2015 International Conference on Advanced Technologies for Communications (ATC)

Performance Analysis of IEEE 802.11n CSMA/CA 4×4 Multi-User MIMO in Erroneous Channel Duc Nguyen Thanh∗ , Gyoung Tae Ha† , Seokjoo Shin∗‡ ∗ Computer

Engineering Department, Chosun University, South Korea. e-mail: {ducnt, sjshin}@chosun.ac.kr † IsaacLandKorea, Inc. e-mail: [email protected] ‡ Corresponding author: Seokjoo Shin

Abstract—Multi-user multiple-input multiple-output (MUMIMO) aware carrier sense multiple access with collision avoidance (CSMA/CA) is a simple MAC-layer approach toward MIMO adaptability in next generation IEEE 802.11n to boost the overall network performance. However, it is hypothetically that, the performance in terms of MAC throughput and delay of CSMA/CA-adopted MU-MIMO WLANs significantly degrade as the number of active stations increases, especially in scenarios where each station’s load approaches its saturated condition as well as in environments where channels experience faded. In this paper, we propose modified MAC-layer control frames including request-to-send and control-to-send frames for CSMA/CA 4×4 MU-MIMO transmission. We then numerically model a system adapted Markovian chain to characterize the exponential backoff distribution of CSMA/CA process in 4×4 MU-MIMO WLAN scenario, taking the erroneous channel into account. Based on the probability model, the network performance in terms of MAC saturation throughput and average access delay are analyzed. The numerical results clearly demonstrate the substantial impacts of the number of active stations involved in transmission as well as erroneous channel on the performance. Index Terms—4×4 MU-MIMO, CSMA/CA, IEEE 802.11n, exponential backoff, numerical performance, transmit probability.

I. I NTRODUCTION IEEE 802.11n has standardized the carrier sense multiple access with collision avoidance (CSMA/CA) scheme as the shared-channel MAC protocol for multiple access in wireless local area network (WLAN), which has also been implemented in many wireless testbeds and simulation tools to reduce collision occurrence and hence to boost the network performance [1] [2]. CSMA/CA mechanism utilizes request-to-send (RTS) and clear-to-send (CTS) messages to assure both parties involved in the transmission are ready for the process. In this mechanism, if a station keeps track of the channel activity and remarks it idle for more than the DIFS interval, the station sends RTS packet to inform specifically intended receivers a upcoming packet. The RTS packet also triggers the intended receivers to response their receptivity with a CTS packet. Other stations within the network which overhear the RTS and CTS should update their network allocation vector (NAV) and defer their transmissions until the deferred time has elapsed. The transmitting station is only allowed to transmit its packet if the CTS packet is correctly received. The last ten years have witnessed the transition of multipleinput multiple-output (MIMO) communication from a theo-

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retical concept to a practical technique for enhancing performance of a wireless networks [3]. Realizing the advantages of the MIMO system over existing WLANs requires dramatic modifications in its MAC protocol [4], [5]. There are two possibilities for MAC protocol modifications that are taken into consideration. The first possibility is to replace the dominant MAC protocol CSMA/CA by a novel MIMO aware MAC protocol and the second is to upgrade CSMA/CA MAC protocol into MIMO aware CSMA/CA [6]. Nevertheless, the simplest approach would be inheriting the concurrently widely deployed MAC CSMA/CA protocol and upgrading it with MIMO awareness. An appropriately modified control packet exchanges provisioned with an adequately carried out channel access mechanism based on CSMA/CA request-to-send/clearto-send access scheme can upgrade it into a simple yet practical MIMO aware MAC protocol. Additionally, properly modified CSMA/CA MAC protocol cognized MIMO can support both the single user spatial multiplexing based MIMO (SU-MIMO) and the multiuser spatial multiplexing based MIMO (MU-MIMO), which are expected to flexibly boost the network performance in wide range of communication conditions. However, to take the full advantages of MU-MIMO in existing WLANs, significant changes are required in order to upgrade conventional MAC protocols into MU-MIMO aware MAC. The modified MUMIMO aware CSMA/CA MAC protocol differs from conventional CSMA/CA in which the channel state information (CSI) of all intended receivers is required at the transmitter such that the interference situations are known. Fig 1 illustrates CSMA/CA 4x4 MU-MIMO transmission scheme with modified RTS and CTS. An AP wishes to send up to four independent data streams to up to four different receivers by the use of MU-MIMO technique. It initializes MU-MIMO technique by broadcasting an RTS packet explicitly containing all series MAC addresses in address field of the intended receivers. Each individual receiver station replies a received RTS packet with a individual CTS packet, which also contains the CSI, in the same serial order. When the negotiation procedure is finished, the AP with known CSIs are able to determine the interference situation and it applies precoding and sends parallel data streams. Finally, upon successful reception packets, each individual receiver acknowledges their receiving by ACK packet transmission in the same order as the CTS transmission.

2015 International Conference on Advanced Technologies for Communications (ATC)

Fig. 1: CSMA RTS/CTS 4×4 MU-MIMO transmission technique

The performance characteristic of the modification of CSMA/CA aware 4x4 MU-MIMO MAC protocol in different wide channel fading conditions is the interest of this paper. Specifically, we numerically model 4x4 MU-MIMO transmission, taking into account the CSMA/CA modified protocol by adapting a well-known Bianchi model. Then, the performance in terms of throughput and delay are able to be analyzed. II. R ELATED W ORK Modifications of CSMA/CA MAC protocol detailed for MU-MIMO deployment have been explicitly studied in prior researches [5]- [7] by either mathematical analysis or simulation models. For instance, [5] presented a modified DCF-MAC protocol with multiple RTS handshake MAC and modified channel access mechanism to use for MU-MIMO transmission. Anup in [6] investigated three basic types of modification approaches for control frames (RTS and CTS), and then provided detailed performance analysis based on built-in mathematical expressions adapted Markov chain. Next, a distributed MUMIMO MAC protocol using a leakage based precoding scheme from [4] had been proposed by Lin Cai in [8]. The authors used modified RTS and CTS control packets exchange with an accordingly modified channel access mechanism to have a negotiation about the antenna weights between transmitter and receivers. Along with simulation studies, an analytical model to study the performance related to network throughput of the proposed MAC protocol was also presented. Similarly, in [9] MIMO-DCF MAC, using modified control packets and channel access mechanism to exchange the antenna selection information for both the SU-MIMO and MU-MIMO in AdHoc WLANs, had been proposed. The paper [7] compared the implicit and explicit methods of providing channel state information (CSI) to the transmitter in a MU-MIMO system as specified in the draft specification IEEE 802.11ac. The comparison was made on the basis of packet-error-rate (PER) performance and signal-to-noise (SNR) parameter represented as quality of the channel with different modulation and coding schemes. Up to the author’s knowledge the impact of erroneous channels has not be considered analytically therein references. Therefore, the numerical derivation of 4×4 MUMIMO transmission in erroneous channel is the primary

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interest of this paper. Then, we provide detailed performance analysis regarding throughput and delay based on the analytically modeling and derived expressions. III. S YSTEM M ODEL In this section, we propose a mathematical system for IEEE 802.11n MU-MIMO transmission based on a well-known 2D discrete time Markov chain [10], taking the non-ideal channel into account as an extension, in order to estimate the transmission probability τ of the 4×4 MU-MIMO system with modified CSMA/CA mechanism. Then, using the computed τ , we analyze the different discrete events that can occur within the MU-MIMO channel transmission. A. Modeling of CSMA/CA IEEE 802.11 DCF Let us consider a scenario consisting of a fixed number n of contending station, with each is modeled by a twodimensional Markov process denoted (s(t),b(t)). And let s(t) be the stochastic process that represents the backoff stage of a given station at a time slot t. Let b(t) be the stochastic process representing the size of the backoff window of the station at the time slot t. In the IEEE 802.11 DCF backoff algorithms, a station will enter backoff procedure if the channel is sensed during DIFS duration by uniformly choosing a backoff time in the range (0, W − 1). A station will transmit a packet at the beginning of a time slot if its backoff value is decremented and reaches zero. Otherwise, the station will enter the next backoff i with exponential backoff time Wi = 2i W . After each unsuccessful transmission, backoff window is doubled, up to a maximum value 2m W with m is the maximum retransmission attempt. The transition probabilities p from one stage to another (e.g. transition from row i − 1 to row i in the Fig 2) provided in 3 are precisely explained in [11]. Probability p is also the probability of an unsuccessful (re)transmission attempt seen by a test station as its frame is being transmitted on the channel. The unsuccessful (re)transmission attempt can happen due: 1- Collision of this station with as least one of the n − 1 remaining stations, thus, causing the collision probability p1 : p1 = 1 − (1 − τ )n−1

(1)

2015 International Conference on Advanced Technologies for Communications (ATC)

Note that the transmission occurs only when the station is in the stage (i, 0), the transmission probability τ that a station transmits in a randomly chosen slot can be obtained as: τ=

m X

bi,0 =

i=0

m X

pi · b0,0 =

i=0

1 − pm+1 · b0,0 1−p

(6)

Then, the probability bi,k can be generally expressed as: bi,k =

Wi − k · bi,0 Wi

(7)

The normalized stationary distribution of the chain is 1, then we have: Fig. 2: Finite-state station model in saturation based on Markov chain of the backoff window size

1= =

m WP i −1 P

i=0 k=0 m P

i=0

2- An error frame, occurring with probability Pf (due to the channel error and/or noise). The relation of Pf and SNR are explicitly studied in [7] and inherited in this research. Since both events are independent, the probability p can be expressed as: p = 1 − (1 − p1 )(1 − Pf ) = p1 + Pf − p1 Pf

(2)

In case of an unsuccessful transmission retry, after the backoff window reaches zero in the stage (i − 1, 0), the station moves to the backoff stage (i, k) with probability p/Wi (contention window k which is uniformly chosen in the range (0, Wi − 1)). Following a successful transmission (that occurs with probability 1 − p) while the station is in stage (i, 0), a new frame is arrived in the queue, the station returns backoff stage (0, k) with probability (1 − p)/W0 , contention window k is any integer in range (0, W0 − 1). If the station reaches its maximum backoff stage m, and once its backoff timer decrements to zero, the transmission can be done successfully or unsuccessfully. In both cases, the station resets its backoff stage to zero (0, k), k ∈ (0, W0 − 1) with probability 1/W0 and is ready for new transmission with a new frame arrived in the queue. P {i, k|i, k + 1} = 1; k ∈ (0, Wi − 2); i ∈ (0, m) P {0, k|i, 0} = (1 − p)/W0 ; k ∈ (0, W0 − 1); i = 0 P {i, k|i − 1, 0} = p/Wi ; k ∈ (0, Wi − 1); i ∈ (1, m)

(3)

P {m, k|m, 0} = p/Wm ; k ∈ (0, Wm − 1); i = m Let the stationary distribution of the chain be bi,k = lim P {s(t) = i, b(t) = k}, i ∈ (0, m); k ∈ (0, Wi − 1), t→∞ denoting the probability of a station to be in the stage (i, k). Clearly observe the probability of a station to be in the stage (i, 0) can be obtained from the probability of the station to be in the stage (i − 1, 0) as follows: bi,0 = bi−1,0 · p

(4)

bi,0 = b0,0 · pi

(5)

Thus, lead to:

402

bi,k =

m P

i=0

bi,0

WP i −1 k=0

Wi −k Wi

=

m P

i=0

bi,0 Wi2+1

b0,0 · pi · Wi2+1

(8) Deriving this numerical equation by using Mathematica tool, we can derive the Equation 10. Thus, probability when a station is at first backoff stage and its backoff window size is zero can be ontained as in the Equation 11. We finally attain the transmission probability τ , which is the main target of the numerical model, as expressed in the Equation 12. B. MU-MIMO Saturation Throughput Now, we use the numerical model to compute the 4×4 MUMIMO system throughput S in saturation conditions, defined as the fraction of time the channel is used to successful transmit payload bits. Following a similar reasoning model from [11], during the MU-MIMO transmission in an errorprone channel, the throughput can be given as in Equation 13. Where Ptr is the probability that there is at least one active transmitting station in a given time slot with n stations contending for the channel, with each has transmission probability τ: Ptr = 1 − (1 − τ )n (9) )n−1 Ps = nτ (1−τ Ptr Ps is the probability of a successful transmission. Pf , as aforementioned, is the frame error probability in the erroneous channel. Similarly, E[Pj ] is the average frame payload size in bits transmitted for the stream j, 1 ≤ j ≤ K; K ∈ [1, N ], although to establish upper performance limit in the numerical analysis, we assume all active stations within the backhaul transmit fixed packet lengths and similar Access Category (AC). Where N is the number of supported antennas. In 13, Ts and Tc are the average times when the channel is found to be busy because of the successful transmission or collision, respectively, whereas σ is the duration of an empty slot time. Note that the value units of Ts , Tc and σ must be presented the same. Ts and Tc in our investigated approach can be attained as in the Equation 14. Where K is the number of active stations in MU-MIMO transmission scheme. In 4×4 MU-MIMO, the value of K is four.

2015 International Conference on Advanced Technologies for Communications (ATC)

1=

(1 − 2p − p1+m + 2p2+m + W − pW − 21+m p1+m W + 21+m p2+m W )b0,0 2(−1 + p)(−1 + 2p)

(10)

2(1 − p)(1 − 2p) (1 − 2p − p1+m + 2p2+m + W − pW − 21+m p1+m W + 21+m p2+m W )

(11)

b0,0 =

τ=

2(1 − 2p)(1 − pm+1 ) 2(1 − 2p)(1 − pm+1 ) + W (1 − p)(1 − 2m+1 pm+1 ) Ps Ptr (1 − Pf )

SM U −M IM O =

K P

(12)

E[Pj ]

j=0

(1 − Ptr )σ + Ptr Ps (1 − Pf )Ts + Ptr (1 − Ps )Tc + Ptr Ps Pf Te

Ts = TDIF S + TRT S + (2K + 1)TSIF S + KTCT S + TDAT A + KTACK Tc = TDIF S + TRT S

(13)

(14)

C. Average Delay Let D be the average access delay, defined as the time difference between a time point when a packet is at the head of its MAC queue waiting to be transmitted and a time point that ACK packet is received for that packet. In our analysis, the average access delay can be derived following the mathematical model given in [10] as: D=

Fig. 3: The modified control frame format for CSMA/CA 4×4 MU-MIMO MAC protocol

E[n] S/E[P ]

(15)

where the numerator E[n] is the average number of competing stations that will successfully delivers their packets, and the denominator S/E[P ] represents the packet delivery rate. E[n] can be obtained from following expression: E[n] = n[1 − Pdrop ]

(16)

where Pdrop is the packet drop probability depending on the number of already suffered transmissions and that is computed from [10]: Pdrop = τ (1 − p)

m pm+1 X (1 + E[bi ]) 1 − pm+1 i=0

(17)

Final, with the above circulated relations, D can be achieved as: m n pm+1 X D= ¯ (1 + E[bi ]) − E[Slot](1 − B0 ) 1 − pm+1 i=0 S/E[P ] (18) where S¯ is the throughput of the corresponding antenna element while E[Slot] is as:

E[Slot] = (1 − Ptr )σ + Ps Ptr T¯s + (1 − Ps )Ptr Tc

Fig. 4: The transmission probability performance

(19)

with T¯s is the average of the successful transmission times for the respective antenna elements, and B0 = W01+1

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2015 International Conference on Advanced Technologies for Communications (ATC)

(a) ’Saturation Throughput’.

(b) ’Average Access Delay’

Fig. 5: 4×4 MU-MIMO performance TABLE I: System parameters with the modified CSMA/CA MAC protocol for 4×4 MU-MIMO. Parameters DIFS SIFS Slot interval PHY header MAC header RTS packet CTS packet ACK packet Basic data rate Minimum contention window Maximum backoff stage

Value 34 µs 16 µs 9 µs 40 µs 272 bits 304 bits 144 bits 112 bits 13 Mbps 16 6

Fig. 7: The transmission probability with respect to SNR values

IV. P ERFORMANCE A NALYSIS In this section, we present the numerical performance based on the above derived mathematical expressions taken into account all parameters shown in the Table I, the parameters are obtained from IEEE 802.11n [12]. The parameter selections for the numerical analysis have been adopted in such a way that they could insure the interoperability between MIMO adapted and MIMO less WLANs. The MAC header and PHY header have been adopted from IEEE 802.11n mixed mode transmission. A slightly modified header has been made to accomplish maximum up to four MU-MIMO receivers. Fig 3 shows the modified control frames for 4×4 MU-MIMO transmission, where the RTS and CTS packets are modified from the conventional forms to append information relating to

Fig. 6: The packet drop probability

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2015 International Conference on Advanced Technologies for Communications (ATC)

for transmission, leading to the collision probability follows the increasing trend and that ultimately increase the delay. The effect of erroneous channel on the network performance is also evidently seen from these above-mentioned figures and clearly shown in Fig 7, Fig 8. The performance reaches its fully optimum when the channel is error-free. As the channel is becoming worse (smaller SNR), causing to the more number of wrongly-detected packets is received, and as a consequences degradation of the throughput and increase of the delay are obtained. V. C ONCLUSION

Fig. 8: The average access delay with respect to SNR values

the receiver addresses and CSI, correspondingly. In our analysis, we consider the frame aggregation scheme defined in IEEE 802.11n, which is mainly purposed for MUMIMO transmission, to specify the length of individual packet then use them for numerical throughput calculation. It is important to note that frame aggregation is the technique that compresses two or more frames into a single frame before transmitting it within a single transmission opportunity (TXOP). The scheme aims at reducing the PHY and MAC headers when transmitting multiple packets during a single TXOP, thus explicitly boost the overall throughput. IEEE 802.11 standardizes two types of frame aggregation schemes: aggregate MAC service data unit (A-MSDU) and aggregate MAC protocol data unit (A-MPDU). In our analysis, an AMSDU aggregation scheme in which the MSDU size is kept constant at 1500 bytes is put into consideration. The numerical results in terms of transmission opportunity probability, saturation throughput and average access delay, frame error probability as well as packet drop probability due to erroneous channel with respect to the number of active stations in the 4×4 MU-MIMO are presented in Fig 4, Fig 5a, Fig 5b and Fig 6 respectively. Clearly shown that the number of active stations n has critical impact on the network performance as its increased values lead to degrade overall throughput and increase access delay. This is because when there is fewer number of stations wishing to hold the channel, the probability of ideal slots is high. When there are more active stations joining the network, the probability of freechannel is reduced, and as a result that leads the decrease in the throughput. This trend again can be clearly seen from transmission probability in Fig 4, since there are more stations involved in the network the transmission opportunity degrades. The average delay performance within the same scenario is shown in Fig 5b, in which showing that the delay increased with the number of stations. It is obvious that as the number of station increased, there are more packets waiting

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In this paper, we numerically model CSMA/CA IEEE 802.11n MAC protocol deployed in 4×4 MU-MIMO transmission adapted Markovian chain with modified control frames in non-ideal channel. Then, we analyze the achieved saturation throughput and delay performance with respect to the number of active stations and frame error probability due to erroneous channel. The numerical results clearly show the substantial impacts of channel error and the number of station involved transmission on the network performance. R EFERENCES [1] G. David, K. Marios, W. H. J. Robert, C. Chan-Byoung, and S. Thomas, “Shifting the mimo paradigm,” IEEE Signal Processing Magazine, vol. 24, pp. 36–46, Oct 2007. [2] Z. Hongqiang, K. Younggoo, and F. Yuguang, “Performance analysis of ieee 802.11 mac protocols in wireless lans,” Wireless Communications and Mobile Computing, vol. 4, pp. 917–931, Nov 2004. [3] P. Arogyaswami, G. Dhananjay, N. Rohit, and B. Helmut, “An overview of mimo communications - a key to gigabit wireless,” Proceedings of the IEEE, vol. 92, pp. 198–218, Nov 2004. [4] Z. Sheng and N. Zhisheng, “Distributed medium access control with sdma support for wlans,” IEICE Transactions on Communication, vol. E93-B, pp. 961–970, April 2010. [5] Z. Ting, Y. Yaoqing, E. Steven, Z. Zhangdui, and S. Hamid, “A novel distributed mimo aware mac protocol design with a markovian framework for performance evaluation,” in Military Communications Conference, MILCOM IEEE, Nov 2008, pp. 1–6. [6] T. Anup, P. Subodh, and S. Seokjoo, “Performance characterization of csma/ca adapted multi-user mimo aware mac in wlans,” EURASIP Journal on Wireless Communications on Networking, vol. 1, pp. 1–11, Oct 2011. [7] L. Hanqing, G. Monisha, X. Pengfei, and O. Robert, “A comparison of implicit and explicit channel feedback methods for mu-mimo wlan systems,” in IEEE 24th International Symposium on Personal, Indoor and Mobile Radio Communications: Fundamentals and PHY Track, Sep 2013, pp. 419 – 424. [8] L. Cia, S. Hangguan, Z. Weihua, S. Xuemin, M. Jon W, and W. Zongxin, “A distributed multi-user mimo mac protocol for wireless local area networks,” in Global Telecommunications Conference. IEEE GLOBECOM, Dec 2008, pp. 1–5. [9] M. Jelena, Z. Jing, and D. Dee, “A mac protocol with multi-user mimo support for ad-hoc wlans,” in IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Sep 2007, pp. 1–5. [10] B. Giuseppe and T. Ilenia, “Remarks on ieee 802.11 dcf performance analysis,” IEEE Communications Letters, vol. 9, pp. 765–767, Aug 2005. [11] K. Ponnusamy and A. Krishnan, “Throughput analysis of the ieee 802.11 distributed coordination function considering erroneous channel and capture effects,” International Journal of Automation and Computing, vol. 8, pp. 236–243, May 2011. [12] “802.11n-2009-ieee standard for information technology–local and metropolitan area networks–specific requirements–part 11: Wireless lan medium access control (mac) and physical layer (phy) specifications amendment 5: Enhancements for higher throughput,” Oct 2009, pp. 1– 565.