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Design of coherenceaware channel indication and prediction for rate adaptation
EURASIP Journal on Wireless Communications and Networking volume 2019, Article number: 201 (2019)
Abstract
A number of rate adaptation protocols have been proposed using instantaneous channel quality to select the physical layer data rate. However, the indication of channel quality varies widely across platforms from simply a received signal strength level to a measurement of signaltonoise ratio (SNR) across subcarriers, with each channel quality indicator having differing levels of measurement error. Moreover, due to fast channel variations, even aggressive channel probing fails to offer an uptodate notion of channel quality. In this paper, we propose a coherenceaware Channel Indication and Prediction algorithm for Rate Adaptation (CIPRA) and evaluate it analytically and experimentally, considering both the effects of measurement errors and the staleness of channel quality indicators. CIPRA uses the minimum mean square error (MMSE) method and firstorder prediction. Our evaluation shows that CIPRA jointly considers the time interval over which the prediction will occur and the coherence time of the channel to determine the optimal window size for previous channel quality indicator measurements. Also, we demonstrate that CIPRA outperforms existing methods in terms of prediction fidelity and throughput via experimental results. By combining a strong channel indicator with the coherenceaware MMSE firstorder channel prediction algorithm, CIPRA nearly doubles the throughput achieved in the field from the indication and prediction method currently used by offtheshelf WiFi interfaces.
Introduction
Channel fluctuations often exist in wireless communication systems and present great challenges in selecting the best data rate or modulation coding scheme (MCS) for communication. When there is a change in direction of the transmitter/receiver, antenna elevation and polarization, interference from nearby devices, or scatter distributions, the channel quality can vary, resulting in fluctuations in signal reception, even within the same environment. Depending on the magnitude of the variation, the received signal strength (RSS) can drastically change the link performance [1–4]. Rate adaptation protocols can be implemented to combat the fading channels and achieve high spectrum efficiency by dynamically changing the data rate according to the channel quality.
Rate adaptation protocols that depend upon packet success/failure information have been implemented in commercial equipment and widely discussed [5–10]. However, these lossbased protocols usually require tens of data frames to develop a reasonable estimate of the channel conditions. Other factors such as hidden terminals and interference can lead to inappropriate conclusions about the causes for the losses [11]. Thus, for fastfading channels (e.g., in vehicular networks), these protocols cannot accurately track the changing channels, resulting in wrong selections of MCS. Moreover, packetlevel estimation is too coarse to achieve an accurate estimation of the instantaneous channel conditions. With interfering sources, the transmitter can not distinguish the reason for packet loss and jitter (i.e., whether it is from a poor channel or interference). These factors contribute to frequent underselection of the transmission rate by lossbased protocols [11].
To enable fastfading channel tracking, various channelindicatorbased rate adaptation protocols have been proposed [12–15]. It is well known that for a certain MCS, there is a theoretical bit error rate (BER) versus signaltonoise ratio (SNR) relationship [16]. SNR values can be reported to the transmitter at the physical layer (PHY)frame level to enable selection of the optimal rate in fastfading channels. Some of the SNRbased rate adaptation protocols leverage the received signal strength indicator (RSSI) to calculate the SNR. However, for different commercial wireless network devices, the RSSI varies significantly for the same received signal strength. Moreover, in the presence of interference and noise, the estimates of the signal power reported from RSSI measurements can be highly distorted [17]. In [13], the authors propose a SoftRate metric to indicate channel quality and select the optimal rate for transmission. However, this scheme requires a softin, softout decoder to calculate the SoftRate indicator, which is not available for most of the existing network transceivers and may also be resourceintensive for the design of future transceivers. AccuRate, a constellationquality based indicator is provided in [15]. Nevertheless, the hardware cost and complexity of AccuRate is also high, often precluding the calculation of the channel indicator in the implementation. The Effective SNR metric [14] leverages the channel response in the frequency domain and the noise variance on each subcarrier to predict the best rate to transmit a packet. The information required is already available in several wireless network interfaces.
In our previous work [12], we consider RSSI as the unique channel indicator under limited comparison matrices, which has been shown to be inaccurate and inconsistent across vendors [13]. In this work, in addition to the original channel indicator of RSSI, we study and analyze two more advanced channel indicators: SNR and Effective SNR. We implement channel prediction and rate adaptation based on these two advanced metrics to evaluate their performance in combination with traditional channel prediction methods and our proposed channel prediction method, showing significant throughput improvement. We additionally analyze the prediction error performance for our proposed algorithm at various time intervals, predicting the importance of our work on nextgeneration protocol design with higher frequency bands and tighter timing parameters. At last, we implement the Minstrel rate adaptation and compare our proposed rate adaptation method with it, showing that our proposed rate adaptation method outperforms Minstrel significantly.
Typically, in SNRbased rate adaptation, the receiver decides the rate of the next transmitted packet according to the measured SNR of the current packet, whether the measurement originates from the RTS/CTS or DATA/ACK exchange [11]. Several potential problems exist with this mechanism. First, if the channel changes quickly or there is a large time interval between two adjacent packets, the SNR reported by the last transmission may not accurately represent the instantaneous channel quality. Second, the SNR reported during the last transmission may not be accurate due to measurement errors. Even for slowly varying channels, there might be rate overselection or underselection due to channel quality estimation errors.
The rate selection problems caused by channel quality estimation errors have been studied [16, 18]. In order to increase the accuracy of rate selection, both works as leveragefiltering techniques to reduce channel quality estimation errors. However, the delay incurred in filtering can make rate selection even more stale to track with ongoing channel quality changes. To address the channel quality staleness problem, channel prediction has been extensively studied [19–23]. However, most work assumes perfectly accurate channel measurements to predict the future channel state, which may not be possible in hardware. Moreover, the estimation error can make the prediction highly erroneous if using the reported value from the last transmission.
In this paper, we propose a coherenceaware MMSE firstorder prediction algorithm that takes into account both the measurement inaccuracy and measurement staleness. Prediction intervals and channel coherence time are jointly considered to select the optimal size of prediction window. We perform simulation studies as well as infield experimentation on emulated and infield channels, respectively. For our analysis, we implement an IEEE 802.11 PHY system on WARP (Wireless OpenAccess Research Platform), an field programmable gate array (FPGA)based platform [11]. We also implement and compare three different channel indicators, RSSI, SNR, and Effective SNR, and combine each with the proposed prediction algorithm to investigate the indicator’s impact on the performance of channel prediction. To generate repeatable channel effects, we test our design on a channel emulator and compare the three indicators in diverse channel conditions. In addition to lab experiments, we also conduct field tests to show the in situ throughput improvements provided by our algorithm.
The main contributions of our work are as follows:

1
We propose a coherenceaware MMSE firstorder channel quality prediction algorithm, which takes into account both the measurement errors and staleness of the channel quality. This scheme adapts the measurement processing parameters to the Doppler shift to achieve good performance under various mobility scenarios.

2
We implement and evaluate a family of the most commonly used channel quality indicators for rate adaptation, including RSSI, SNR, and Effective SNR.

3
We analyze different channel prediction approaches and compare them in terms of prediction errors as well as overselection and underselection probabilities for rate adaptation.

4
We present and implement a Doppler shift estimation method based on LCR (levelcrossing rate) with a homogeneous window to remove the effect of channel quality measurement errors, achieving a good balance of complexity and accuracy.

5
We implement the existing channel prediction algorithm and the proposed algorithm on WARP and experimentally compare them in terms of system throughput through both repeatable channel emulator tests and infield experiments. By combining Effective SNR with the coherenceaware MMSE firstorder channel prediction algorithm, channel indication and prediction for rate adaptation (CIPRA) achieves up to a 98% throughput improvement in the field over the indication and prediction method currently used in offtheshelf cards.
The rest of this paper is organized as follows. Section 2 introduces the online Doppler shift estimation method and discusses various channel quality indicators. Then, we describe the framework of our proposed CIPRA algorithm and compare its performance with conventional prediction algorithms in Section 3. In Section 4, we introduce the hardware setup for CIPRA evaluation and provide numerical results in Section 5. Finally, we conclude our work in Section 6.
Background and related work for channel indication and prediction
In this section, we first introduce the channel fading model used in this work. Then, we describe a Doppler shift estimation method for our platform implementation. Finally, in addition to the typical performance metrics developed to indicate the channel quality, such as RSSI and SNR, we study and analyze a more advanced channel quality indicator: Effective SNR.
Channel characteristics
Wireless channel quality is often affected by changing environments and interference. With the transmit signal power fixed, channel quality can be quantified by the received signal quality. We use a Rayleigh fading channel model in the following analysis and simulation. The normalized autocorrelation function, R(τ), of a Rayleigh fading channel with motion at a constant velocity is a zerothorder Bessel function of the first kind [24, 25]:
Here, τ is the time delay, and f_{d} is the maximum Doppler shift. The autocorrelation functions of a Rayleigh fading channel with a maximum Doppler shift of 10 Hz and 20 Hz are shown in Fig. 1. This autocorrelation reflects the statistical dependence between the channel gains at different times, which is leveraged in the prediction.
Online doppler shift estimation
In this work, we introduce a Doppler shift estimation method that we implement and evaluate on our hardware platform. This method can be applied to our channel prediction algorithm discussed in Section 3. In general, Doppler shift estimation can leverage channel estimates, LCR, a maximum likelihood function, or correlation function [26]. LCRbased Doppler shift estimation achieves a good balance between complexity and accuracy. For Rayleigh fading channels, LCR is expressed as [27]:
Here, ρ is the threshold normalized to the root mean square (RMS) signal level [27]. For a fixed Doppler shift, the LCR achieves its maximum value, LCR_{max}, when \(\rho =\sqrt {0.5}\), and is given by
In hardware, the received signal is also corrupted by additive noise. The LCR resulting from the noise usually leads to overestimation of the channel levelcrossing rate. In [28], an fast Fourier transform (FFT)based Doppleradaptive noise suppression method is proposed to remove the effect of additive noise on LCRbased Doppler shift estimation. However, the FFT/IFFT processing is computationally expensive, requiring approximately \(\frac {34}{9}N\log _{2} N\) real multiplications and additions for an Npoint FFT/IFFT [29]. In this paper, we create a homogeneouswindow method to avoid overestimation caused by the additive noise. The main steps to this method are the following:

1
Pick a threshold value from a predefined threshold set and compare the RSSI samples with this threshold. If the RSSI value of sample i is greater than the selected threshold for each indicator, c_{i}=1. Otherwise, c_{i}=0, meaning that the RSSI is below the selected threshold.

2
Apply a sliding time window τ to the results in step 1. If c_{i}==1 for all the samples in window τ, we denote the system state S_{i}=1. If c_{i}==0 for all the samples in window τ, we denote the system state S_{i}=−1. Otherwise, S_{i}=0. For multiple adjacent system state samples with the same value, only record one sample.

3
Calculate the derivative of the state vector recorded in step 2 and count the number of transitions of the derivative from negative to positive in one second, denoted by n.

4
Repeat step 1 to step 3 for all the values in the predefined threshold set, and finally, find the maximum value of n.
To decide the time window τ, we jointly consider the RSSI sample period and the Doppler shift range we want to estimate. In the IEEE 802.11 standard, the RSSI is reported every packet. For the maximum Doppler shift range of 10 to 100 Hz, τ of 3 ms achieves a normalized square error of 0.003 in our experiments using the channel emulator. Figure 2 shows the Doppler shift estimation by using the WARP board and the channel emulator (both are described in Section 5).
Channel quality indicators
RSSI: a poor channel indicator
Wireless channel quality is often affected by changing environments and interference. With the transmit signal power fixed, channel quality can be evaluated by the received signal quality. The most accessible channel quality indicator is RSSI [17]. RSSI is a relative value with offtheshelf devices in which vendors usually use arbitrary scales from 0 to maximumRSSI, where maximumRSSI is vendorspecific. RSSI is often not associated with any particular power scale and not required to be of any particular accuracy or precision [30]. Hence, the received signal strength numbers reported by a network interface are inconsistent across vendors and should not be assumed to be representative of a particular channel state.
We now carry out experiments to evaluate the reliability of using RSSI as the channel indicator. We use one WARP as the transmitter to send a signal with 10 MHz bandwidth and  62 dBm power and directly connect it to another WARP receiver with a coaxial cable. The reported RSSI values from our WARP receiver are shown in Fig. 3. We can see that, even with the same transmit power and channel state, the reported RSSI values can vary as much as 14 dB. Even if we use a filter to reduce the variance of the reported RSSI, other factors may also greatly affect the RSSIbased channel quality prediction accuracy. The general system architecture for the signal path is shown in Fig. 4. Any error or interference generated by the components in group 1 may vastly affect the received BER, but may not affect the RSSI value. Any error or interference generated by the components in group 2 may affect the RSSI value, but may not significantly affect the BER. Therefore, for different transmitter and receiver pairs, system components internally have different performances. The factors that might affect the channel quality estimation accuracy using RSSI include the following:

1
Phase noise. With the same RSSI, there might be different phase noises caused by the jitter of the clocks on both the transmitter and the receiver, leading to different values of BER. However, the phase noise may not affect the received signal power level.

2
Amplifier nonlinearity. For orthogonal frequencydivision (OFDM) systems, the nonlinearity of both the transmit amplifier and the receive amplifier often cause intercarrier interference (ICI) [31]. ICI may not affect the RSSI, but often affects the received BER performance.

3
RSSI signal noise. RSSI is measured in the transceiver and output in the form of an analog signal, which often suffers from noise and interference on the board.

4
RSSI analog to digital converter (ADC) performance. In a system, an ADC is typically used to convert the RSSI signal from the analog to digital domain. The noise on the board, the resolution of the ADC, and the reference voltage stability of the ADC may all affect the digitized RSSI value.

5
RSSI sample duration. In the IEEE 802.11 standard, RSSI is calculated during the preamble of a PHY frame. The limited duration of the preamble can not guarantee an accurate RSSI estimate.
Considering all the effects listed above, with the same received BER, the receivers often report different RSSI values for different transmitter and receiver pairs. We compare the RSSI values reported (shown in Fig. 5) from two different receivers but with the same signal source and emulated channel. Even with the same received signal, there is about 1.5dB difference of reported RSSI between receivers on average. As a result, the RSSI inconsistency may severely handicap an optimal rate selection decision.
SNR: a more reliable channel indicator
Most of the soft decoders need the SNR or noise variance to calculate the decision probabilities of the demodulated signals. There are diverse SNR estimation methods for OFDM systems. In [32], the author proposes iterative SNR estimation based on pilot subcarriers in an 802.11n system. In [33], an algorithm based on finding the difference between a noisy received sample in the frequency domain and the best hypothesis of the noiseless sample is proposed to estimate the SNR. In this work, we implement an SNR estimation method based on the SchmidlCox algorithm [34] because of its high accuracy and low complexity. In addition, we use the IEEE 802.11 PHY frame as the frame structure in this work, as shown in Fig. 6. One frame is composed of a preamble, a header symbol, and the number of OFDM symbols forming the data payload. One preamble consists of one short preamble and one long preamble [35]. In our design, we take advantage of the known training symbols (two identical OFDM symbols with a 1/2 symbol prefix) in the long preamble to calculate the SNR of the received packet. A detailed calculation can be found in the Appendix 1. We show the SNR distribution plotted in Fig. 7. The SNR has a mean value of 16 dB, with a standard deviation of 0.91 dB. Comparing the RSSI distribution which has a standard deviation of 1.5 dB, we can show that SNR is more accurate than the RSSI as the channel quality indicator.
Effective SNR: a robust channel indicator
Although the SNR estimation is more tightly bounded and consistent with the channel state than the RSSI, a frequencyselective fading channel may disturb the mapping from SNR to BER. However, in a multipath channel, the frequencyselective characteristics may result in a higher BER than a flatfading channel with the same SNR, which corresponds to a lower Effective SNR than the actual SNR (demonstrated in Fig. 8). To solve this problem, Halperin [14] proposed the Effective SNR metric to improve the rate selection accuracy in multipath fading channels. Instead of averaging the SNR on all the subcarriers for SNRbased rate adaptation algorithms, systems implementing the Effective SNR not only average the BER on all the subcarriers but also obtain an equivalent SNR with the same BER as narrowband systems. This process can be represented by [14, Eqs. (1) and (2)]:
Here, ρ_{s} is the SNR on subcarrier s. Assuming the average SNR is ρ and the channel gain on subcarrier s is H_{s}, then ρ_{s} can be calculated as \(\rho _{s} =\rho \frac {H_{s}^{2}}{\bar {H^{2}}}\), where \(\bar {H^{2}}\) is the mean square of the channel gain across all the subcarriers.
In an additive white Gaussian noise (AWGN) channel, the relationship between SNR and BER varies among different modulations [14, 36], as shown in Table 1. In the following discussion and experimental evaluation, we see that Effective SNR outperforms the other channel indicators due to its ability to capture both timeselective and frequencyselective fading effects.
Design of CIPRA
In this section, we analyze different channel prediction algorithms and propose an advanced algorithm to keep the transmitter in step with the fluctuating channel quality. In order to improve prediction accuracy, we take into account both the measurement error of the channel indicator and the staleness of the channel quality reported by the receiver.
Existing prediction methods
The wireless channel usually changes continuously and randomly with time, which makes the implementation of accurate closedform characterization challenging. Nevertheless, a Rayleigh fading channel model is a good approximation and agrees well with empirical observations for mobile communications [25]. In order to select the optimal rate, the transmitter constantly needs the channel quality measurement from the receiver. Prior SNRbased protocols have frequently used the channel quality measured from the last packet transmission to the pertinent receiver [18]. Whether the last packet is a probe packet from the RTS/CTS exchange or simply the last data packet, these channel indicator measurements are stale in fastfading channels. There are several mechanisms to make full use of the previous channel quality measurements for rate adaptation.
Follower
For this mechanism, the transmitter simply copies the channel measurements from the last packet transmission as the predicted value of the ongoing channel quality [18]. In particular, Follower can simply be denoted as \( \hat {\gamma }_{n,\text {follower}}=\gamma _{n1}\), where \(\hat {\gamma }_{n,\text {follower}}\) is the estimate of the ongoing channel quality and γ_{n−1} is the channel quality measurement reported during the last packet transmission. This estimate has minimal complexity but suffers from both measurement errors and staleness of the past channel indicator values.
Moving Average
There are three main kinds of moving average methods: simple moving average, linear weighted moving average (LWMA), and exponential weighted moving average (EWMA) [23]. Simple moving average is the unweighted mean of the previous points in a window size of w. The estimated channel quality \(\hat {\gamma }_{n,\text {MA}}\), is denoted as
Simple moving average method reduces the effect of the measurement errors, while making the staleness effect more serious than the Follower method.
For LWMA, weight factors are assigned to the past measurements in a linear progression with a window size of w. The estimated value \(\hat {\gamma }_{n,\text {LWMA}}\), can be expressed as
LWMA puts greater weight on more recent measurements, which results in a balance between the prediction staleness and the measurement errors.
For EWMA, the weight of the measurements decreases by a factor of δ.
EWMA reduces the number of previous measurements to one and has less computational complexity.
Each of the moving average methods reduces the effect of the measurement errors but introduces more severe staleness effect than the Follower method.
Linear prediction
By assuming that the channel quality indicator has a constant firstorder derivative across three adjacent transmissions [23], we can predict the ongoing channel quality from the last two channel measurements.
Here, γ_{n−1} and γ_{n−2} are the channel measurements at time t_{n−1} and t_{n−2}, respectively. This method is more robust to the prediction staleness. However, the errors of the past measurements may make Δγ twice as noisy, leading to a prediction with an intolerable noise level in some cases.
Coherenceaware MMSE firstorder prediction
Our previous discussion reveals that some of the methods are more robust to the measurement errors, while others are more robust to the prediction staleness. For a good prediction, both the measurement errors and staleness should be considered. In this section, we propose a coherenceaware MMSE firstorder prediction.
In Section 2.1, we introduced the Rayleigh fading model and its autocorrelation. When conducting the prediction, we need the previous measurements within a time window T. From Fig. 1, we see differing dependence between measurements with the same maximum Doppler shift and differing time delay, or with the same time delay and differing maximum Doppler shift. Thus, when selecting the time window T, we should take the Doppler shift into account. We can denote T as \(T=\frac {\beta }{f_{d}}\), where f_{d} is the Doppler shift that can be estimated by the method we proposed in Section 2. β is a constant factor. In our simulation and experiments, we select β=0.064, which empirically achieves the highest prediction fidelity.
Assuming that within the time window T, there are w channel measurements γ_{n−1},γ_{n−2},⋯,γ_{n−w} at time t_{n−1},t_{n−2},⋯,t_{n−w}, respectively. From all the measurements within the window, we perform a linear regression firstorder curve fit with the constraint of minimum square errors. To do so, we first assume the objective first order curve is f(t)=at+b, where a and b are parameters to be calculated. Then, we have
The detailed process of computing a and b in (10) can be found in the Appendix 2.
We know that the fading channel does not strictly maintain a constant firstorder derivative, especially for long intervals between packets. In a more extreme case, if the interval between the last packet and the ongoing packet exceeds a certain value, the prediction may be uncorrelated with the real channel quality. Considering this interval, we use a weighting factor δ to weight the preprediction and the channel quality with the maximum probability. Consequently, the estimated channel quality \(\hat {\gamma _{n}}\) is:
where
In (12), f_{d} is the maximum Doppler shift, and \(\bar {\gamma }\) is the channel quality that has the greatest statistical probability of occurrence. For computational simplicity, we approximate \(\bar {\gamma }\) as the mean value of the channel quality measurements during the last 10 s.
Note that within the time window T, there is the probability of w≤2. When w=2, our algorithm turns out to be the Linear prediction. Similarly, if w=1, our algorithm matches the Follower mechanism. For the case of w=0, we choose the maximum probability channel quality \(\bar {\gamma }\) as our prediction.
In Fig. 9, we show the result of the MMSE firstorder channel quality prediction. There is a 15 dB measurement error compared to the channel quality. The reconstructed channel response approaches the theoretical curve well. The square errors of the prediction is about 38 dB compared to the theoretical one, which means a 23 dB accuracy gain.
In order to evaluate the prediction performance of our proposed algorithm under various time intervals between packets, we control the delay between the data packets decoded for channel estimation and the channel feedback packets received by the transmitter. We use a Rayleigh fading channel model to compare our proposed algorithm with three other mechanisms (Follower, EWMA, and Linear prediction), as shown in Fig. 10. We set a Doppler shift of 10 Hz and set the channel measurement error to 20 dB compared to the average channel quality. We can see that the prediction performances based on the time interval seem to follow the same pattern for all prediction algorithms: the prediction error increases as the time interval increases, as shown in Fig. 10a. Our evaluation shows that CIPRA presents the least prediction error of all prediction algorithms. Although similar patterns can be found at both overselection probability, underselection probability, and wrong selection probability, as shown in Fig. 10b, c, and d, it is interesting to note that the performance of CIPRA becomes identical to that of Linear prediction at a time interval above 3.6 ms. Considering that the MAC layer design in current and future IEEE 802.11 standards requires only smaller time interval between packets, we predict that the impact of CIPRA will only increase with the development of higher frequency band protocols such as those with millimeter wavelengths and smaller timing parameters. For example, a minimum interval between transmission packets, called Short Inter Frame Space (SIFS), has shortened from 28 μs in IEEE 802.111997 to 16 μs in IEEE 802.11n to 3 μs in WiGig/IEEE 802.11ad. Moreover, many timing parameters of the backoff process for the carrier sense and channel access are also reduced.
The computational complexity of the proposed algorithm is higher than the other algorithms discussed above. However, it takes less than 1 μs on the PowerPC embedded on WARP (we use an 80MHz clock frequency for the PowerPC), which is much less than the DIFS/SIFS time of the transmission. As a result, it does not affect the system throughput.
Hardware setup
In this section, we describe the implementation of our CIPRA algorithm on the WARP board, a fullycustomized, crosslayer softwaredefined radio (SDR) platform. Moreover, we use the Azimuth ACEMX channel emulator to generate controllable channel effects, which allows repeatability of wireless channels over which to test diverse protocols.
WARP
The experiments are carried out using the WARP board, a useful wireless communication system supporting a fullycustomized, crosslayer design [11]. We conduct our experimental evaluation based on a full OFDM physical layer design per the IEEE 802.11 PHY frame structure. The design operates in realtime, transmitting and receiving wideband signals. We implement complete realtime signal processing, synchronization, and control systems in the fabric of the FPGA on WARP.^{Footnote 1}
Channel emulator
In addition to the practical infield wireless channels, we use the Azimuth ACEMX channel emulator to generate repeatable and controllable channel effects, which isolates the impact of interference and approximates well complex overtheair channels. Figure 11 illustrates our experimental setup. We use one WARP as the transmitter and another WARP as the receiver. We connect the transmitter and the receiver with RF cabling to the channel emulator. The transmitter sends data packets periodically to the receiver. The receiver measures the channel and feeds the channel indicator back to the transmitter with ACK packets following controllable time interval.
In our evaluation with the channel emulator, we set the packet size to 1536 bytes. We use a twotap Rayleigh fading channel with an average SNR of 15 dB. Both taps have a 0dB relative attenuation, and the time delay between the taps is 0.5 μs. The resulting throughput is shown in Table 2 and indicates that Effective SNR performs best among all three channel indicators. The EWMA method performs better with less of a Doppler shift because there is less staleness when the Doppler shift is low. With an increasing Doppler shift, the linear method becomes comparatively better because of the increasing staleness of Follower and EWMA. SNRbased rate adaptation mechanisms on offtheshelf devices use the RSSI metric and Follower prediction. Thus, with a Doppler shift of 10 Hz, CIPRA achieves a throughput improvement of 18% over the offtheshelf configuration. If further combined with the advanced effective SNR, a total improvement of 33% could be achieved over the offtheshelf method. Later, we show that infield experimental results exceed these gains as the channels become more complex.
Experimental evaluation and discussion
In this section, we implement the existing channel prediction algorithm and the proposed algorithm on WARP and experimentally compare them in terms of system throughput through both indoor pedestrian experiments and outdoor vehicular experiments.
Indoor pedestrian test
We conduct our indoor experiment on the eighth floor of the SMU Expressway Tower (floor plan shown in Fig. 12). Before evaluating the performance of our proposed algorithm with other mechanisms, we take actions to reduce the ambient interference power in our selected measurement locations by disabling or shielding interfering WiFi access points. Yet, the interference cannot be fully eliminated due to the existence of institutional WiFi access points that are beyond our control. We set up two transmitter/receiver pairs, which are operating independently, but simultaneously. Two transceivers use orthogonal channels: 2484 MHz (Ch. 14) and 2462 MHz (Ch. 11), respectively. For each experiment, we run CIPRA on a tx/rx pair, and one of the other three methods on the other tx/rx pair. We use RSSI with all four prediction methods to measure the throughput. We also provide additional experiments combining CIPRA and effective SNR to obtain the throughput. We colocate the transmit antennas and colocate the receive antennas to ensure the two links have very similar channels. For each comparison, we flip the links back and forth for each experimental trial to remove any unfair advantage between the two channels. The transmitters are located on the table in the lab, and we select four office rooms to put the mobile receivers, as shown in Fig. 12. We randomly move the receiver nodes in each office to create timevarying channels. We show the average throughput of the four methods on the four different locations in Fig. 13. CIPRA greatly outperforms other methods at all four locations with up to a 66% throughput improvement, with an improved prediction algorithm from the currently one used in practice. When further combined with the advanced Effective SNR, a maximum improvement of 98% could be achieved over the offtheshelf method, nearly doubling the achieved throughput. In addition, compared with the experimental results using channel emulator, our evaluation demonstrates the performance improvement of CIPRA in real environments even with the impact of interference.
Outdoor vehicular test
In addition to lab experiments, we also conduct infield experiments to show the throughput improvement provided by our algorithm for in situ highly mobile scenarios. We perform outdoor experiments in the parking lot of the SMU Expressway Tower (shown in Fig. 14). The transmitter and receiver settings are the same as with the indoor experiments. We place the transmitters in the entrance of the tower and the receivers in a car with the antennas mounted on the roof. We drive the car along the path shown in Fig. 14, with an average speed of 32 km/h. We also switch the channels of the two tx/rx pairs to remove the unfairness of different channels for each comparison. We show the average throughput of the four methods in Table 3. Due to a higher Doppler shift in the vehicular environment, the Linear method has improved performance. CIPRA also outperforms the three other methods with up to 50% of the throughput improvement. When further combined with Effective SNR, a total improvement of 67% could be achieved over the offtheshelf method.
Throughput comparison between CIPRA and Minstrel
Minstrel is reported to be one of the best rate adaptation methods based on packet loss/success [37]. We implemented Minstrel according to the specifications in [37] and evaluated the throughput of Minstrel and CIPRA with the same experimental settings as in Section 4.2. We use SNR as the channel indicator for CIPRA and train the CIPRA rate adaptation threshold with a Doppler shift of 10 Hz, corresponding to a walking velocity for WiFi 2.4 GHz band. The Doppler shift can be approximately by
Here, v is velocity and c is the light speed. Then, we apply the same SNR threshold in all the different Doppler shift cases for CIPRA. We show the throughput of CIPRA and Minstrel in Fig. 15. We can see that, with a very low Doppler shift, CIPRA and Minstrel have similar throughput. However, as the Doppler shift increases, Minstrel degrades faster than CIPRA. This is explained by the long statistical time that composes rate decisions in Minstrel that prevent it from adapting as quickly to fastfading channels.
Conclusion
In this paper, we proposed a coherenceaware MMSE firstorder prediction algorithm (CIPRA), which considered both the measurement inaccuracy and staleness. Prediction intervals and channel coherence time were jointly considered to select the optimal prediction window. We also implemented a Doppler shift estimation method to assist our prediction algorithm. We compared CIPRA to the traditional channel quality prediction for rate adaptation protocols, performing experiments on an FPGAbased platform over emulated and infield wireless channels. We showed that our proposed algorithm can provide better prediction fidelity and results in nearly double the throughput versus the current configuration in offtheshelf devices in the field. Lastly, we estimated that the benefits brought by CIPRA will only increase with the development of nextgeneration protocols such as those with higher frequencies and higher packet rate.
Appendix 1
his appendix presents the SNR computation for IEEE 802.11 OFDM systems. As shown in Fig. 6, the long preamble is composed of two identical OFDM symbols with a 1/2 symbol prefix. Denote the OFDM symbol in the long preamble as X(k),k=0,1,...,K−1, where k is the sample index in the time domain of one symbol. According to the frame structure specified in [35], the long preamble S(n) can be expressed as
where n is the sample index in the long preamble.
We assume this signal passes through a multipath channel with a time spread of L, \(0\leq L\leq \frac {K}{4}\). Moreover, we make the assumption that the channel remains constant during one frame slot. Then, the received signal Y(n) with additive white Gaussian noise is
where \(n=0,1,...,\frac {5}{2}K+l2\). It is then straightforward that
We then compute the crosscorrelation between the last symbol and the first symbol as
Because Y(n) and Z(n) are uncorrelated, we have
We then compute the autocorrelation on the first symbol as
Since Y(n) and Z(n) are uncorrelated, we have
Then, P_{s} is the estimated signal power, and P_{t} is the estimated total power. The noise variance will be P_{t}−P_{s}. Also, we can calculate the SNR as SNR=\(\frac {P_{s}}{P_{t}P_{s}}\).
Appendix 2
We provide the parameter computation for the firstorder SNR prediction. The sum of the square errors between the samples on the curve γ′_{n−i} and the actual measurements γ_{n−i} are
Our objective is to find the value of a and b when E achieves its minimum value. We can expand (21) as
Let us use the following notation for ease of expression: \(\alpha _{1}=\sum \nolimits _{i=1}^{w} t^{2}_{ni}, \alpha _{2}=\sum \nolimits _{i=1}^{w} t_{ni}, \alpha _{3}=\sum \nolimits _{i=1}^{w} \gamma _{ni} t_{ni}, \alpha _{4}=\sum \nolimits _{i=1}^{w} \gamma _{ni}, \alpha _{5}=\gamma ^{2}_{ni}, \alpha _{6}=w\). Then, we can simply express (22) as
To find the minimum value of E, we take its derivative in terms of a and b, respectively. Then, we force both the derivatives to 0 to obtain the following pair of equations:
From (22), we know that E≥0 for all a and b, which means that there exists a minimum value of E. From (22), we can see that E is a convex function of a or b. As a result, the solution of a and b in the above equation pairs will enable E to achieve its minimum value. With a and b obtained, we can obtain our preestimate of \(\hat {\gamma _{n}} \prime \) as
Notes
 1.
While existing OFDMbased models have existed on the WARP repository (http://warp.rice.edu), they use System Generator to create the design, whereas our design is completely based upon Verilog HDL for system control and efficiency of compilation and realtime operation.
Abbreviations
 ACD:

Analog to digital converter
 AWGN:

Additive white Gaussian noise
 BER:

Bit error rate
 CIPRA:

Coherenceaware channel indication and prediction algorithm for rate adaptation
 EWMA:

Exponential weighted moving average
 FFT:

Fast Fourier transform
 FPGA:

Field programmable gate array
 ICI:

Intercarrier interference
 IFFT:

Inverse fast Fourier transform
 LCR:

Levelcrossing rate
 LOS:

Line of sight
 LWMA:

Linear weighted moving average
 MCS:

Modulation coding scheme
 MMSE:

Minimum mean square error
 NLOS:

None line of sight
 OFDM:

Orthogonal frequencydivision
 PHY:

Physical layer
 RSS:

Received signal strength
 RSSI:

Received signal strength indicator
 SDR:

Softwaredefined radio
 SIFT:

Short Inter Frame Space
 SNR:

Signaltonoise ratio
 WARP:

Wireless openaccess research platform
 WiFi:

Wireless fidelity
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YD and PH conceived the framework design and performed the data analysis. YS improved the work and took charge of all the work of paper submission. DR and JC reviewed and revised the manuscript. All authors have read and approved the final manuscript.
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Correspondence to Yan Shi.
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Keywords
 Rate adaptation
 Prediction
 Channel indication
 Channel coherence
 MMSE