Transmit Center Frequency Tolerance

The frequency error should be a half of the sub-carrier spacing. As an example we can calculate the value of this limit for the IEEE802.11a system. For the short training symbols, the symbol time is 50ns. Thus the maximum allowable frequency error is fmax = 1/(2·16·50·10^-9) = 625kHz. This can be compared with the maximum possible frequency error in the IEEE802.11a system. The carrier frequency is approximately 5GHz, and the maximum oscillator error specified in the standard is 20ppm. So the relative frequency between the transmitter and the receiver can be ±40ppm. That means the maximum frequency offset is f = ±40·10^-6·5·10⁹ = ±200kHz. If the pseudo CFO is set to be 50ppm in the proposed algorithm, the maximum frequency offset will be f = ±90·10^-6·5·10⁹ = ±450kHz. Hence the maximum possible frequency error is well within the range.

Now we consider the case of the IEEE802.11g system. The carrier frequency is approximately 2.4GHz, and the maximum oscillator error is 25ppm. So the relative frequency between the transmitter and the receiver could be ±50ppm. That means the maximum frequency offset is f = ±50·10^-6·2.4·10⁹ = ±120kHz. If the pseudo CFO is also set to be 50ppm, the maximum frequency offset will be f = ±100·10^-6·2.4·10⁹ =

±240kHz. Although this proposed algorithm multiplies an additional exponential term (pseudo CFO), yet it can meet the standard specification from the above analysis.

3.4 Simulation and Performance

To evaluate the proposed algorithm, a typical OFDM system based on IEEE802.11g for WLAN is used as a reference-design platform. The parameters used in the simulation platform are: OFDM symbol length is 64 and cyclic prefix is 16. In IEEE802.11g, there are 10 short training symbols for coarse estimation and 2 long preambles for fine estimation. A satisfactory accuracy can usually be reached if enough data samples are used to calculate the estimate from the short training symbols.

Hence, in the proposed method, only short training symbols are used to measure the frequency offset. With the presence of IQ-M, the gain error and phase error are set to be 2dB and 20 degree as the design target. The CFO amount is simulated at the maximum value 50 ppm and -50 ppm, respectively at a 2.4GHz carrier frequency, and the additional P-CFO is set to be 30 ppm in the proposed scheme. TABLE 3-1 shows the simulation parameters for a frequency selective fading channel. In Fig. 3-7, it shows the estimation of frequency offset vs. the exact CFO value, referred to the simulation parameters in TABLE 3-1. This result shows that the proposed algorithm can estimate the CFO value more accurately than the conventional methods belonging to two-repeat preamble based.

TABLE3-1 SIMULATION PARAMETERS

Channel RMS:100ns, Tap:6

SNR 19dB

Data rate 54Mbps

Gain error 2dB

-50 -40 -30 -20 -10 0 10 20 30 40 50

Avg. of estimated CFO [ppm]

SNR:19dB, RMS:100ns, Tap:6

P-CFO (gain:2dB, phase:20degree) P-CFO (phase:20degree) P-CFO (gain:2dB)

Two-repeat preamble based (gain:2dB, phase:20degree)

Figure 3-7. Frequency offset estimation.

Figures 3-8 and 3-9 show the average estimation error of the frequency offset estimation under different IQ-M, and the frequency offset is set to be 50 ppm. It is clear to see that the estimation error of the conventional method will be enlarged as IQ-M gets larger, thus it is not robust with different IQ-M conditions. From Figure 2-9, it is obvious that the estimation error of the proposed method is an order small than the conventional method based on two-repeat preamble, and the proposed method is also independent of the IQ-M. Note that for a negligible degradation of about 0.1 dB caused by CFO, the maximum tolerable frequency offset is less than 1% of the sub-carrier spacing [24]. For instance, the oscillator accuracy needs to be about 3kHz or 1.25ppm for an OFDM system at a carrier frequency of 2.4GHz and a sub-carrier spacing 312.5kHz. As a result, the proposed algorithm is accurate in estimating frequency offset with IQ-M and makes little system performance loss.

Figure 3-8. CFO estimation by the two-repeat preamble based method.

The estimated frequency offset can be characterized by a Gaussian probability density function (PDF) as shown in Figure 3-10. From Figure 3-10, it is clear to see that the mean value of the proposed P-CFO algorithm can approach to the original CFO, but the conventional method always has an offset. And the variance of the conventional method is also larger than the proposed P-CFO scheme. A detailed result when SNR is equal to 20dB is shown in Figure 3-11. From Figure 3-11, it is obvious that the estimated CFO by the proposed P-CFO algorithm is accurate than the conventional method. And the estimated CFO calculated by the method based on two-repeat preamble always has a bias compared with the proposed P-CFO method.

Figure 3-12 shows the mean square error (MSE) of frequency estimation vs. SNR under different I/Q imbalance conditions. From Figure 3-12, we see that for almost entire SNR range, the P-CFO algorithm under the condition of 2dB gain error and 20-degree phase error performs better than the conventional method under the same condition or moderate IQ-M scenario, i.e., 1dB gain error and 10-degree phase error.

That means the P-CFO algorithm can improve the estimation accuracy under IQ-M. It is also noticeable that the MSE of P-CFO algorithm is still smaller than the conventional method even if there is no IQ-M, thus the P-CFO algorithm is also compatible with the conventional method. From Figure 3-12, it is clear that the phase error has more effect on the estimation of frequency offset since the MSE is larger than the case of gain error only. TABLE 3-2 summarizes the required SNR when the MSE is on the order of 10^-6. Since the proposed scheme decreases the impact of CFO greatly, a technique for I/Q compensation can be applied more easily [23].

40

Figure 3-10. Probability density function of 50ppm CFO: (a) P-CFO algorithm (b) Two-repeat preamble based.

40 42 44 46 48 50 52 54 56 58 60 0

5 10 15 20 25

Carrier Frequency Offset [ppm]

Probability (%)

Probability Density Function

Proposed method Conventional method

Figure 3-11. Probability density function.

15 20 25 3010^-8

MSE of frequency estimates

P-CFO (gain:2dB, phase:20degree)

Figure 3-12. Mean square error (MSE) of frequency estimation vs. SNR under different I/Q imbalance conditions with 50ppm CFO.

TABLE3-2

Gain: 1dB, Phase: 0degree 19 23.6

Gain: 1dB, Phase: 10degree 21 > 30

Gain: 0dB, Phase: 0degree 19 23.6

3.5 Implementation

Figure 2-13 illustrates the architecture of the P-CFO algorithm, where the P-CFO scheme contains of three main parts, including P-CFO shifter, CFO calculation and inverse cosine. When the training symbols are arrived, the P-CFO shifter module is noticed to work. The task of P-CFO shifter module is to rotate the received training symbols by pseudo frequency offset. As shown in Figure 2-13, a look-up table and a complex multiplier are employed to achieve the rotation. In order to reduce complexity and hardware cost of complex multiplier, we need to modify its direct-form implementations. From TABLE 2-3, it is clear that there are four multipliers and two adders if the direct implementation is applied. However, the modified implementation only needs three multipliers and five adders to reduce the hardware cost (if the wordlength is long enough). When the rotation is finished by the P-CFO shifter module, CFO calculation module starts to do correction based on the proposed algorithm. As shown in Figure 2-13, 6 multipliers (4 for multiplication and 2 for division) and 4 adders are used to realize the correction function. After calculation of CFO, the output of CFO calculation module is sent to inverse cosine module. The task of inverse cosine module is to find the angle of the correction calculated from CFO calculation module, and then add/minus the pseudo frequency offset to extract the final CFO. The synthesis result of the proposed algorithm is listed in TABLE 2-4 and the target clock rate is 120MHz in 0.13μm CMOS. The layout of the proposed algorithm is also presented in Figure 2-14 and its summary is listed in TABLE 2-5..

Figure 3-13. Hardware design of P-CFO scheme.

TABLE3-3 COMPLEX MULTIPLIER

(a+bj)(c+dj) Gate counts

(process: 0.13μm CMOS)

Blocks Gate Counts P-CFO shifter(LUT) 333 (1%)

Complex multiplier 2,650 (8%) Combinational 7,498 (22%) Non-combinational 6,190 (18.5%) P-CFO

Shifter Module

Module 1 13,688 (41%) Combinational 7,980 (23%) Non-combinational 6,826 (20%) CFO

Calculation

Module Module 2 14,806 (43%)

Inverse cosine(LUT) 339 (1%) Combinational 5,406 (16%) Non-combinational 162 (0.5%) Inverse

Cosine Module

Module 3 5,568 (16%)

Total 34,062 (100%)

Figure 3-14. Layout of the P-CFO design.

TABLE3-5 CHIP PROFILE

Technology 0.13μm CMOS process No. of Cells 48028

Core Size 4.5427e+05 um² Chip Size 1.3877e+06 um²

No. of IOs 34

Max. Speed 120MHz

3.6 Summary

This chapter has described the effect of frequency offset in OFDM systems. Then a joint problem of CFO and IQ-M is introduced to see how it degrades the system performance. Thus, a novel scheme based on P-CFO is proposed to estimate the frequency offset with IQ-M in direct-conversion OFDM receivers. The detailed analysis of the proposed scheme is also given, and then simulation results show that the average estimation error of P-CFO algorithm is small enough for little system performance loss under different Q-M. The result of the hardware implementation of the proposed P-CFO design is also given in this chapter. In next chapter, detail expression of IQ-M will be introduced.

Chapter 4