Youwen Yi, Daiming Qu, Tao Jiang, Guangxi Zhu, Jun Chen, Zhiqiang Wang. Department of Electronics and Information Engineering. Huazhong University of ...
Low Complexity Iterative Interference Estimation and Decoding for OFDM-Based Cognitive Radio Systems Youwen Yi, Daiming Qu, Tao Jiang, Guangxi Zhu, Jun Chen, Zhiqiang Wang Department of Electronics and Information Engineering Huazhong University of Science and Technology Wuhan, Hubei 430074, China Abstract— Coexistence of different users in cognitive radio (CR) network sharing the same frequency band can cause severe in-band interference. In this paper, we propose a novel scheme of joint interference estimation and decoding to combat the narrowband interference for OFDM-based (orthogonal frequency division multiplexing) CR systems in an iterative way. Moreover, we present some complexity reduction techniques including frequency domain partial averaging which only requires the knowledge of the number of interfered subcarriers. By exploiting the results of decoding, the proposed scheme can achieve an accurate estimation of noise plus interference variance, and a quasi-optimal bit error ratio (BER) performance. It is also robust against the variation of interference power and bandwidth, and the positive error of the knowledge of the number of interfered subcarriers.
I. I NTRODUCTION Driven by consumers’ increasing interest in wireless services, demand for radio spectrum has increased dramatically. Moreover, with the emergence of new wireless devices and applications, the compelling requirements for broadband wireless access are expected to continue in the future. Unfortunately, radio spectrum is very scarce. Although orthogonal frequency division multiplexing (OFDM) technique can help improve the spectrum efficiency [1], the deployment of new wireless services has to coexist with each other or with the existed systems by sharing spectrum, e.g., IEEE 802.11b shares the 2.4GHz ISM band with Bluetooth [2]. Cognitive radio (CR) technology [3] has been proposed to solve the predicament of spectrum scarcity. CR technology allows spectrum reuse in various dimensions including space, frequency and time to obliterate the spectrum and bandwidth limitations. Although in an OFDM based CR system, OFDM technique enables the system to alleviate the destructive effect of the interference by simply avoiding transmission in the narrow/partial band interference jammed subcarriers, current sensing techniques cannot guarantee accurate detection of the interference in practice [4], hence, interferences of licensed primary users on unlicensed secondary users or among secondary users are inevitable and may result in severe performance degradation. This work was supported in part by the National Natural Science Foundation of China (No. 60702039), the International S&T Cooperation Program of China (No. 2008DFA12100), and the National High Technology Development 863 Program of China under Grant 2009AA011803.
As a result, the receiver is posed a challenge to detect the transmitted data in the presence of unknown narrowband interference. Optimal decoder in the maximum likelihood sense can be performed to achieve an acceptable error rate performance with the noise and interference distribution. However, the exact timely knowledge of the noise plus interference variance is normally hard to be obtained in reality. Traditionally, noise plus interference variance estimation and decoding are operated separately. EM (expectation maximization) and decisiondirected algorithms were given for noise variances estimation in [5], whose drawback is the large amount of data that needs to be processed for an accurate estimate. In [6], two algorithms, i.e., median filtering and differentiation in frequency direction, were proposed to detect Bluetooth interference in IEEE 802.11b networks. However, the effectiveness of these algorithms is reduced for high order modulation schemes. Another method adopts a filtering technique to optimally estimate the noise and interference power on each subcarrier in the sense of minimum mean square error (MMSE) [7], which considers the variation of the noise statistics across both subcarrier index and OFDM symbols. Shortcomings of this method include the difficulty in obtaining the second-order statistics of interference and noise, and the high complexity in calculating the optimal filter coefficients. A joint interference detection and decoding scheme was considered in [8], which exploits the code structure and can achieve a performance close to that of the optimal maximum likelihood decoder without requiring accurate estimates of the interference power. Although some complexity reduction techniques are presented, this scheme is still very complicated, and it has to modify the decoding trellis of existing decoders, which is not preferred in practice. In this paper, we are motivated to investigate the combination of interference plus noise variance estimation and decoding for an OFDM system that is subject to frequencyselective fading and time-varying narrowband interference. We first propose an iterative scheme of noise plus interference variance estimation for each subcarrier. Since this scheme exploits the results of decoding, it is able to obtain an accurate estimation and achieve a performance close to that of the optimal maximum likelihood decoder with the full knowledge
of the interference distribution. To reduce the complexity, we simplify the most complicated component in our scheme with minor performance degradation, and add a partial averaging in frequency domain using only rough prior information about the interference which decreases the amount of data needed for estimation. Hence, the complexity is greatly reduced, and quite acceptable in practice. The remainder of the paper is organized as follows. In Section II, the baseband OFDM system model and some assumptions are given. In Section III, a joint noise plus interference variance estimation and decoding scheme is derived. In Section IV, we propose some complexity reduction techniques to simplify the estimation and decoding process. Comprehensive simulation results and discussion are given in Section V. Finally, some conclusions are drawn in Section VI. II. S YSTEM M ODEL In this paper, we consider the baseband OFDM system which is the same as that in [8]. First, the information sequence is convolutionally encoded, and the length-N codeword c = (c1 , c2 , ..., cN ) is bit-wise interleaved [9]. Then, every mtuple of the interleaved codeword is mapped to an M -ary (M = 2m ) symbol in the signal set χ = {χ1 , χ2 , ..., χM } based on a mapping function μ. The M -ary symbol sequence (x1 , x2 , ..., xK ) is mapped to an OFDM symbol by the inverse discrete Fourier transform (IDFT). Each OFDM symbol is appended by a cyclic prefix that is set to be longer than the delay spread of the multipath fading channel. In this paper, slow fading is considered, i.e., the channel is assumed to be unchanged during certain OFDM symbols. At the receiver, by removing the cyclic prefix and performing discrete Fourier transform (DFT), the effective channel for each subcarrier becomes flat fading. Due to the coexistence of other communication systems, part of the subcarriers may be jammed by interference. The kth received symbol yk (k = 1, 2, ..., K) after the DFT can be represented as yk = αk xk + nk
(1)
where αk is the fading factor, and nk is the additive channel noise plus interference for the kth symbol. In this paper, the noise and interference are assumed to be Gaussian distributed. The conventional decoding scheme contains a demodulator, a deinterleaver and a Viterbi decoder [9]. For each received symbol yk , the demodulator calculates the metrics for all the m bits cik = b (b = 0, 1; i = 1, 2, · · · , m) that correspond to the kth symbol as [8]: λ(cik = b) = log p(cik = b|yk ) ∝ log p(yk |xk = χk ) ≈ maxi log p(yk |xk = χk ) χk ∈χb
χk ∈χib
= mini
χk ∈χb
(2)
2
|yk − αk χk | + const σk2
i where χib = {μ(c1k , · · · cik , · · · cm k )|ck = b} is the signal subset with the ith bit cik equals to b. Then the bit metric of each
demodulated bit can be represented by its log-likelihood ratio (LLR): Λ(cik ) = λ(cik = 1) − λ(cik = 0) (3) The conventional decoding scheme assumes that the noise plus interference variance σk2 is identical for all the symbols, i.e., σk2 = σ 2 , and can be abandoned in the bit metric calculation. When narrowband interference exists, the noise variance is no longer a constant for all the subcarriers, and dropping the noise plus inteference variance σk2 in the bit metric may result in serve metric mismatch. Knowing the position of the interference jammed subcarriers and the variance of the interference, the optimal decoder, i.e., maximum likelihood decoder (MLD), weights each symbol differently depending on whether the symbol is hit by background Gaussian noise 2 2 (σk2 = σG ) or noise plus interference (σk2 = σG + Ik2 , where 2 Ik is the interference power on the kth symbol). When the power and position of interference is unknown, a reasonable alternative scheme of data detection is to demodulate with estimated power of the noise and interference at each subcarrier. Suppose that interference distribution remains stationary over the observation time, for the kth subcarrier, a set of observations {yk1 , yk2 , · · · , ykL } are used to estimate the noise plus interference variance σk2 , where the subscript l denotes OFDM symbol index and takes on values from 1 to L. A straightforward method of noise plus interference variance estimation uses the rough decision of the transmitted data symbols: x ˆlk = arg min |ykl − αk χj |2 (4) χ
where x ˆlk is the estimate of the lth transmitted symbol in kth subcarrier based on the received data. According to (1), noise plus interference variance is estimated as σ ˆk2 =
L
L
l=1
l=1
1 l 2 1 l |ˆ nk | = |yk − αk x ˆlk |2 L L
(5)
The estimation accuracy of this method is limited by the erroneous decision of the transmitted data. However, through exploiting the results of decoding, we can obtain a more accurate estimation of the noise plus interference variance. To simplify the analysis, we assume that the channel estimation is perfect as in [8], since there are many published papers focusing on channel estimation with interference, which are based on pilot-based, blind estimation techniques and so on. III. I TERATIVE N OISE PLUS I NTERFERENCE VARIANCE E STIMATION AND D ECODING In this paper, we propose an iterative scheme of noise plus interference variance estimation and decoding for OFDM systems. The block diagram of the proposed scheme is illustrated in Fig. 1. L received OFDM symbols are demodulated with the estimated noise plus interference variance provided by the noise estimator. After demodulation and deinterleaving, the soft-input soft-output (SISO) decoder outputs a posterior estimate of the input symbols which are used to update estimation
Fig. 1.
Block diagram of the proposed scheme.
Fig. 2.
of noise plus interference variance in noise estimator. The received data is processed iteratively in the loop before the recovered information is obtained. The proposed noise plus interference variance estimate in the pth iteration for the kth subcarrier is given as 2 σ ˆk,p+1 =
L
M
1 ωp (xlk = χj )|ykl − αk χj |2 L j=1
(6)
l=1
where
M j=1
ωp (xlk = χj ) = 1, ωp (xlk = χj ) is the probability of
the jth candidate symbol to be transmitted in the kth subcarrier of lth symbol, which is derived from the output of the SISO decoder. The SISO decoder can output the APP of each coded bit to be 0 or 1 based on its inputs and knowledge of the trellis structure of the code using maximum a posteriori (MAP) algorithms [10]. The SISO decoder accepts at the input the sequences of probability distributions ΛI (cn ) and ΛI (uq ), and outputs the sequences of probability distributions ΛO (cn ) and ΛO (uq ) for the coded bit cn and decoded bit uq . The ΛI (uq ) is a prior information about the original binary information, and can seldom be able to acquire by the receiver in practical, hence it is set to be zero. The decoded bit uq can be obtained from ΛI (uq ) with a hard decision. The LLR of the coded bit cn renewed by the SISO decoder is: ΛO (cn ) = log p(cn = 1) − log p(cn = 0)
(7)
We denote ci,l k,p as the ith bit of the kth subcarrier in the lth OFDM symbol during the pth iteration, ΛO (ci,l k,p ) is the bit i,l metric of ck,p , which is obtained by interleaving the output of SISO ΛO (cn ). The probability of ci,l k,p = b (b ∈ {0, 1}) is given as [11]: p(ci,l k,p = b) = =
exp{(2b − 1)ΛO (ci,l k,p )}
is: ωp (xlk = χj ) =
m i=1
p(ci,l k,p = bi )
(9)
where χj = μ(b1 , b2 , · · · , bm ), bi ∈ {0, 1} It becomes an iterative procedure in which the new estimate 2 2 σ ˆk,p+1 generated at pth iteration takes the place of σ ˆk,p , which 2 is used in (2) as σk for demodulation. After demodulation, deinterleaving and SISO decoding, the estimate is renewed 2 2 until a stationary point is reached ( i.e., σ ˆk,p+1 ≈σ ˆk,p ), or the number of iterations p achieves the preset value P . IV. C OMPLEXITY R EDUCTION The data detection complexity can be estimated by counting the number of operations in all elements. To reduce the complexity, we present some complexity reduction techniques which will make the proposed scheme more practical. A. SISO decoder replacement Obviously, the SISO decoder is far more complicated than other components in the block of data detection using our scheme. Therefore, we employ a Viterbi decoder and an encoder to replace the SISO decoder. The new block diagram of this simplified iterative scheme is illustrated in Fig. 3. We interpret the output of Viterbi decoder as the probability of each uncoded bit to be 1, then the recoded bits of Viterbi decoder output represents p(cn = 1). Correspondingly, p(cn = 0) can be generated by: p(cn = 0) = 1 − p(cn = 1)
(10)
After interleaving, p(ci,l k,p = b) can be obtained. As the value of Viterbi decoder output is either 0 or 1, so does p(ci,l k,p = b), only the probability of one candidate in χ is 1 according to (9), we denote it as x ˆlk,p . In this context, x ˆlk,p can be obtained with a modulator: 2,l m,l xlk,p = μ(c1,l k,p , ck,p , · · · , ck,p )
1 + exp{(2b − 1)ΛO (ci,l k,p )}
i,l 1 cosh[ 12 ΛO (ci,l k,p )]{1 + (2b − 1) tanh[ 2 ΛO (ck,p )]}
Block diagram of the proposed simplified scheme.
(11)
Then, (6) can be simplified as: (8)
2 cosh[ 12 ΛO (ci,l k,p )] 1 1 = {1 + (2b − 1) tanh[ ΛO (ci,l k,p )]} 2 2
Then the probability of the jth candidate transmitted symbol
2 = σ ˆk,p+1
L
1 l |yk − αk xlk,p |2 L
(12)
l=1
The rest of the initial scheme stays unchanged. As the SISO decoder is also the bottleneck of the processing speed in
our initial data detection structure, this complexity reduction technique could decrease the computational load, and thus accelerate the data processing in our scheme. Simulation results in the next section show that the performance degradation is ignorable.
0
10
IED−FPA LIED−FPA IED LIED
To obtain an more accurate estimation with less amount of data, we add frequency domain partial averaging to the iterative scheme, using the fact that the background noise variance is nearly the same for those subcarriers without interference. We assume that the number of the subcarriers interfered is known to be s in advance. For kth subcarrier, the estimated noise plus interference variance is given as ⎧ 2 ⎨ 1 ˆk,p k∈R k∈R σ K−s 2 σ ˜k,p = (13) 2 ⎩σ ˆk,p k∈R where R + R is the group of the index of all the subcarriers, R is the subset of the index of suspicious jammed subcarriers that are excluded in the averaging, which contains s elements. R can be obtained by finding the largest s estimated noise plus interference variances after each iterative process: R = {(k1 , · · · , ks )|∀ki ∈ R, ∀kj ∈ R, σ ˆk2i ,p σ ˆk2j ,p } (14) In practical cognitive radio systems, the required knowledge of s can be acquired from history information of the interferers, or from the shared information of cooperative spectrum sensing [12]. According to the simulation results in the next section, this requirement is not restrict, because a positive error ( s is larger than the exact number of interfered subcarriers ) results in an ignorable BER performance degradation. Hence, only an upper bound is required which is much easier to be obtained than the exact value. V. S IMULATION R ESULTS In this paper, we use as baselines both the performance of conventional receiver with Viterbi decoder designed for AWGN channel without considering interference, and that of optimal maximum likelihood decoder (MLD) with exact knowledge of noise plus interference variance on each subcarrier. The initially proposed iterative scheme of noise plus interference estimation and decoding is denoted as IED in the figures. The iterative scheme with low complexity Viterbi decoder is denoted as LIED. Accordingly, these schemes with frequency domain partial averaging are denoted as IED-FPA and LIED-FPA, respectively. In fact, the IED-FPA and LIEDFPA reduce to the conventional one by setting R = ∅. When there is no interference, the four decoding schemes: the conventional one, IED-FPA, LIED-FPA and MLD are effectively equivalent. Throughout the simulation, a rate-1/2 64-state convolutional code and 16QAM with Gray mapping is considered. We suppose that each frame contains exactly one codeword and each codeword is mapped to L OFDM symbols with the number of subcarriers K = 200, the fading at each subcarrier
NMSE
B. Frequency domain partial averaging −1
10
−2
10
0
1
2 3 Iterative Numbers p
4
5
Fig. 3. NMSE versus iteration numbers using proposed schemes with SNR=12dB, SIR =5dB, L=10, fivesubcarriers are interfered.
is independent, and the fading factor is perfectly known at the receiver [8]. From Fig. 3 to Fig. 5, the exact number of interfered subcarriers is known. A normalized mean square error (NMSE) of the noise plus interference variance estimation is used as a performance measure versus the iteration numbers p for the proposed scheme, which is defined as follow [7]: K 2 σk,p − σk2 )2 k=1 (ˆ 2 NMSE(σ ) (15) K 4 k=1 σk In Fig. 3, the NMSE is evaluated when SNR=12dB, SIR=5dB, L = 10, five subcarriers are interfered. It is observed that iteration greatly improves the accuracy of the noise plus interference variance estimation, and two iterations are enough for the convergency of all schemes. With frequency domain partial averaging, the NMSE of proposed schemes decreases quickly and the needed number of iterations is also reduced to only one. Fig. 4 shows the impact of the number of interfered subcarriers on BER performance using the conventional decoder, the maximum likelihood decoder (MLD) and proposed LIED-FPA and IED-FPA decoders when SIR=5dB, SNR=12dB. The BER increases as the number of interfered subcarriers increases. There is only an ignorable gap between the IED-FPA, LIEDFPA and MLD. Fig. 5 shows the BER performance of the proposed scheme when SIR=5dB, five subcarriers are interfered and SNR values varies. It can be observed that the proposed LIED-FPA significantly outperform the conventional one and effectively approach the optimal decoding performance for a wide range of SNR using only 10 OFDM symbols. It is shown that without iteration (P=0), the performance degradation is about 1.8dB in BER 10−6 . Finally, we illustrate in Fig. 6 that the BER performance of the LIED-FPA does not highly rely on the accuracy of the knowledge of the number of the interfered subcarriers as long as it is not smaller than the actual one. Without knowing
0
−1
10
10
MLD conventional LIED−FPA, s=3 LIED−FPA, s=5 LIED−FPA, s=10 LIED−FPA, s=15
MLD conventional IED−FPA, P=1 LIED−FPA, P=1 LIED−FPA, P=0
−1
10
−2
BER
BER
10
−2
10
−3
10 −3
10
−4
10
−4
10
20
30 40 Number of interfered subcarriers
50
10 −10
60
Fig. 4. Impact of the number of interfered subcarriers on BER performance when SNR=12dB, SIR=5dB, L=10.
−8
−6
−4
−2
0 SIR (dB)
2
4
6
8
10
Fig. 6. Impact of the accuracy of prior information about the number of interfered subcarriers on BER using the proposed scheme when SNR=12dB, five sunbcarriers are interfered.
−1
10
MLD conventional LIED−FPA, P=0 LIED−FPA, P=1
−2
10
hence, the complexity of the proposed LIED-FPA is very low. Moreover, the proposed scheme is robust against the variation of the number of interfered subcarriers and against the positive error of the prior information about it.
−3
10
BER
R EFERENCES −4
10
−5
10
−6
10
−7
10
12
13
14
15
16 SNR (dB)
17
18
19
20
Fig. 5. BER versus SNR using proposed scheme when SIR=5dB, L=10 five subcarrier are sinterfered.
the accurate number of jammed subcarriers, the performance degradation of LIED-FPA is ignorable. Hence, we only require an upper bound of the number of interfered subcarriers for the proposed scheme. Moreover, the performance of LIED-FPA remains unchanged when the power of interference varies. Therefore, the LIED-FPA algorithm is fairly robust under various interference conditions and feasible in practice. VI. C ONCLUSIONS In this paper, we derive a low complexity scheme of joint noise plus interference variance estimation and decoding for OFDM-based CR systems. Without knowing the exact interference distribution, the proposed scheme significantly outperforms the conventional one and effectively achieves the performance of the MLD. With iteration and the complexity reduction techniques, we can obtain an accurate estimation and reduce the number of OFDM symbols needed for processing,
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