To verify our proposed HD-FAC algorithm, we apply ERP-OFDM in IEEE 802.11g [28] as our OFDM simulation vehicle. In this system, data rate ranges from 6M to 54Mbps, and the QAM has different modulation order from BPSK to 64QAM.
Also, the receiver is concatenated with an outer receiver, which applies Viterbi algorithm for the final data decoding. In order to verify the proposed algorithm, the most sensitive transmission mode, 54Mbps with 64 QAM, is chosen. Since OFDM is robust to fading channel, we also target the simulation environment on Rayleigh fading channel with coherent bandwidth 20MHz. In the simulations, 1024 packets are sent at each SNR value, and each packet consists of 1024 information bytes. To see how IQM degrades system performance without compensation, we simulate the PER performance in sweeping different gain and phase errors to the system under Rayleigh fading channel. When PER reaches 0.1, we can see the SNR distribution with different phase and gain errors as shown in Fig. 3-10. If we trace the axis where only phase error exists, we found that the SNR value degrades more than 30 dB. On the other hand, we can find the system has dramatic degradation even with only gain error.
So, gain error has larger impact on the system. It can be observed not only system
degrades fast but unrecoverable errors occur with increased gain and phase errors, especially when the two effects exist together. Therefore we cannot get a high performance OFDM processor without any compensation.
(a)
(b)
Fig. 3-10. System performance without IQM correction under Rayleigh fading channel. The reached SNR at PER 0.1 with different gain and phase error values (a) the 3-D view (b) the
Before examining overall system performance of our proposed algorithm, we first look at the impact of different step sizes on adaptive tracking and system behavior. The absolute value of Δ is simulated under Rayleigh fading channel at β SNR 25 dB and depicted in Fig. 3-11, and the PER with corresponding step sizes are shown in Fig. 3-12.
Although different step sizes result in different convergence time and variation, the system reaches the similar performance. This is due to the convergent time is fast enough and the residual estimation error does not dominate the system performance.
Therefore, we choose a step size 0.5 for our further simulation since this number will simplify the computation and update process.
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 0
0.02 0.04 0.06 0.08 0.1 0.12 0.14
0.16 Estimation Error Δδ under Different Adaptive Step Size
Packet Number
|Δ δ|
Step Size 0.7 Step Size 0.5 Step Size 0.3 Step Size 0.1
Fig. 3-11. Δβ convergence with G.E. 1dB and P.E. 10 degree in Rayleigh fading channel @ SNR 25dB.
19 20 21 22 23 24 25 26 27 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Performance with Different Step Size under Rayleigh Fading Channel
SNR(dB)
PER
Step Size 0.7 Step Size 0.5 Step Size 0.3 Step Size 0.1 Target PER 0.1
Fig. 3-12. PER simulation with different step sizes under gain error 1dB and phase error 10 degrees
In the following, we set up three channel conditions to verify our algorithm and system. First is the pure AWGN environment. The second is Rayleigh fading channel with RMS 50ns. The third is Rayleigh fading channel in addition to 120kHz CFO, which is equivalent to 38.4% subcarrier frequency spacing or 50 ppm at 2.4G carrier frequency as specified in [28]. To verify HD-FAC algorithm, gain and phase errors are set to be 1dB and 10 degree as suggested in [35], and the results are shown in Fig.
3-13. In Fig. 3-13(a) of AWGN and IQM channel, we apply a non-adaptive MSE-based algorithm for IQM estimation as our reference design, which can be seen in [32] for example. Due to the limited available samples for IQM calculation, the estimation is not accurate enough. Therefore, as we apply our proposed HD-FAC algorithm, the system performance is largely improved more than 2dB at PER 0.1, and the performance has only 0.3dB SNR loss in pure AWGN environment. In the Rayleigh fading channel with RMS 50ns, which consists of exponential decaying power with uniform random distributed phase, our system results in 0.5dB SNR loss
whereas the reference design possesses about 1.5dB SNR loss. In the last simulation condition, the channel is applied with fading channel in addition to CFO 120 kHz, and the CFO is estimated by correlation in long-preamble field of a packet. There exists an estimation error of CFO amount, but this provides HD-FAC an initial CFO value for Δ estimation. Then the IQM compensated signal will make a more accurate β CFO estimation, and in turn improve the IQM estimation and compensation by adaptation. From Fig. 3-10(c), we see the performance has only about 0.5dB SNR loss, showing the stability and robustness under Rayleigh fading channel and CFO environment. We summarize the simulation performance in terms of SNR loss in Table 3-1.
19 20 21 22 23 24 25 26 27 28 29 30 31 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
AWGN channel
SNR(dB)
PER
AWGN only
Proposed HD-FAC : GE1dB / PE10deg.
Non-Adaptive MSE : GE1dB / PE10deg.
PER 0.1
(a)
20 21 22 23 24 25 26 27 28 29 30 31 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rayleigh Fading Channel with RMS 50ns
SNR(dB)
PER
Rayleigh Fading only CD-FAC : GE1dB / PE10deg.
Ref. [7] : GE1dB / PE10deg.
PER 0.1
(b)
20 21 22 23 24 25 26 27 28 29 30 31 32 33 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Rayleigh Fading Channel with CFO 120kHz
SNR(dB)
PER
Rayleigh Fading only
Proposed HD-FAC : GE1dB / PE10deg.
Non-Adaptive MSE : GE1dB / PE10deg.
PER 0.1
(c)
Fig. 3-13. IQM compensation performance with GE 1 dB and PE 10 degree under (a) AWGN channel (b) Rayleigh fading channel (c) Rayleigh fading and CFO channel.
TABLE 3-1.SNRLOSSUNDERDIFFERENTCHANNELCONDITIONS
GE / PE 1 dB / 10 degree
Rayleigh Fading Rayleigh Fading (RMS 50ns)
Channel AWGN
(RMS 50ns) CFO (120kHz)
Proposed HD-FAC 0.3 0.5 0.5
Non-Adaptive MSE 2.2 1.5 Inf
The performance is evaluated under (a) AWGN (b) Rayleigh Fading channel with RMS 50ns (c) Rayleigh Fading channel with RMS 50ns and CFO with 120kHz.
To illustrate the system operation, we show the estimated channel response before and after IQM compensation in Fig. 3-14. In the initial state, the channel is estimated without any correction, so there are obvious amplitude transitions in the estimated channel. After the proposed HD-FAC, the estimated channel becomes more continuous and approaches the primitive channel response. In initial state, the data compensated by IQM and the initial estimated channel has the constellation shown in Fig. 3-15(a). On the other hand, when the estimated IQM parameter αˆ and
β
ˆ become more accurate, the IQM compensation is improved and also the data is compensated by a more realistic channel response, which has the steady state constellation shown in Fig. 3-15(b). Both of the channel conditions in Fig. 3-14 and Fig. 3-15 are simulated under Rayleigh fading channel with CFO 120kHz at SNR 30dB.0 10 20 30 40 50 60 0
0.5 1 1.5 2
Estimated Channel under IQM
Subcarrier Index (k)
abs(H)
Primitive Channel Response Initial State Estimated Channel Steady State Estimated Channel
Fig. 3-14. Estimated channel resopnse with the proposed HD-FAC under gain/phase errors 1dB and 10 deg., and Rayleigh fading channel RMS 50ns @ SNR 30dB
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Real Part
Imaginary Part
Initial State under Rayleigh Fading Channel
(a)
-1.5 -1 -0.5 0 0.5 1 1.5 -1.5
-1 -0.5 0 0.5 1
1.5 Steady State under Rayleigh Fading Channel
Real Part
Imaginary Part
(b)
Fig. 3-15. Constellation with the proposed HD-FAC under gain/phase errors 1dB and 10 degrees and Rayleigh fading channel RMS 50ns @ SNR 30dB (a)Initial State (b)Stable State.
The computation requirements for HD-FAC are listed and compared without considering Hˆk and
X ’s calculation and storage since they do not belong to IQM
k estimation or compensation. In HD-FAC, the value2 2 | ˆ| ˆ|
| ˆ 1
β α
−=
K
is calculatedand stored for the use of both compensation and dMG computation. Therefore, we need three value storage elements for αˆ, βˆ, and
Kˆ in compensation stage. Then,
the stored value2 2 | ˆ| ˆ|
| 1
β
α
− is used for Δβ computation as indicated in (3-26), and do not need to compute its value again. In comparison with time-domain non-adaptive least-square algorithm [34], it applies a delay-line filter for IQM compensation. Assume a 5th order filter is used, so it needs five coefficients and an additional gain factor for data filtering, resulting in 6 multiplications and 5 additions.To determine the values of filter coefficients, a minimum cost function search is applied, largely increasing the computation requirements. The computation
requirements for HD-FAC and time-domain non-adaptive least-square algorithm are summarized in TABLE 3-2.
TABLE 3-2.COMPUTATIONREQUIREMENT
5th Order Time-Domain Non-Adaptive Proposed HD-FAC
LS-based Algorithm
Compensation ΔβComputation Compensation Coeff. Calc.
Multiplication 5 3 6 10
Addition 5 4 5 5
Differentiation 0 0 0 5
Value Storage 3 0 6 2