the feedback as well as estimation errors at the receiver,

the CQI information is not highly reliable. The problem of

adaptive learning of the achievable spectral efficiency for a

user, given a sequence of a vector of CQI measurements, is

addressed in this paper.

Adaptive rate prediction to maximize rate with guarantees

on a desired quality of service (as per the application needs) is

critical to ensure good quality of experience over the wireless

network. The problem we address is a method to provide such

a guaranteed quality of service, measured in terms of a packet

delay metric, or maintaining e.g., a target frame/block error

rate, while achieving high spectral efficiency. LTE provides

various metrics for CQI feedback, including wideband and

narrowband CQI, MIMO codeword CQIs etc, all of which

carry partial information of the achievable rate. An adaptive,

or online approach to estimate the achievable spectral effi-

ciency is thus needed, given these noisy and delayed feedback

measurements.

Rate control has been the subject of a number of studies,

see e.g., [2], [3], [4], [5]. In the current 3G and 4G standards,

varied approaches for rate prediction or prediction have been

in existence, such as in EV-DO [6], or UMTS HSPA [1]).

In EV-DO, rate prediction for the downlink is performed at

the mobile, and a quantized achievable rate is fed back to the

base-station, which is expected to be used when transmitting

to that user. In HSPA, a finer granularity CQI is fed back, also

in terms of a measure of achievable rate, but then the base-

station has the additional task of doing a fine tuning of the

achievable rate based on this feedback.

In the literature, CQI estimation using a recursive IIR filter

with an MMSE cost criterion is presented in [2], where QoS

control is not explicitly addressed. In [7], a neural network

approach with sparsity based basis functions is proposed

for packet loss rate estimation. The approach is that of a

suprervised learning problem and does not address online or

adaptive rate prediction. A rate prediction method for power

minimization is developed in [4], where channel modeling

assumptions are invoked for the purposes of rate prediciton. In

[8], a CQI estimation framework keeping the average HARQ

error rate constant is proposed. This approach uses modeling

assumptions for describing CQI errors, and its performance is

thus heavily dependent on those models, which can lead to

non-robust performance in practice. Reinforcement learning

approaches to the rate prediction problem are proposed in [9],

[10].

In Section II, we motivate the need for adaptive rate predic-

tion in 4G systems. The adaptive or online framework for rate

prediction is proposed in Section III, along with a discussion

of some well-known approaches for rate prediction. In Section

IV, we develop the adaptive filtering solution corresponding to

this framework, referred to as Assymetric Cost Minimization

(ACM). In Section V, we detail a couple applications of this

technique along with simulation results. Finally, conclusions

are given in Section VI.

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II. ADAPTIVE RATE PREDICTION PROBLEM

Consider for example, the downlink link of a cellular broad-

band network. Given that a user is picked by the scheduler

for packet transmission, one has to allocate a “transmission”

spectral efficiency to that user, in terms of the modulation and

coding scheme (MCS). The MCS allocation function, given

CQI feedback information, is referred herein as rate prediction.

Feedback and scheduling delays along with errors in mea-

surement and detection of CQI mean that the MCS can not

be allocated purely on the basis of the last received CQI

value; rather, further refinements are needed to accurately

estimate the achievable rate at the time of transmission. Since a

statistical model of these imperfections and the CQI variations

is not easily derived, it is desirable for the rate prediction

function to be adaptive, where the achievable rate is learned

in an online fashion. In the Hybrid-ARQ (HARQ) protocol,

a feedback of whether a packet transmission is successful or

not is sent to the transmitter in the form of a 1-bit Ack/Nack

indication 1. The choice of the first transmission MCS is

critical in non-adaptive HARQ (which keeps the MCS fixed

across re-transmissions), since the packet delay depends solely

on the initial MCS allocated. Therefore, the rate prediction

function’s main responsibility can be stated as choosing an

initial transmission MCS such that the first transmission error

rate is well controlled, since Quality-of-Service (QoS) has to

be guaranteed by the scheduler for specific types of flows to

meet a certain delay or throughput guarantees.

Broadband 4G systems such as LTE have multiple mech-

anisms for CQI feedback from the user equipment (UE), but

the problem of rate prediction becomes more involved than

previous 3G systems due to the numerous transmission modes

available. Some examples include:

• A UE’s CQI may be quite delayed, which makes this

information stale and the base-station has to estimate

the current spectral efficiency given multiple noisy CQI

reports from the past.

• For a user feeding back Rank-2 MIMO CQI information,

the transmitter may choose use Rank-1 to ensure robust

performance, which requires a translation from MIMO

CQI values to an achievable Rank-1 rate.

• For beamforming or MU-MIMO, a UE feeds back a

transmit diversity CQI [1], and the base-station has to

determine the beamforming rate [5].

• In the case of frequency-selective scheduling (FSS), a

UE may feed back a wideband CQI and a best sub-band

CQI. If the UE is scheduled on a different set of resource

blocks than its best reported sub-band, the base-station

has to extrapolate the rate from limited feedback.

• In heterogeneous networks, with enhanced inter-cell in-

terference co-ordination (eICIC) [1], the base-station has

to adaptively estimate the achievable rate using CQI

measurements taken under varied interference conditions.

1In the case of two-layer MIMO transmissions in LTE, there are two bitsthat are fed back corresponding to the two codewords.

The proposed rate prediction framework that can handle these

use-cases is developed in the next section.

III. RATE ESTIMATION AND CONTROL FRAMEWORK

The CQI is usually defined in terms of spectral efficiency,

measured in bits/symbol, and is represented by the time-series

{xt}t∈T , where T ⊂ I are the integer subframe instances at

which the base-station gets CQI reports. At the transmission

time t, we denote the true channel spectral efficiency by ηt.

The allocated spectral efficiency is denoted by ηt.

We seek to allocate ηt by (causally) predicting the true

spectral efficiency ηt using a function of the past CQI values

(or any appropriate non-linear transformations thereof) xt =[xto , xt1 , xt2, . . . , xtN−1

]T , where tN−1 ≤ tN−2 ≤ . . . ≤t1 ≤ to ≤ t and ti ∈ T , i = 0, 1, . . . , N − 1. Note that

this formulation is very generic and includes all the use-cases

outlined in Section II.

A. Adaptive Filtering Framework for Rate Estimation-Control

We have motivated the need for adaptive (online) estimators,

but for purposes of understanding the properties of such

estimators, it is useful to consider also an offline estimator

that optimizes certain Bayesian cost functions. Below, we

outline an offline estimator, and also propose a scheme for

online estimation (predicton) that uses an adaptive filtering

framework:

• Offline or “batch” estimator: Here we assume that the

joint statistics between the observation of the feedback

information (input to the estimator) and the estimated

quantity (achievable spectral efficiency) is known or

estimated offline. Therefore, we are interested in a general

mapping between the observables (x) and the desired

output η - note that we have dropped the explicit de-

pendency on the time variable t here for simplicity. The

estimator does not have any structured restrictions (like

e.g., linear) in this case. A possible implementation of

such an estimator would be one that collects the statistics

offline in a “batch” mode, builds/trains the model, and

the result is applied as a rate-prediction function using

the real-time CQI feedback.

• Proposed online predictor: Since we cannot assume

knowledge of the distribution of the underlying random

variables (or even learn it offline in many instances), we

propose a linear filter framework. The linear filter model

(prior to MCS quantization) is:

η(xt) = u+ vTxt = w

Txt (1)

xt = [1 xTt ]

T ∈ RN+1

Note that the map may not be linear with respect to the

CQI values themselves, and non-linear transformations of

the CQI can be used as inputs for the filter. The objective

is to adaptively estimate the weight vector w; we denote

this sequence of adaptive filter coefficients by {wt}.

The key idea of the the proposed framework is that the

scheduler should allocate a spectral efficiency at time t

using an estimate of an adaptive filter weight vector at

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time t − 1. We denote this estimated rate as ηt|t−1, and

the final applied MCS as ηt, which are given by:

ηt|t−1 = wTt−1xt

ηt = Q[ηt|t−1] (2)

The final applied MCS is a quantized version of the

predicted rate, and Q = min[max[η, ηmin], ηmax] is a

quantizer that takes an estimate of the spectral efficiency

and maps it into a finite set of available MCSs2.

We refer to this as a rate predictor since the predicted

estimate of the spectral efficiency is immediately used as the

MCS for the next transmission in the next interval, and thus

controls the system throughput and QoS. With this approach,

the error between the achieved and the allocated spectral

efficiency turns out to be the prediction error that is needed for

updating adaptive filters, ignoring the quantization operation.

This point will be key in the susequent developments where

we show that certain forms of the prediction error are available

at the transmitter in the form of Ack/Nack feedback. The

proposed framework is depicted in Figure 1.

UE Measurements

Feedback { xt }

Predicted Spectral Efficiency

nt| t-1=wt-1Txt

Quantizer

Allocated Spectral

Efficiency

nt

UE Packet

Decoding Feedback

WirelessChannel True

Spectral Efficiency nt

^

^

Fig. 1. Rate prediction framework

Note that the prediction error of this filter is given by:

δt = ηt − wTt−1xt = ηt − ηt|t−1 ≈ ηt − ηt (3)

where the last approximation to the prediction error arises from

the near-linearity of the quantization function. The goal then is

to develop an adaptive filtering algorithm that can recursively

adapt the weight vector wt, using feedback of some form

of prediction error from the receiver. Before developing the

proposed algorithm, we outline a few traditional approaches

for rate prediction.

B. Traditional Estimation Approaches

The traditional approaches outlined below encompass both

online and offline estimators, and we discuss some of their

drawbacks at controlling the FER or QoS.

2The 4G standards define a very fine granularity and high range of availableMCSs, thus this quantization function can be effectively ignored in thesubsequent algorithms.

1) Offline MMSE-based and Online Recursive Least

Squares (RLS)-based Estimators: The optimal non-linear

MMSE estimator for the true spectral efficiency is the con-

ditional mean estimator, which results in an offline estimator

given by:

ηt = Q[

E[ηt|xto , xt1 , . . . xtN−1]]

Let ηt have a mean µη and variance σ2η , and the observables

vector [xto , . . . , xtN−1]T have mean µx and covariance Rxx,

with a cross-correlation vector defined as rη,x = E[(ηt −µη)(xti −µxi

)]. If we restrict to linear estimators, the solution

is the well-known linear MMSE estimator:

wTmmse =

[

(µη − rTηxR

−1xx

µx) rTηxR

−1xx

]

ηt,mmse = Q[

wTmmsext

]

(4)

There are the following issues with this type of estimator:

• The underlying cross-correlation statistics between the

observed CQIs and the true spectral efficiency is unknown

in practice. They cannot be estimated online either,

because we do not have training data in the form of

true spectral efficiency measurements at the transmission

times.

• The MMSE solution has no notion of explicitly controling

the frame error rate, and thus, cannot directly control the

QoS.

We can consider an adaptive filter approach using RLS, but

such an estimator would need an estimate of the prediction

error δt, as defined in (3), which is currently not supported

by any wireless standard. Further, the algorithm would con-

verge to the linear MMSE solution and not control the FER

explicitly.2) CQI Bias Adaptation: The CQI Bias Adaptation (CBA)

algorithm works on the principle of adjusting a bias term to the

last measurement to ensure a certain first transmission packet

error rate. This follows the approach taken in outer-loop power

control (OLPC) in CDMA systems [11], wherein an offset to

the SINR target is adjusted to ensure the required FER is

maintained. In this application, an offset to the last reported

CQI is adapted based on the Ack/Nack’s received from the

UE, as follows:

ηt = xto +∆t (5)

∆t =

{

∆t−1 + δU if Ack received at t− 1∆t−1 − δD if Nack received at t− 1

δU =Pe,T

(1− Pe,T )δD, (6)

where Pe,T is a target error frame probability for the first

transmission. Once δD is chosen, the step size δU can be

fixed as a function of δD per Equation (6). A key limitation

of this approach is that the framework does not handle

estimation using a vector of observations. Another obvious

drawback is that the formulation does not degrade smoothly

as the correlation between the true and the observed spectral

efficiencies goes to zero, since it continues to use the previous

CQI report.

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IV. ASYMMETRIC COST MINIMZATION (ACM)

ALGORITHM

The previous approaches suffer from either the issue of

not explicitly controlling the QoS/FER, or not being able

to consider a vector of input observations. In the proposed

approach, we address both these drawbacks, and develop an

adaptive filtering algorithm that controls QoS/FER directly.

The offline version of this solution is also developed, mainly

to develop certain properties of this estimator.

The adaptive filtering problem is formulated as a design

of the rate predictor function ηt ≡ ηt(xt) in order to meet

a certain target probabilty of error for the first transmission,

Pe,T . Note that this target error probability controls the latency

of the packet through the HARQ process, and thus can be

chosen based on the type of multimedia flow, depending

on whether it is latency sensitive or not. The HARQ delay

budget for a specific flow is given by higher layers and

depends on the end-to-end network delays. In order to further

develop this framework, we need a model of the probability

of error of a packet’s first transmission. With Turbo codes

used in 4G systems, the frame error rate as a function of the

SINR has a sharp transition - below a certain SINR threshold

that depends on the allocated spectral efficiency (product of

modulation order and code rate), the packet is almost surely in

error; above the threshold, the packet decodes correctly. This

motivates the following definition of frame error rate for the

first transmission:

Definition A first packet transmission at time t is said to be

successful if ηt(xt) ≤ ηt. Average probability of error for the

first transmission is defined as:

Pe = Pr[ηt < ηt(xt)] (7)

The following observation therefore is key to the development

of the subsequent algorithms:

UE Ack ⇔ ηt − ηt ≥ 0≈⇒ δt = ηt − ηt|t−1 ≥ 0

UE Nack ⇔ ηt − ηt < 0≈⇒ δt = ηt − ηt|t−1 < 0

where again the approximation comes from ignoring the

quantization of the MCS.

This observation motivates us to consider an adaptive filter-

ing approach with a cost function that is based on the `1 norm

of the error. This is because the gradient of the cost function,

used in the filter updates, would be the sign of the prediction

error, which is the information available to the base-station, in

the form of the Ack/Nack bit. For example, we can define a

stochastic gradient algorithm that minimizes the least absolute

error (LAE):

wlae,t = wlae,t−1 + ν sign(ηt − wTlae,t−1xt) xt (8)

≈

{

wlae,t−1 + ν xt if ηt − ηt ≥ 0 ⇒ Ack at t

wlae,t−1 − ν xt if ηt − ηt < 0 ⇒ Nack at t

for some small step-size ν > 0. From the above, we see

that the LAE minimizing algorithm uses only the Ack/Nack

sequence for adaptive estimation of the prediction filter, which

can be interpreted as the Ack/Nack sequence produces a highly

quantized sounding of the channel state information.

The adaptive LAE algorithm is a analogous to the Bayesian

minimum absolute error (MAE) estimator [12]; therefore, the

above algorithm still converges to solution that results in a

probability of error of 0.5. For an arbitrary estimator (not

necessarily restricted to be linear), we have:

η(x) = argmin Eη,x[|η − η(x)|] = {y|Pr[η < y|x] = 0.5}

In practice, we require a probability of error not equal to

0.5. Intuitively then, any cost function that places symmetric

penalties to positive and negative errors will not suffice. For

achieving any arbitrary target error probability, we consider an

assymetric cost function, similar to the quantile estimator in

machine learning literature [13], [14]. Consider a modification

of the `1 norm cost criterion, based on the idea of penalizing

the excursions from zero error differently, depending on the

sign of the error. Define the following error cost:

φ(e) =

{

νU |e| if e ≥ 0νD |e| if e < 0

(9)

The Bayesian risk minimizing estimator based on the above

cost function:

η(x) = argmin Eη,x[φ(η−η(x))] =

{

y|Pr[η < y|x] =νU

(νU + νD)

}

(10)

It can be shown [13], [14] that to achieve a certain required

target error (arbitrary quantile of the error), the step sizes

should be related as:

Pe,T =νU

νU + νD

Next, we characterize the ACM solution under certain

generative model assumptions on η.

Proposition 4.1: If η = α(x) + ε, for some α(·) and ε is

independent of x, then the ACM solution is of the form:

1) If ε is zero mean, then η(x) = ηmmse(x) + δ∗,

where ηmmse(x) is the MMSE estimator given by

ηmmse(x) = E[η|x]2) If ε has a zero median, then η(x) = ηmae(x) + δ∗,

where ηmae(x) is the minimum absolute error (MAE)

estimator given by ηmae(x) = {y : Pr[η ≤ y|x] = 0.5}

where δ∗ is a constant that does not depend on x, and is given

by the(

νD

νU+νD

)th

percentile of ε.

Proof: We know the ACM solution satisfies:

νU

∫ η(x)

−∞

fη|x(u)du = νD

∫ ∞

η(x)

fη|x(u)du

where fη|x(·) is the conditional distribution of η given x.

Define δ(x) = η(x) − α(x). Since fη|x(u) = fε(u − α(x)),we have:

νU

∫ η(x)

−∞

fε(u− α(x))du = νD

∫ ∞

η(x)

fε(u− α(x))du

⇒ νU

∫ δ(x)

−∞

fε(t)dt = νD

∫ ∞

δ(x)

fε(t)dt

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Therefore, δ(x) = δ∗ ∀x, where δ∗ is the(

νD

νU+νD

)th

percentile of ε. Thus, η(x) = α(x) + δ∗. The result follows

by noting that:

1) The conditional mean (MMSE) estimator is given by:

ηmmse(x) = α(x)+E[ε|x] = α(x) since ε is indepen-

dent of x and E[ε] = 0.

2) The conditional mediam (MAE) estimator is given by:

ηmae(x) = {y : Pr[α(x) + ε ≤ y|x] = 0.5} = α(x) +{u : Pr[ε ≤ u|x] = 0.5} = α(x), since ε is independent

of x and Pr[ε ≤ 0] = 0.5.

The offline quantile estimator proposed above depends on

the knowledge of the conditional distribution f(η|x), which

is impractical. For a corresponding online estimator, we re-

strict attention to a linear (affine) estimator, and consider the

following assymetric cost minimization (ACM) criterion:

Jt,acm(w) =1

t

∑

1≤τ≤t

φ(ητ −wTxτ ) (11)

A stochastic gradient algorithm for the ACM problem takes

the form:

wacm,t =

{

wacm,t−1 + νU xt if Ack @t

wacm,t−1 − νD xt if Nack @t(12)

This algorithm is referred to the adaptive ACM algorithm.

The key features of this solution are:

• Estimates the true spectral efficiency given a vector of

noisy CQI observations,

• Controls the allocated rate to achieve any arbitrary re-

quired probability of error, and,

• Uses the existing feedback from the UE, in terms of

Ack/Nack information, for updating the estimator.

In the next section, a couple of example applications of this

technique are outlined, along with simulation results.

V. APPLICATIONS AND SIMULATION RESULTS

A. Wideband Spectral Efficiency Estimation

The first application is in basic wideband achievable spectral

efficiency prediction, based on a set of time-delayed wideband

CQI or spectral efficiency measurements. The simulation con-

sists of modeling the CQI time-series as a truncated Gaussian

process with a given mean, variance and autocorrelation func-

tion:

ηt = Q [µη + ση ν1,t]

ηt−1 = Q[

µη + ρ (ηt − µη) + ση

√

1− ρ2 ν2,t

]

where µη is the mean spectral efficiency and ση is the stan-

dard deviation of the channel spectral efficiency. The random

processes νi,t are zero-mean i.i.d. Gaussian processes, and

mutually independent for i = 1, 2. This model captures the

essential feature that a UE’s CQI is predominantly around a

typical average spectral efficiency value, and bounded. The

model allows us to gain insight into the behavior of the

different rate predictors as a function of the correlation of the

current CQI with its previous value. The following algorithms

were evaluated: (1) Online CBA, (2) Offline MMSE, (3)

Adaptive ACM, and (4) No prediction. The target error rate

was set to 10% for the CBA and adaptive ACM algorithms. We

can see from Figure 2 that the proposed algorithm gives higher

spectral efficiency than CBA and offline MMSE. Further, it

was observed that the converged average error rate was 10%for both adaptive ACM and CBA. Both the offline MMSE and

no prediction converge to 50% error rate, and are significantly

inferior in rate compared to the proposed adaptive ACM algo-

rithm. Figure 3 shows the converged weight vector coefficients

for the different algorithms, from which we can gain the

following insights into the different algorithms’ behaviors (1)

it can be observed that the ACM weight coefficient for the

previous CQI was the same as the MMSE weight but had

a lower bias, empirically validating Proposition 4.1, (2) the

weight given to the previous CQI value increases linearly as

a function of the CQI correlation value ρ, which is expected

behavior, (3) when ρ is high, the adaptive ACM gives the same

model as CBA does, namely setting the weight coefficient of

the previous CQI value to be close to 1, with a bias that

is identical to the CBA algorithm, (4) the CBA algorithm,

especially in the case of low correlations, has to give a large

negative bias to the previously reported CQI value in order

to achieve the target FER. Note that the best estimate in this

case is a fixed rate ignoring the CQI feedback, which is not

allowed within the CBA model. The adaptive ACM algorithm

can be seen to gracefully degrade in performance as the CQI

correlation goes down.

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Fig. 2. Achieved rate as function of CQI correlation.

B. MIMO Rank-1 CQI Prediction

In the SU-MIMO mode of LTE, if the UE computes that

it can support spatial multiplexing, it reports a Rank-2 CQI

to the base-station. The problem is that in many cases, the

UE’s rank estimation is optimistic, or delays in CQI reporting

can result in the channel not supporting Rank-2. In [5], a rate

prediction method is proposed for extrapolating MU-MIMO

achievable rates from corresponding Rank-1 SU-MIMO rates

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in a closed-form fashion, which is an easier problem than the

problem considered here.

In SU-MIMO, we get two CQI reports corresponding to

the two MIMO codewords, denoted as CQIcw,1 and CQIcw,2.

Given these CQI measurements, which include the effect of

the inter-codeword interference, we need to predict the equiv-

alent Rank-1 spectral efficiency. We consider the following

transformation of variables, knowing that the Rank-1 spectral

efficiency would be greater than x1 = max(CQIcw,1,CQIcw,2)and likely less than x2 =

∑

i CQIcw,i. With this, the model

can be: η(x) = w0 + w1x1(+w2x2). We apply the ACM

algorithm for achieving a target error probability for Rank-

1 transmissions given Rank-2 reported CQIs. To evaluate

the performance of the proposed scheme in this scenario,

we consider a downlink system simulation with 2 Tx and

2 Rx. The inter-site distance (ISD) is 500m, with all cells

transmitting at full power. All system aspects such as HARQ,

proportional fair scheduling, and fading channel (enhanced

Pedestrian A channel with 5km/h fade rate) are modeled in

the simulator. The simulation is for 10 UEs per cell, all having

full buffer in their queue.

Results are from the outcome of predicting the Rank-1

spectral efficiency for all users in the center-cell of the system,

based on their reported Rank-2 CQIs, where we found it was

better to use only x1 in the model. As can be seen from Figure

(4), fast convergence and good tracking across range of SEs

can be observed in the results. It can be observed that all

the 10 users are initialized with an estimated Rank-1 spectral

efficiency of 0, and the adaptive ACM algorithm converges in

less than 500 steps to the true spectral efficiency for each user.

VI. CONCLUSIONS

We presented an adaptive filtering and control framework

for rate prediction in wireless broadband networks. The pro-

posed formulation can be applied to numerous rate predic-

tion problems in wireless networks. A QoS-controlling rate

estimator was proposed, which uses the Ack/Nack feedback

from the receivers as input to update the filters and control

� � � � � 2 � E ���� �� 2�E�F� �

6 . � , � G � � � - � � . � � � � � � � � H � I 0 � � �J K"L# A! "L� $MNOP@ *K ++ C&"K&Q%#! &' &()% *+R , � G � � � � � � � � � � � � � � � � � , � G � � � � � / 5 � � � S � T U � V 0 W � � � � X Y T / � � � X Y V �

Fig. 4. Rank-1 predicted vs. actual spectral efficiency for 10 UEs in the cell.

the QoS. Simulation results for two possible use-cases were

presented, that showed the efficacy of the proposed algorithm

in providing high spectral efficiency.

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