## 2 Related Work and Our Motivation
### Related Work  
The majority of existing researchers have only attempted to achieve optimization via the trade-off between maximizing throughput and minimizing delay. However, under the effects of uncertain conditions of heterogeneous traffic patterns and channel conditions in a network, throughput and delay are the two most important performance metrics [5; 6; 7; 8; 9] that must be analyzed in frame-aggregation algorithms. Throughput can be improved by increasing the size of the average payload or by reducing the size of overhead frames such as the MAC and PHY headers in a frame. This can be achieved by adopting frame-aggregation algorithms. An adaptive aggregation algorithm called the adaptive aggregation mechanism (AAM) was proposed in [5] that allowed an adaptive trade-off between maximizing throughput and minimizing delay in a single-user WLAN channel. This approach considered the varying nature of the packet size and the packet arrival time to assemble the target aggregate packet size within the minimum delay. However, this approach did not consider the effects of transmission errors and competing stations. The work in [6] demonstrated the existence of the throughput upper limit (TUL) in a WLAN while considering assumptions such as only one sender and one receiver existing in the wireless network, the sender always having frames to be transmitted, and each frame having the same size operating in the distributed coordination function (DCF) mode. They also assumed ideal channel conditions when there were no transmission errors present. The delay lower limit (DLL) in the IEEE 802.11 wireless network using the DCF model was also demonstrated in [6]. The researchers considered best-case scenarios such as an ideal channel condition with only one active station that always has frames to send while other stations can only receive frames and send acknowledgments (ACKs) during any transmission cycle. The main source of delay in the frame-aggregation algorithm was the time spent waiting for more frames to arrive. However, the assumptions of this approach were unrealistic and could not function in the MU-MIMO channel. Moreover, this approach only considered the transmission delay. However, delay of both the queuing time and waiting time in the MAC are the key factors of delay that can significantly increase when using frame aggregation [5]. In [9], a novel method was proposed to determine the frame-aggregation size in a MU-MIMO channel to improve channel utilization while considering the delay during which data frames waited in transmission queues. They attempted to reduce the delay by appropriately determining the aggregation size according to the traffic variation. However, the main focus of this study was to enhance channel utilization, and the effects of channel errors were not elaborated. Some studies have contributed frame-size-aggregation schemes in WLAN downlink MU-MIMO channels [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. For instance, the algorithm in [10] proposed a new approach that aimed to enhance the system throughput performance of a WLAN by employing a dynamic adaptive aggregation selection scheme to determine the optimal length of the frame size in downlink MU-MIMO transmission. The effects of heterogeneous traffic demand among spatial streams were considered under the assumption of an ideal channel. According to the simulation results, the maximum system throughput performance and channel utilization were achieved. By extending this work, an adaptive frame-aggregation algorithm was proposed in [11] while considering the effects of transmission errors. However, both of these studies did not consider the expense of delay. Thus, this led to a suboptimal solution. The current study enhanced the scheme of [11] by considering the issue of delay to achieve the maximum system throughput performance of a WLAN in the downlink MU-MIMO channel. The frame-size-optimization problem has been studied by several researchers for IEEE 802.11 networks.