 Research
 Open Access
Adaptive CSI and feedback estimation in LTE and beyond: a Gaussian process regression approach
 Alessandro Chiumento^{1, 2}Email author,
 Mehdi Bennis^{3},
 Claude Desset^{1},
 Liesbet Van der Perre^{1, 2} and
 Sofie Pollin^{1, 2}
https://doi.org/10.1186/s1363801503880
© Chiumento et al.; licensee Springer. 2015
 Received: 20 December 2014
 Accepted: 14 May 2015
 Published: 12 June 2015
Abstract
The constant increase in wireless handheld devices and the prospect of billions of connected machines has compelled the research community to investigate different technologies which are able to deliver high data rates, lower latency and better reliability and quality of experience to mobile users. One of the problems, usually overlooked by the research community, is that more connected devices require proportionally more signalling overhead. Particularly, acquiring users’ channel state information is necessary in order for the base station to assign frequency resources. Estimating this channel information with full resolution in frequency and in time is generally impossible, and thus, methods have to be implemented in order to reduce the overhead. In this paper, we propose a channel quality estimation method based on the concept of Gaussian process regression to predict users’ channel states for varying user mobility profiles. Furthermore, we present a dualcontrol technique to determine which is the most appropriate prediction time for each user in order to keep the packet loss rate below a predefined threshold. The proposed method makes use of active learning and the explorationexploitation paradigm, which allow the controller to choose autonomously the next sampling point in time so that the exploration of the control space is limited while still reaching an optimal performance. Extensive simulation results, carried out in an LTEA simulator, show that the proposed channel prediction method is able to provide consistent gain, in terms of packet loss rate, for users with low and average mobility, while its efficacy is reduced for highvelocity users. The proposed dualcontrol technique is then applied, and its impact on the users’ packet loss is analysed in a multicell network with proportional fair and maximum throughput scheduling mechanisms. Remarkably, it is shown that the presented approach allows for a reduction of the overall channel quality signalling by over 90 % while keeping the packet loss below 5 % with maximum throughput schedulers, as well as signalling reduction of 60 % with proportional fair scheduling.
Keywords
 5G
 Channel state information
 OFDMA
 Signalling overhead
 LTE
 Dual control
 Active learning
1 Introduction
Future cellular networks are envisioned to provide extremely high quality of service to an ever increasing number of interconnected users [1]. Many technologies are currently being explored in order to evolve from current 4G networks to future 5G communication. One aspect that has yet to be fully addressed is the signalling overhead imposed on a network with billions of connected devices [2–4]. The control information overhead is, in fact, still a very relevant problem for 4G cellular networks, such as long term evolution (LTE). Future 5G networks will, most likely, make use of the same radio access technology utilised by LTE: orthogonal frequency division multiple access (OFDMA). In this work, we present techniques to predict and minimise a user’s packet loss by means of limiting the control information in the time domain for a downlink OFDMA network. The simulations are carried out in an LTE environment as this is the most advanced cellular network available today but the methods presented and the results achieved can be easily generalised for future 5G scenarios. In LTE, OFDMA divides the bandwidth into orthogonal blocks, called physical resource blocks (PRBs), and a frequency domain scheduler assigns such PRBs to the served users based on their channel conditions [5]. In order to provide each user with the highest quality of service, the base stations employ adaptive modulation and coding (AMC) techniques which adjust different modulation and coding schemes (MCS) used for transmission according to the channel state information (CSI) signals fed back from the users. Therefore, relevant and timely CSI signalling is extremely important to allocate the wireless resources to the users and maximise the overall network capacity. Full CSI feedback (FB), although optimal in maximising the downlink capacity, cannot be used in LTE as the standard quantises both the amount of channel state information the users feed back in the frequency domain as well as how often this information can be reported in time [6].
In [7], we have shown that it is possible to limit channel state information, in frequency, without loss in performance if the freed uplink bandwidth is allocated for payload communication. We have also shown that the number of served users under different fairness strategies, imposed by the frequency resource allocation mechanisms, influence the impact of FB allocation strategies and that it is possible to determine the optimal FB allocation. The impact of FB information is then a function of the number of users served by the base station, their channel quality and the scheduling algorithm used to assign the PRBs. In this work, we show that it is possible to compensate for the capacity loss due to reducing the CSI signalling in time, even with already quantised frequency resolution, via the usage of peruser channel quality prediction and peruser dynamic assignment of prediction time windows.
Considerable work has been devoted by the research community to either channel quality prediction or feedback overhead reduction. In [8], the authors implement and compare various signaltointerferenceandnoise ratio (SINR) prediction algorithms and conclude that high gains can be expected when using covariancebased predictors for low mobility users. In [9], the authors present a prediction method used to compensate for CSI delay. The estimation is performed at the mobile user side and the predictor takes into account the Doppler shift of each user for more accurate estimation. Both works make use of the users’ Doppler shift to determine the time duration of the channel quality estimation; this procedure, although well established, might lead to erroneous predictions, a negative correlation is generally present between prediction quality and Doppler shift. On the other hand, a high mobility user might witness a better, less variable channel than a low mobility user. Furthermore, users have to predict the SINR themselves, depleting their battery life. In [10], the authors propose a dynamic Channel Quality Index (CQI) allocation method, which is a quantised value indicative of the SINR experienced by the users and predicted at the base station. The CQI allocation time of each user is adapted based on the instantaneous packet loss of each user. In [11], the same authors expand their results by including CQI prediction at the base station. They use a linear predictor and compensate for errors by reducing or increasing the prediction windows based on the users’ packet loss. In [12], the authors present a nonpredictive signalling reduction scheme where only users with low SINR are allowed to feed back expensive instantaneous CQI information while high SINR users only transmit wideband information. Even though the method decreases the signalling information, it is carried out for a limited and fixed time window (2 ms) and a single cell scenario, ignoring the underlying network dynamics due to interference, traffic load, etc.
The main objectives of this work are twofold. Firstly, we propose an online and adaptive CQI prediction scheme to estimate users’ channel quality variations at the base station side, while compensating for some of the quantization noise introduced by sampling the SINR at certain CQI values. The proposed CSI estimation approach is based on Gaussian process regression which has been shown to be efficient in the presence of noisy measurements [13]. Gaussian processes (GPs) are also used to estimate the distribution of variables rather than their values, making them attractive for solid predictions over noisy datasets. Furthermore, GPs provide a principled framework in which their parameters can be estimated with maximum likelihood techniques removing constraints related to the finetuning of such predictors [14].
Secondly, we leverage the GPbased prediction mechanism for the CQI assignment problem, in which a base station controller is able to monitor the behaviour of each served user and assign a personalised prediction time window based on that user’s performance and requirements. For this procedure, a dualcontrol system based on active learning, as introduced in [15], is used. The dual controller is able to monitor and predict the base station’s performance and assign a time window to each user based on specific requirements. The active learning component is used to limit the amount of necessary data sampling before an optimal policy is reached. In order to demonstrate the effectiveness of the proposed methods, we consider a multiuser, multicell LTE network. The quality of the GPR for CQI prediction is presented for different user speeds, and afterwards, simulation results for the dualcontrol system are shown for both proportional fair and maximum throughput scheduling.
This paper is structured as follows: Section 2.1 introduces the considered system model, the standardcompliant CSI allocation strategies and the resource allocation mechanisms used throughout this work. In Section 3, the prediction model used to estimate the users’ channel quality is presented. In Section 4, the online dualcontrol mechanism is proposed to determine dynamically the optimal prediction window for a given user. In Section 5, the performance of the proposed solutions is presented. Finally, in Section 6, the concluding remarks are drawn.
2 System model
2.1 Network model
where P _{ i } and G _{ i } are the transmit power and transmission gains of the serving base station i while P _{ j } and G _{ j } are the transmit power and transmission gains of the interfering base stations j and n _{ k } is the additive Gaussian noise.
SINR and CQI mapping to modulation and coding rate
SINR  CQI  Modulation  Code rate  Efficiency 

(× 1024)  (information bits per symbol)  
−6.9360  1  QPSK  78  0.1523 
−5.1470  2  QPSK  120  0.2344 
−3.1800  3  QPSK  193  0.3770 
−1.2530  4  QPSK  308  0.6016 
0.7610  5  QPSK  449  0.8770 
2.6990  6  QPSK  602  1.1758 
4.6940  7  16QAM  378  1.4766 
6.5250  8  16QAM  490  1.9141 
8.5730  9  16QAM  616  2.4063 
10.3660  10  64QAM  466  2.7305 
12.2890  11  64QAM  567  3.3223 
14.1730  12  64QAM  666  3.9023 
15.8880  13  64QAM  772  4.5234 
17.8140  14  64QAM  873  5.1152 
19.8290  15  64QAM  948  5.5547 
Once the eNB has collected the CQIs for the entire bandwidth, it schedules resources for each user according to its resource allocation function.
2.2 LTE feedback schemes
2.2.1 2.2.1 “Frequency domain feedback”

Wideband: each user transmits a single 4bit CQI value for all the PRBs in the bandwidth.

Higher Layer configured or subband level: the bandwidth is divided into q subbands of S consecutive PRBs and each user feeds back to the base station a 4bit wideband CQI and a 2bit differential CQI for each subband. The value of k is bandwidth dependent and is given in Table 2, where \(N_{\textit {PRB}}^{DL}\) is the total number of downlink PRBs in the bandwidth (table 7.2.12 in [6]).Table 2
Subband size (S) vs. system bandwidth for subband level feedback
System bandwidth
Subband size
\(N_{\textit {PRB}}^{DL}\)
(S)
6–7
NA
8–10
4
11–26
4
27–63
6
64–110
8

Userselected, or BestM: each user selects M preferred subbands of equal size S and transmits to the base station one 4bit wideband CQI and a single 2bit CQI value that reflects the channel quality over the selected M subbands. Additionally, the user reports the position of the selected subbands using P _{ FB } bits, where P _{ FB }, as given in [6], is:$$ P_{FB} = \left\lceil log_{2} {N_{PRB}^{DL} \choose M} \right\rceil \;, $$(3)where \({N_{\textit {PRB}}^{DL} \choose M}\) is the binomial coefficient. The value of M and the amount of PRBs in each subband are given in Table 3 (table 7.2.15 in [6]):Table 3
Subband size (S) and number of subbands (M) vs. system bandwidth for userselected feedback
System bandwidth
Subband size
M
\(N_{\textit {PRB}}^{DL}\)
(S)
6–7
NA
NA
8–10
2
1
11–26
2
3
27–63
3
5
64–110
4
6
Bit cost of the frequency selective standard complaint FB methods
Feedback scheme  Bit cost 

Wideband  2·(4·N _{ U }) 
Subband level  2·(4+2·q)·N _{ U } 
Userselected  \(2 \cdot (4 + 2 +\lceil log_{2} {N_{\tiny {PRB}}^{\tiny {DL}} \choose \tiny {M}} \rceil)\cdot N_{U} \) 
2.2.2 2.2.2 “Time domain feedback”
The CSI is limited in the time domain. The periodicity of CQI reporting is determined by the base station, and the CQI signalling is divided into periodic and aperiodic reporting [18]. In case of aperiodic CQI signalling, the eNB specifically instructs each user on which frequency granularity to use and when the reporting has to occur. With aperiodic reporting, the eNB can make use of any of the CQI standard compliant feedback methods discussed above. Periodic CQI reporting, on the other hand, is more limited and only wideband and userselected feedback methods can be used. In this case, the CQI messages are transmitted to the base station with constant periodicity, e.g. in case of periodic wideband feedback in an FDD system, each user can report its CQI values every 2, 5, 10, 16, 20, 32, 40, 64, 80 and 160 ms. For the remainder of this work, we assume that an aperiodic feedback is used, as this allows the eNB controller to adapt the CQI transmission time more freely than with periodic reporting.
2.3 Resource allocation mechanisms

Best CQI (BCQI), or maxrate, is a greedy scheduler designed to maximise the cell throughput. For each PRB, only the user with the highest channel quality indicator is scheduled.

Proportional Fair (PF): this scheduler is designed to aim for high throughput while maintaining fairness amongst users. PF schedules users when they are at their peak rates relative to their own average rates, at a given time instant t, PF schedules user \(x_{i} = \arg \max \frac {r_{i,k}(t)}{R_{i}(t)}\), where r _{ i,k }(t) is the instantaneous data rate of user x _{ i } on PRB k at time t and R _{ i }(t) is the average throughput, computed with moving time window T, such that \(R_{i}(t) = \frac {1}{T}\sum _{j= tT}^{t} r_{i}(j)\).
3 CQI prediction
We now turn our attention to the description of the CQI estimation methods. The estimation process is carried out to compensate for the reduction in CQI reporting in time. Given the relationship between CQI and SINR described in Section 2.1, predicting the CQI is equivalent to predicting a noisy function of the relative effective SINR. Due to the Gaussian nature of the SINR distribution and the inherent flexibility of Gaussian Processes for regression, these have been selected in this work.
3.1 Gaussian process regression
The best estimate for \(\hat {y}\) is given by the mean of such distribution \(m(\boldsymbol {\hat {Y}}) = K(\boldsymbol {X},x_{*})\left [K(\boldsymbol {X},\boldsymbol {X})+ {\sigma _{n}^{2}}\boldsymbol {I}\right ]^{1}\boldsymbol {Y}\) and the variance \(Var(\boldsymbol {\hat {Y}}) = k(x_{*},x_{*})  K(\boldsymbol {X},x_{*}) \left [K(\boldsymbol {X},\boldsymbol {X})+ {\sigma _{n}^{2}}\boldsymbol {I}\right ]^{1}K(\boldsymbol {X},x_{*})^{T}\) represents the uncertainty of the current estimate. The GP is then fully defined by its covariance and mean functions and their parameters.
3.2 Covariance function selection
By using any multivariate optimization algorithm, the set of hyperparameters θ can be estimated analytically. After the optimization process has reached the analytical solution, the numerical values of the hyperparameters are simply obtained by using the measured input and output signals. This is a great advantage over other types of regression as it allows the system to evolve without prespecifying the parameters and thus limiting the range of estimations [22].
3.3 GPR for CQI prediction
In this work, the eNB makes use of GPR to predict the CQIs values for every subband seen by each user. In order to make realistic predictions, the output vector Y is used to train the GP. For each user, the base station receives the CQI information for the complete bandwidth, using the subbandlevel FB quantization scheme discussed in Section 2.2 every t _{ samp }=2m s. The value of the sampling window t _{ samp } is chosen as the minimum allowed by LTE standard to acquire a high number of samples in a short time [23]. After the observation time elapses, say at instant t _{0}, the eNB uses GPR to predict the future CQI values in each subband as shown in Algorithm 1.
4 Dynamic time window optimisation
In this section, we introduce a control mechanism to determine the appropriate duration of the CQI prediction window so that the eNB can maintain each user’s performance within a specified loss margin. Firstly, the dualcontrol system based on active learning is introduced and, secondly, its implementation in an LTE base station for time windows optimisation is presented.
4.1 Dual control with active learning
A dualcontrol agent is tasked with controlling a system based on the current knowledge of its behaviour and to perturb it in order to minimise the uncertainty and make better predictions. By their nature, these objectives are conflicting. In this work, we follow the adaptive dualcontrol method proposed in [15], which provides a solution to the control problem while also limiting the amount of overhead.
The dual control with active learning can be formally described as (Proposition 4 in [15]): Let the inputoutput relationship of a discretetime dynamic system be defined as in Equation 12.
where w _{ a } and w _{ e } represent the action and exploration weights to steer the controller towards either steepest descent to the closest optimal solution (w _{ e }=0) or to a complete exploratory behaviour (w _{ a }=0). Generally, the weights can be adjusted so that the controller behaves more exploratory at the beginning of the learning procedure and then moves to a more active controlling role.
4.2 Dual control for signalling reduction
where r _{ u,t h } is the reference packet loss for user u. At time \(\phantom {\dot {i}\!}t_{0} + t_{w_{u}}(t_{0})\), the eNB measures the actual packet loss suffered by the user. The controller then corrects the CQI prediction window accordingly to provide better predictions and the process is repeated. Algorithm 2 provides a concise view of the solution above.
5 Results
In this section, we will first define the simulation environment and then provide the results for the proposed models.
5.1 Simulation parameters
System parameters
Parameters  Values 

Number of macrocells  19 
Sectors per macrocell  3 
Intercell distance  500 m 
Macro antenna gain  15 dB 
Macro transmit power  46 dBm 
Macro users per sector  2 to 100 
Frequency  2.1 GHz 
System bandwidth  20 MHz 
Number of PRBs  100 
Access technology  OFDMA FDD 
Number of antennae  1(Tx and Rx) 
Channel model  Winner Channel Model II [25] 
Block fading mean  0 dB 
Block fading deviation  10 dB 
Fast fading  10 dB 
Thermal noise density  −174 dBm/Hz 
Users speed  5 to 60 km/h 
5.2 Simulation results
It is visible that there is a loss in goodput when either the CSI frequency sampling methods are used or the CSI sampling time interval is increased. On the other hand, the effects of increasing the duration between sampling instants are less pronounced when the CQI information is quantised in frequency. This is particularly visible for the wideband FB scheme, where the initial goodput is just above one third of the full feedback but the loss in time is almost null. For large time sampling intervals, the three standard compliant FB schemes behave better than the full feedback. For the remainder of this work, the subband level method is employed, as it presents, for almost all the sampling delays considered, the highest gain amongst the standard compliant schemes.
When users operate in high mobility, such as in Fig. 6, the prediction remains valid only for a very small time duration. This is due to the fact that the fast varying channel does not allow for reliable estimation for extended time intervals. Nonetheless, it is possible to exploit the GPR estimation’s gain over the sampling if short time windows are used.
Percentage FB necessary with dual control
PL threshold  FB amount needed [%]  

[%]  Proportional fair  Best CQI 
5  40  6.2 
10  23  4 
20  9.7  3.3 
30  6.3  3.3 
6 Conclusions
In this work, we have shown that the feedback overhead cannot be overlooked as the number of connected devices keeps increasing. Some solutions are implemented in the frequency domain to limit the impact of this signalling information on the uplink bandwidth but additional restrictions in the time domain are also necessary. We presented a GPR technique to predict the users’ channel quality for various speeds limiting the loss incurred by increasing the time sampling period. The proposed CQI prediction method is able to estimate a user’s channel with good accuracy. Furthermore, we have presented a dualcontrol method based on active learning, able to determine the optimal prediction window given a packet loss threshold. The same method is also able to probe the system in such a way that an optimal solution is reached while also limiting the system’s exploration by maximising the impact of the information collected. The proposed method shows gains of up to 94 % in signalling reduction if best CQI scheduler is used when compared with state of the art if the packet loss is capped to 5 %.
Declarations
Authors’ Affiliations
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