Modeling LTE-advanced cell capacity estimation using packet bundling and carrier aggregation

Motivation

Today, staying connected is more important. Speed and good user experience are equally important. We are living in the invention age, and the adequate technology is also limited. We are witnessing massive transformation and development in the industrial sector, smart education system, healthcare, automotive industry, smart economy, smart lifestyle, and many more. In particular, the exponential growth of mobile users raises many challenges for the operators in terms of quality of service (QoS). To retain the desired QoS, operators must satisfy the subscriber’s requirement by providing adequate radio resources. Physical radio resources are one of the precious entities in wireless communication, and it is essential for the network operator to optimize the radio resource usage properly. This essentially requires a mechanism to estimate and enhance the active subscribers within an LTE-A cell. Hence, in this article, CCa estimation model and algorithm is proposed in a simplistic scenario as well as using the packet bundling approach considering CA.

4G-LTE Advanced is still of significant importance for several reasons. Although 5G is the current focus, 4G continues to play a crucial role in the global cellular communication landscape. As per the work reported in Saha & Cioffi (2024), dynamic spectrum sharing between LTE and 5G New Radio has become an important aspect where both systems can co-exist on the LTE spectrum. The work reported in Wang & Xu (2023), study has been conducted on shared aperture 4G LTE and 5G mm-wave antenna in mobile phones with enhanced mm-wave radiation in the display direction. In Zhao & Wang (2024), a mobile antenna with a 0.5-mm clearance, which operates in 11 bands, is proposed for 4G and 5G metal-bezel smartphones. From the literature, it is found that 4G LTE is still an area of interest, and especially in rural and under-served areas, it is the most cost-effective. However, research is continuing to improve the performance of 4G in terms of efficiency, coverage, and QoS specifically for those under-served regions.

Contributions

The major contributions of this article are outlined as follows:

• The proposed model explicitly uses some LTE-A-specific enhancements i.e., beyond standard LTE features such as CA and channel quality indication (CQI)-based resource allocation.

• The study proposes a CQI-based clustering approach with packet bundling and CA to optimize radio resource utilization and enhance LTE-Advanced cell capacity.

• To be able to optimize the radio resource utilization, it is proposed to divide the LTE-A cell logically into clusters such as the Silver, Platinum, Gold, and Diamond classes. These clusters are formed based on the reported CQI by the user equipment (UE) to eNodeB (eNB).

• An LTE-A CCa estimation model for voice traffic using CA is developed in this article considering a simplistic scenario and then LTE-A CCa estimation algorithm is proposed based on that model.

• Further, LTE-A CCa estimation model is proposed using Packet bundling. Using the proposed model, LTE-A modulation selection and capacity estimation algorithm is proposed.

• Finally, the impact of different factors on CCa is discussed through the result analysis.

Organization of article

The rest of this article is presented as follows. The system model is presented in “Related Works”. LTE-A CCa estimation model considering CA is presented in “System Model” followed by an algorithm. Resource distribution criteria and model parameters are presented in “LTE-A Capacity Estimation Model and Algorithm using Carrier Aggregation”. Numerical results are provided with a detailed discussion in “Resource Distribution Criteria and Model Parameter”. Finally, the conclusions are presented in “Numerical Results”.

LTE-A CCa estimation model at DL for voice service using CA

In this section, an analytical model is presented to estimate the number of subscribers that can be accommodated within a cell using CA. In this model, the CCa is estimated by dividing the total number of physical resources available in a given bandwidth and the resources required for a subscriber to establish a connection and transmit a voice packet. The capacity estimation model is calculated using the following expressions. All the symbols used in this model are presented in Table 1.

The total number of resource blocks for a slot $N_{RB\mathrm{\_}cc}$ in a particular bandwidth is a fraction of the given bandwidth $N_{BW\mathrm{\_}cc}$ and the product of subcarriers available in a resource block and the bandwidth of a subcarrier, which is expressed in Eq. (3).

(3) $$N_{RB\mathrm{\_}cc}=\frac{N_{BW\mathrm{\_}cc}}{N_{RB\mathrm{\_}cc}^{sc}\times B{W}_{cc}^{sc}}.$$

The maximum number of available resource blocks that can be used for packet transmission can be calculated using Eq. (4).

(4) $$R{B}_{total\mathrm{\_}cc}=N_{TTI\mathrm{\_}cc}^{VoLTE}\times N_{RB\mathrm{\_}cc}^{TTI}.$$

The voice payload is calculated using Eq. (5).

(5) $$P_v=C_r\times V_t+O_v.$$

The target payload i.e., the combination of voice payload and the overhead can be calculated using Eq. (6).

(6) $$P_{VoLTE}=P_v+O_h.$$

Finally, the resource block required to carry the target payload can be calculated using Eq. (7).

(7) $$R{B}_{cc}^{reqd}=\lceil \frac{P_{VoLTE}}{P_{MCS}}\rceil .$$

Now, LTE-A CCa in downlink (DL) denoted by $N_{sup}^{cc}$ for a CC can be expressed as given in the following expressions.

(8) $$N_{sup}^{cc}\le \{\begin{array}{cc}\hfill & {\sum }_{i=1}^4\frac{R{B}_{total\mathrm{\_}cc}}{R{B}_{cc,i}^{reqd}},if{\mathrm{\forall }}_i{R}_i^{avr\mathrm{\_}re}=0\hfill \\ \hfill & {\sum }_{i=1}^4\frac{R{B}_{total\mathrm{\_}cc}}{R{B}_{cc,i}^{reqd}\times (1+R_i^{avr\mathrm{\_}re})},otherwise\hfill \end{array}$$where $R{B}_{cc,i}^{reqd}$ denotes the physical resources required by each voice payload in $i^{th}$ cluster and $R_i^{ave\mathrm{\_}re}$ denotes the average re-transmissions required in $i^{th}$ cluster.

Now, the capacity of an LTE-A cell considering CA can be defined as:

(9) $$N_{sup}=n\times N_{sup}^{cc}.$$where $n$ denotes the number of carrier components needs to be aggregated by an eNB in an LTE-A network.

LTE-A CCa estimation model using packet bundling and carrier aggregation

Physical resources is one of the smallest entities to schedule a voice packet. If the voice packet is smaller than the physical resource element, then some portion of the physical resources may be wasted. Hence, it is possible to bundle multiple voice packets for transmission in a single physical resource element. The consumption of radio resources varies depending upon the radio channel condition. For example, in good radio condition, a packet may require fewer radio resources due to the use of a higher modulation scheme; in such a case, more than one packet can be bundled together. However, the same may not be possible in weaker radio conditions. Therefore, we can apply a packet bundling mechanism in favorable channel conditions, taking into account the channel quality. Furthermore, we can bundle the number of packets based on the radio condition. For instance, up to three or five packets can be bundled together when using 64QAM or 256QAM modulation in very good radio conditions. In average radio conditions, up to two packets can be bundled together when using 16QAM and the AMR-WB voice codec. Again, this packet bundling technique is influenced by the voice codec being used for encoding the voice packet. This part talks about analytical models that can be used to figure out how many subscribers an LTE-A cell can handle while taking into account different factors.

The number of resources required for transmitting voice packets of subscribers can be represented as Senapati & Pati (2019b),

(10) $$R{B}_{cc}^{reqd}=(1+R^{avr\mathrm{\_}re})\times N_{ave}\times (1-p)\times v+N_{ave}^{\mathrm{\prime }}\times p,$$

In general, the total number of mobile voice users can be served within the network is $\frac{R{B}_{total}}{R{B}^{reqd}}$. Now, the number of mobile voice users that an LTE-A network can support in UL/DL can be expressed as:

(11) $$N_{sup}^{cc}=\frac{R{B}_{total}}{(1+R^{avr\mathrm{\_}re})\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times p}$$

As per the assumption considered in “Related Works” of this article, the radio condition varies in different clusters based on the position of equipment within an LTE-A cell. Further, based on their CQI report, the modulation schemes being used also vary. Hence, the capacity of an LTE-A network within each cluster also varies. It is quite obvious that the cluster positioned near the base station may require fewer radio resources to transmit a voice packet as compared to the other clusters positioned far away from the base station. Therefore, it is possible to optimize the use of radio resources by utilizing packet bundling. Now the packet bundling factor $\omega$ can be used in the model presented in Eq. (11) to further estimate the capacity of the LTE-A network in DL. We ignore packet bundling when estimating capacity in UL because it has no impact on UL. Now, the LTE-A capacity in UL and DL using the packet bundling factor $\omega$ can be estimated as presented in Eq. (12).

(12) $$\begin{array}{rl}& N_{sup}^{cc}=\frac{R{B}_{total}}{[(1+R^{avr\mathrm{\_}re})\times \omega \times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times {\omega }^{\prime }\times p]}\\ & +\frac{R{B}_{total}}{[(1+R^{avr\mathrm{\_}re})\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times p]}\end{array}$$

$N_{sup}^{cc}$ is the total number of supported users in a single cell. In general, it is the fraction of total number of resources available to carry voice packets and the required number of resources for voice packet transmission. Equation (12) is derived based on this concept. Now, the capacity of an LTE-A cell considering packet bundling and CA can be estimated as presented in Eq. (13).

(13) $$N_{sup}=n\times N_{sup}^{cc}$$where $n$ denotes the number of carrier components needs to be aggregated by an eNB in an LTE-A network.

Now, the number of users supported in Silver class, Platinum class, Gold class, and Diamond class can be determined through Eqs. (14) to (17).

(14) $$N_{sup}^{Silver}=\frac{R{B}_{total}}{[(1+R^{avr\mathrm{\_}re})\times {\omega }_{QPSK}\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times {\omega }_{QPSK}^{\prime }\times p]+[(1+R^{avr\mathrm{\_}re})\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times p]}$$

(15) $$N_{sup}^{Platinum}=\frac{R{B}_{total}}{[(1+R^{avr\mathrm{\_}re})\times {\omega }_{16QAM}\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times {\omega }_{16QAM}^{\prime }\times p]+[(1+R^{avr\mathrm{\_}re})\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times p]}$$

(16) $$N_{sup}^{Platinum}=\frac{R{B}_{total}}{[(1+R^{avr\mathrm{\_}re})\times {\omega }_{16QAM}\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times {\omega }_{16QAM}^{\prime }\times p]+[(1+R^{avr\mathrm{\_}re})\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times p]}$$

(17) $$N_{sup}^{Diamond}=\frac{R{B}_{total}}{[(1+R^{avr\mathrm{\_}re})\times {\omega }_{256QAM}\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times {\omega }_{256QAM}^{\prime }\times p]+[(1+R^{avr\mathrm{\_}re})\times N_{ave}\times (1-p)\times v+N_{ave}^{\prime }\times p]}$$

Now, packet bundling factor ( $\omega$) can be defined based on the cluster (within the cluster all equipment’s generating CQI with in a same range) and their corresponding modulation and voice codec schemes used for voice transmission within that cluster. The factor $\omega$ can be determined by modulation and codec selection algorithm presented in Algorithm 2.

In the proposed algorithm, the packet bundling factor $\omega$ is assumed to be uniform across users in the same cluster. However, the bundling factor can be tuned for individual users within a cluster based on their specific channel conditions and codec requirements. The adaptive $\omega$ can be expressed as ${\omega }_i=f(CQ{I}_i,SIN{R}_i,MC{S}_i)$. Where $CQ{I}_i$ is the reported CQI value of user $i$, $SIN{R}_i$ is the signal-to-interference-plus-noise ratio, $MC{S}_i$ is the modulation and coding scheme, and f(.) is a function that assigns an optimal $\omega$ based on the user’s conditions. Mathematically, $w_i$ can be expressed as $w_i=w_{max}\times \frac{CQ{I}_i}{CQ{I}_{m}ax}$. Using this model, the users with better CQI may get a higher $\omega$ and thereby improve efficiency.

LTE-A modulation selection and capacity estimation algorithm

Different modulation and coding selection algorithms are presented in the literature, and basically those are used to improve the throughput of the network. In this article, a novel modulation and voice codec selection algorithm is proposed to improve the capacity of a network in terms of accommodating voice subscribers. The algorithm is developed using MCS-CQI mapping. The procedure for modulation selection and capacity estimation using packet bundling at downlink is presented in Algorithm 2. The Algorithm 2 is executed as follows.

1. In Step 1, user equipment measures reference signal form eNB.

2. In Step 2, CQI is calculated by user equipment base on the SINR.

3. In Step 3 and 4, based on the CQI, QPSK is assigned to the Silver class Cluster.

4. In Step 5, capacity at Silver class Cluster is estimated considering all the resources are assigned to that cluster.

5. In Step 6 and 7, Based on the CQI, 16QAM is assigned to the Platinum class Cluster.

6. In Step 8, capacity at Platinum class Cluster is estimated considering all the resources are assigned to that cluster.

7. In Step 9 and 10, based on the CQI, 64QAM is assigned to the Gold class Cluster.

8. In Step 11, capacity at Gold class Cluster is estimated considering all the resources are assigned to that cluster.

9. In Step 12 and 13, based on the CQI, 256QAM is assigned to the Diamond class Cluster.

10. In Step 14, capacity at Diamond class Cluster is estimated considering all the resources are assigned to that cluster.

11. In Step 16, LTE-A cell capacity in terms of accommodation of subscribers is estimated considering a factor $f$. The factor $f$ indicates the percentage of resources distributed in each cluster.

12. Finally in Step 17, the capacity is estimated using CA.

Distribution criteria

When things happen in real time, link adaptation is used in LTE-A to let the eNB choose the best modulation and coding scheme based on the channel quality, which is found by the CQI and reported by the UE. According to the work reported in 3GPP (2013), the CQI index consists of 16 values, ranging from 0 to 15. The CQI index 0 is not used. When the CQI index is between 1 and 3, 4 to 6, 7 to 11, and 10 to 15, the corresponding MCS are QPSK, 16QAM, 64QAM, and 256QAM, in that order, to get the best performance. Therefore, in this work, we have considered these modulation schemes for LTE-A capacity estimation. Using 256 QAM may lead to a high bit error rate and significant retransmission overhead. This is a limitation of our study. However, in this study, we have considered a scenario and presented the quantitative results while using the modulation schemes in conjunction with different voice codecs.

Model parameters and assumptions

A single LTE-A cell is considered in this work. The cell is categorized into four clusters (i.e., Silver class, Platinum class, Gold class, and Diamond class) based on their positions from eNB as shown in Fig. 1. In the Silver class cluster, the position of UE is at the cell edge. In this case, the UE generates CQI index in between 1 to 3 based on the SINR value. In the Platinum class cluster, UEs are positioned at the middle distance between eNB and the cell edge. In this case, the UE generates CQI between 4 and 6, based on the SINR value. In the Gold class cluster, UEs are close to eNB and generate CQI in the range of 7 to 11 based on the SINR value. In the Diamond class cluster, UEs are very near to the eNB, and it generates CQI within the range of 12 to 15. An appropriate MCS is assigned by eNB to UE depending on the CQI report. The bandwidths used for capacity estimation within the cell are mentioned in Table 2. The radio conditions inside the cell determine which class is used. The Silver class uses QPSK for CQI between 1 and 3, the Platinum class uses 16QAM for CQI between 4 and 6, the Gold class uses 64QAM(5/6) modulation for CQI between 7 and 11, and the Diamond class uses 256QAM for CQI between 12 and 15. The voice codecs with bit rates used are AMR-WB 12.65, 8.85, and 6.60 kbps. The number of hybrid automatic repeat request (HARQ) re-transmissions used are 0, 1, 2, and 3 for each case scenario. To make the analysis simpler, we have considered the average re-transmission for all the clusters as equal (i.e., $R_{i\mathrm{\forall }i}^{avr\mathrm{\_}re}$ = $R^{avr\mathrm{\_}re}$) within the defined range. The average re-transmissions (i.e., $R^{avr\mathrm{\_}re}$) are used in further numerical calculations and are within the range of 0 to 3. In this work, $f_i$ is set to $0.25$ as per the system parameter defined in Table 2.

The proposed algorithm allocates all the resources for data transmission. However, the control channel overhead may be considered, and the remaining resources may be allocated for data transmission. The actual usable resources for data transmission can be computed as $R{B}_{total\mathrm{\_}cc}=R_{total}-R_c$, where $R{B}_{tota{l}_{c}c}$ is the total available resource blocks for data transmission, $R_c$ is resources allocated to control channels (Physical Downlink Control Channel (PDCCH), Physical channel HybridARQ Indicator Channel (PHICH), Physical Control Format Indicator Channel (PCFICH)), and $R_{total}$ is the total available resource blocks.

LTE-A CCa in silver class cluster

The LTE-A cell capacity is estimated within the Silver class cluster using the proposed model presented in Eqs. (9) and (13) for a simplistic scenario as well as using the packet bundling approach, respectively. The results are presented in Fig. 2, which shows the capacity comparison in a simplistic scenario as well as packet bundling while using the QPSK modulation scheme w.r.t. different AMR-WB voice codecs across the bandwidths available for LTE-A. Further, the capacity is also estimated using CA for $n$ = 2 to 5. From the results presented in Figs. 2A–2C, it is observed that, under the Silver class cluster, AMR-WB 12.65 and 8.85 give the same result, whereas the lower-order voice codec, i.e., AMR-WB 6.60 gives a significantly better result.

LTE-A cell capacity in platinum class cluster

The LTE-A CCa is estimated within the Platinum class cluster using the proposed model presented in Eqs. (9) and (13) for a simplistic scenario as well as using the packet bundling approach, respectively. The results are presented in Fig. 3, which shows the capacity comparison in a simplistic scenario as well as packet bundling while using the 16QAM modulation scheme w.r.t. different AMR-WB voice codecs across the bandwidths available for LTE-A. Further, the capacity is also estimated using CA for $n$ = 2 to 5. From the results presented in Figs. 3A–3C it is observed that, under the Platinum class cluster, AMR-WB 12.65 and 8.85 give the same result, whereas the lower-order voice codec, i.e., AMR-WB 6.60 gives a significantly better result. Further, it is observed that the packet bundling factor gives significantly better capacity as compared to the simplistic approach. Furthermore, it is observed that the Platinum class occupancy is more than the Silver class occupancy in terms of the number of active voice subscribers.

LTE-A cell capacity in gold class cluster

The LTE-A CCa is estimated within Gold class cluster using the proposed model presented in Eqs. (9) and (13) for simplistic scenario as well as using packet bundling approach respectively. The results are presented in Fig. 4, which shows the capacity comparison in simplistic scenario as well packet bundling while using 64QAM modulation scheme with respect to different AMR-WB voice codecs across the bandwidths available for LTE-A. Further, the capacity also estimated using CA for $n$ = 2 to 5. From the results presented in Figs. 4A–4C it is observed that, under Gold class cluster, the lower order voice codec, i.e., AMR-WB 6.60 gives significantly better result then higher order voice codecs. Further it is observed that packet bundling factor gives significantly better capacity as compared to the simplistic approach. Furthermore it is observed that, the Gold class occupancy is more than Platinum class occupancy in terms of number of active voice subscribers.

LTE-A cell capacity in diamond class cluster

Table 2 is presented for system parameters considered for this work. The LTE-A CCa is estimated within Diamond class cluster using the proposed model presented in Eqs. (9) and (13) for simplistic scenario as well as using packet bundling approach respectively. The results are presented in Fig. 5, which shows the capacity comparison in simplistic scenario as well packet bundling while using 256QAM modulation scheme w.r.t. different AMR-WB voice codecs across the bandwidths available for LTE-A. Further, the capacity also estimated using CA for $n$ = 2 to 5. From the results presented in Figs. 5A–5C it is observed that, under Diamond class cluster, the lower order voice codec, i.e., AMR-WB 6.60 gives significantly better result then higher order voice codecs. Further it is observed that packet bundling factor gives significantly better capacity as compared to the simplistic approach. Furthermore it is observed that, the Diamond class occupancy is more than Gold class occupancy in terms of number of active voice subscribers.

LTE-A overall cell capacity

The LTE-A CCa is estimated within Diamond class cluster using the proposed algorithm presented in Algorithms 1 and 2 for simplistic scenario as well as using packet bundling approach respectively. The results are presented in Fig. 6, which shows the capacity comparison in simplistic scenario as well packet bundling. Here the overall LTE-A CCa is obtained by distributing the resources among cell clusters using the factor $f$. The LTE-A CCa is estimated using CA using $n$ = 2 to 5. From the results presented in Figs. 6A–6C it is observed that, lower order voice codec gives better result then higher order voice codecs. Further it is observed that packet bundling factor gives significantly better capacity as compared to the simplistic approach. It is also observed that the radio resource distribution $f$ can be adjusted as per the traffic condition in different clusters to optimize the capacity. Further, $f$ can be used to analyze the data offloading, which improves the network efficiency as it is reported in Agamy & Mohamed (2021).