Performance Tradeoff with Adaptive Frame Length and Modulation in Wireless Network Yafei Hou1, 2 Masanori Hamamura1 Shiyong Zhang2 1
Department of Information Systems Engineering, Kochi University of Technology, Japan 2 Department of Computing and Information Technology Fudan University, P.R.China
[email protected];
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Abstract In this paper, we present the results of analysis which shows that there is much to be gained from variable frame length, different modulations in terms of goodput, range and energy consumption for wireless channel. Using those results, then we obtain three useful rules for the tradeoff with goodput, range and energy consumption with different modulations.
1. Introduction Wireless network links are characterized by rapidly time varying channel conditions and battery energy limitations at the wireless mobile user nodes. Therefore, static link control technology that make sense in comparatively well behaved wired links can not necessarily apply to wireless links and radio channel condition. New techniques are needed to provide robust and energy efficient operation even in the presence of orders of magnitude variations in bit error rates and other radio channel conditions. Recent research has advocated many link layer techniques including error control [1], channel state dependent protocols [2, 3] and variable spreading gain [4]. Especially P. Lettieri and M.B. Srivastava explored one adaptive technique with dynamic sizing of the MAC layer frame [5]. It shows that adaptive sizing of the MAC layer frame in the presence of varying channel noise indeed has a large impact on the user seen goodput (throughput). In addition, it shows that adaptive frame length control can be exploited to improve the energy efficiency for a desired level of goodput, and to extend the usable radio range with graceful throughput degradation. But they assume the modulation is the same and only Maximum Transmission Unit (MTU) changes according to the wireless channel conditions to improve wireless link throughput, range, and energy efficiency. However, with the development of modulation techniques such as SDR (Soft Defined Radio), we can find different modulations can cause different link throughputs, range and energy efficiency. In such a case, the nodes of wireless network can realize the tradeoff between throughputs, range and energy efficiency with different modulations.
The nodes of the wireless network can choose different modulations according to the radio channel condition. Therefore, different symbol lengths of nodes are transmitted into the radio channel, and the success transmission of one node to other nodes depends on two basic independent processes: (1) the time variant radio channel with some specific quality of link must ensure error-free transmission of information packets between nodes; (2) the packets must avoid collision with other nodes. In this paper, we use different modulations to realize the tradeoff between throughputs, range and energy efficiency, i.e. we focus our attention on the process (1) in this paper. The paper is organized as follows. In section II, we show the impact of the length of the MAC layer frames over the user throughput with different modulations. Section III describes the impact of the length on transmission range with different modulations, and the impact of the length on power consumption with different modulations is explained in section IV, then we give the conclusion in sectionV.
2 Frame length versus User Throughput Wireless channel is time varying channel. The channel variations are inherently uncontrollable. Many techniques of modulation and code are developed in order to successfully transmit a packet through a bad radio channel. Fig. 1 gives the probability of bit error (BER) when the system uses QAM with rectangular constellations, a Gaussian channel, and matched filter reception. Many modulations can obtain the same BER with different energy ( Eb / N 0 ) [6], it can be seen from Fig.1, if the system needs the BER not more than 10 −3 , the corresponding Eb / N 0 is about 19.40 [dB] for 256QAM, 14.7 [dB] for 64QAM, 10.5 [dB] for 16QAM and 6.8 [dB] for QPSK. But different modulations will cause different wireless link throughput, range and energy efficiency which we will elaborate the results in following sections. The way we utilize is similar to that of P. Lettieri and M.B. Srivastava [5], but in [5], they only adopt the modulation of QPSK. We develop it to QAM with different rectangular constellations.
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We simulated a wireless link with following parameters: The radio uses M-ary QAM modulations (here we use M-ary QAM with M=4, 16, 64, 256 and incoherent symbol detection). The channel symbol rate is 1M symbols/second MAC uses a CRC field: “bad” frames are reliably detected and dropped.
Fig. 1 BER characteristics for M-QAM modulation
For analysis, we assume a free-space path loss model, with unity gain antennas, no system loss. Note that the results are quite general despite these assumptions. In the first case, we present the system throughput, or goodput. Considering the throughput the user will see, hereafter we prefer to adopt goodput, as a function of frame length over varying bit error rates. The goodput refers to the bandwidth the user actually receives after all overheads are calculated, including such as the MAC and PHY overheads. Beyond these costs however, the goodput will be reduced by the occurrence of frames lost to bit error. Even one bit error inside a frame will result in the loss of that frame, as the CRC will not pass. Each lost frame directly results in wasted bandwidth, as in the time spent sending that frame achieved no forward progress. This loss might also result in the additional signaling overhead of an ARQ protocol. In order to examine the behavior of the system, let us first specify various quantities of interest [5]. Let: LD = length of user data. LO= length of PHY overhead = 52.5 bytes. LH = length of MAC & IP header overhead = 40 bytes. MTU = LD+20bytes. RC = raw bit rate of radio channel = 2 Mbps (QPSK), 4Mbps (16QAM), 8Mbps (64QAM), 16Mbps (256QAM). BER = probability of channel bit error, a function of transmitter power and path loss. G= goodput (i.e. real user level good throughput).
With these quantities in hand, we can specify the normalized goodput as: G LD = (1 − BER ) LD + LH RC LD + LO + LH
1 (1 − BER ) LD + LH (1) LH + LO 1+ LD The equation (1) gives a value for the goodput normalized against raw data in terms of frame length and BER. With the overheads taken constant, we vary the size L of the user data with modulations. The simulated result of Eq.1 for a variety of bit error rates is shown in Fig. 2. The main observation to make from this figure is that as the channel conditions deteriorate, it would be helpful to use a smaller MTU instead of the naive selection of the maximum allowed MTU of 1500. A properly chosen MTU can even improve the goodput on an apparently dead link giving zero goodput. For instance, if the radio channel BER is equal to 5 × 10 −4 and the packet or frame length is longer than 950bytes, system goodput will be zero. But the goodput will be improved to maximum with 0.3 if the packets length will be shortened to the 150 bytes. Fig. 1 shows the same Eb / N 0 for different modulations can cause different BER. With the same Eb / N 0 , the BER of QPSK is the smallest of all four modulations; 256QAM can obtain maximal BER than QPSK, 16QAM and 64QAM but 256QAM can obtain higher RC than QPSK. On the other hand, different BER will result in different goodput which can be seen from Fig. 2. With the above analyses we can get Rule 1: Rule 1: when the power consumption is not the major problem for one node, it is more benefit for this node to adopt modulations with more number of rectangular constellations of QAM, longer length of frame to transmit the packets for obtaining high goodput and RC. But when the energy is limited, the node can maintain high goodput with decreasing number of rectangular constellations of QAM so that the system can maintain the constant BER, for example, using 64QAM, 16QAM and then QPSK with longer length of frame (but shorter length of frame when BER is large(>1e-4)) to replace 256QAM. =
3 Frame length versus Transmission Range Another metric to consider as frame length is varied is transmission range with different modulations. Range of transmitter-receiver distance also means the connectivity of the wireless network. We analyze it in two ways. First, we simulate goodput vs. distance for
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different lengths of packets, as in Fig.3 for different modulations. To do this, we note that for M-ary QAM, we can find the bit error rate is [6]: 6 log L E 2(1 − L−1 ) BER ≈ Q[ ( 2 2 ) b ] (2) log 2 L L − 1 N0 1
where Q ( x ) =
2π
∫
∞
x
exp( −
u2 ) du , and L represents 2
the number of amplitude levels in one dimension (L=2 for QPSK, L=4 for 16QAM, L=8 for 64QAM and L=16 for 256QAM).
Fig.2 Goodput versus packet length
If we further assume a free space path loss model with path loss exponent equal to 2, this simplifies to:
BER ≈ where d =
2(1 − L−1) 6 log L 1 Q[ ( 2 2 ) × ] log2 L d L −1 dr
(Eb / N 0 ) 0 × d 0
(3)
is the transmitter-receiver
separation in some normalized units of distance, Eb / N 0 is the value measured at a receiving point which is distinct from transmitting point with d 0 [m] and d r [m]is the real distance. With the relation between distance and BER, and substituting into the Eq.1, we can find goodput as a function of distance at a particular MTU with different modulations. Fig.3 shows the impact of three types of bit length on the Tx-Rx distance with different goodput and modulations of QPSK, 16QAM, 64QAM and 256QAM. At moderate distances the large MTU is the certainly desirable since goodput is higher, using QPSK as an example, the goodput degrades rapidly with the Tx-Rx distance increasing from 0.4 to 0.6. Over a relatively short distance, goodput goes from maximum to nothing. But if the MTU is variable however, an amount of extension of the range is possible over which meaningful data can be sent. But when the system increases the number of rectangular constellations, that is, using 16QAM, 64QAM, 256QAM to increase the Rc, the Tx-Rx distance will decrease when the system adopts the same bit length.
Fig.3 Goodput versus distance with M-QAM(a: QPSK; b: 16QAM; c: 64QAM; d: 256QAM
On the other hand, in effect, adaptively changing the frame length can allow nodes to smooth the degradation in goodput of a wireless link as distance is
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increased, but the effect decreases with increasing the number of rectangular constellation of QAM. Alternatively, we can simulate range vs. MTU for various values of normalized goodput of different modulations with the same energy as in Fig. 4 (a) to Fig. 4 (d). This is another way of viewing the same equation. First, we choose a constant goodput which the application can accept then set various MTU sizes to show the range with four types of modulations which can be achieved. What these plots shows is that for low levels of desired goodput, a substantial extension in range is possible by reducing MTU to a certain value. If the goodput can be set to 0.1, all four modulations can improve up to 20% in range using minimum length of packet to instead of maximum one. But the improvement in range decreases when the goodput increases. On the other hand, with increasing the number of rectangular constellations of the system, the Tx-Rx distance will decrease when the system adopts the same goodput and energy. With the above analyses we can get Rule 2: Rule 2: when the power consumption is not the major problem for one node, it is more benefit for this node to adopt modulations of more number of rectangular constellations of QAM, longer length of frame to transmit the packets for obtaining high goodput and RC. But with the same energy, the larger the number of rectangular constellation of QAM is, the less the range is. So when the energy is limited, the node can maintain high range with decreasing number of rectangular constellations of QAM, for example, using 64QAM, 16QAM and then QPSK with shorter length of frame (but longer length of frame when goodput is high(>0.8)) to replace 256QAM.
QAM, for QPSK, 1.3 units power will be saved but 26 units for 256QAM.
4. Frame length versus Transmitter Power Consumption Another relationship can be found for battery power to frame sizes with different modulations over various allowable goodput by simulating energy per bit vs. bit length in Fig.6. Fig. 6 shows that there is a substantial improvement in energy consumption for a given level of goodput, especially for the high goodput. For all four modulations, the power consumption increases with increasing the number of rectangular constellations of QAM. 256QAM needs much more power than QPSK at the same level. On the other hand, it is more benefit for the system to use longer packet when the goodput is more than 0.8, in this situation, shorter packets which is smaller than 400bytes will consume more power than that of 800 bytes. More power will be saved with increasing the number of rectangular constellation of
Fig. 4 Range versus length of packets with M-QAM (a: QPSK; b: 16QAM; c: 64QAM; d: 256QAM)
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With the above analyses we can get Rule 3:
Rule 3: when the power consumption is not the major problem for one node, it is more benefit for this node to adopt modulations of more number of rectangular constellations of QAM, moderate length of frame to transmit the packets for obtaining high goodput and RC. But the larger the number of rectangular constellation of QAM is, the more power consumption is. So when the energy is limited, the node can save power with decreasing number of rectangular constellations of QAM, for example, using 64QAM, 16QAM and then QPSK with moderate length of frame (but shorter length of frame when goodput is small(
