Robust Initialization with Reduced Pilot Overhead for Progressive Underwater Acoustic OFDM Receivers

Transcription

1 Robust Initialization with Reduced Pilot Overhead for Progressive Underwater Acoustic OFDM Receivers Jianzhong Huang, Shengli Zhou, and Zhaohui Wang Dept. of Electrical and Computer Engineering, University of Connecticut, Storrs, CT Abstract Recently, a progressive receiver has been proposed to mitigate the intercarrier interference (ICI) in orthogonalfrequency-division-multiplexing (OFDM) transmissions over underwater acoustic (UWA) channels, where the ICI span gradually increases during the receiver iterations. Operating on a blockby-block basis, the progressive receiver is initialized by measurements on pilot subcarriers inserted in each OFDM block. In this paper, we propose an initialization method that exploits channel correlation across blocks to reduce the number of pilots needed. Specifically, channel estimation in the initialization phase is carried out by combining two sets of measurements: a set of artificial measurements icted from the estimated channel of the previous block, and a set of measurements on the pilot subcarriers of the current block, where these measurements have different reliability levels. Performance results based on data recorded in SPACE08 and MACE10 experiments demonstrate the robust system performance with reduced number of pilots, where the transmitter in SPACE08 was stationary and that in MACE10 was slowly moving. Extension to the progressive receiver for multi-input multi-output (MIMO) OFDM is also pursued, where it is shown that the proposed hybrid initialization enables drastically improved receiver performance with a small number of pilots per transmitter. Index Terms Iterative receiver, channel iction, sparse channel estimation, underwater acoustic communications. I. INTRODUCTION Multicarrier modulation in the form of orthogonal frequency division multiplexing (OFDM) has been actively pursued for underwater acoustic communications to achieve high data rate transmissions [1] [11]. These various OFDM receivers can be divided into two main categories: Block-adaptive OFDM receivers. In these receivers [1], [6], [11], the channel estimated from the previous block is used for data detection of the current block, after proper phase compensation. The block-adaptive approach is also used in single carrier transmissions with frequency domain equalization [12]. Block-by-block OFDM receivers. The receivers in [2] [5], [7] [10] operate on a block-by-block basis, and channel estimation is carried out based on a number of pilots inserted in each OFDM block. The block-by-block OFDM receivers can handle abrupt channel variation across OFDM blocks at the expense of large pilot overhead. In this paper, we focus on the progressive The work by J.-Z. Huang, S. Zhou and Z. Wang are supported by the ONR grant N (PECASE). OFDM receiver in [9], which starts from a simple initialization step ignoring intercarrier interference (ICI), and then gradually increases the ICI span during later iterations. The focus of this work is to reduce the pilot overhead while still maintaining the robust performance of the progressive receiver. The idea is to leverage the block-adaptive approach [1], [6], [11] that exploits channel correlation between adjacent OFDM blocks, and combine it with pilot-based channel estimation to robustly initialize the progressive receiver. Specifically, the proposed method has two components. First, it will generate a set of artificial measurements based on the estimated channel of the previous block, where both phase compensation [1], [13], [14] and amplitude compensation are incorporated. Second, the receiver combines the set of artificial measurements with the set of measurements on pilot subcarriers of the current block to perform sparse channel estimation, where the different levels of reliability of the measurements are accounted for. Later iterations of the progressive receiver rely on hard or soft estimates of the symbols from the channel decoder. We use extensive experimental data to verify the performance of the progressive receiver with the proposed hybrid initialization method. The experimental data were recorded from two experiments, SPACE08, (Oct. 14 Nov. 1, 2008) and MACE10 (July 23, 2010), both of which were conducted off the coast of Martha s Vineyard, MA. The transmitters and receivers in SPACE08 were kept stationary while in MACE10 the transducer array was moving slowly. These experimental results confirm the robustness of the proposed hybrid initialization method while reducing the pilot overhead. In both SPACE08 and MACE10, the spectral efficiency can be increased more than 30% with the hybrid initialization method without too much performance degradation. We have also extended the hybrid initialization approach to the progressive receiver for MIMO-OFDM transmissions [10]. The performance improvement in MIMO OFDM systems is more pronounced, as the number of pilots per transmitter is usually small. The rest of the paper is organized as follows. Section II presents the system model. Section III presents the proposed initialization method. Section IV presents the experimental results for SIMO in SPACE08 and MACE10. Section V extends the hybrid initialization method to the MIMO setting. Conclusions are drawn in Section VI.

2 II. SYSTEM MODEL We first consider a zero-padded (ZP) OFDM system with one transmitter. Let T denote the OFDM symbol duration and T g the guard interval. The total OFDM block duration is T = T + T g. A total of K subcarriers are divided into three nonoverlapping sets: one set of pilot subcarriers S P, one set of data subcarriers S D and one set of null subcarriers S N. Denote the set of active subcarriers as S A = S P S D, and the total set of subcarriers as S all := { K/2,...,K/2 1}. Forthe nth OFDM symbol, the transmitted passband signal is ] } e j2πfct {[ x n (t)re k S A s n [k]e j2π k T t g(t),t [0,T ] (1) where g(t) is the pulse shaping filter, and s n [k] is the transmitted data symbol on the kth subcarrier of the nth block. After the transmitted signal passes through a UWA channel, the following pre-processing is applied on the received signal y n (t) at the receiver [2]. A resampling operation is applied to remove the main Doppler effect, leading to the resampled signal z n (t). After downshifting, a carrier-frequency offset compensation is performed on the baseband signal z n (t) by multiplying e j2πεt, yielding z n (t)e j2πεt with ε denoting the carrier-frequency offset. The frequency measurement on the mth subcarrier is obtained after taking the Fourier transform of z n (t)e j2πεt, z n [m] = H n [m, k]s n [k]+w n [m], (2) k S A where H n [m, k] specifies the contribution of the kth symbol to the measurement on the mth subcarrier, and w n [m] is the ambient noise. In this paper, we focus on the receiver structure as shown in Fig. 1, where the main body of the progressive structure was developed in [9]. We next describe the initialization phase and the progressive processing phase in [9], and then propose a new initialization approach in Section III. A. Initialization In the initialization phase, the ICI is assumed negligible, and the system model (2) is simplified to z n [m] H n [m]s n [m]+v n [m], (3) where v n [m] denotes an equivalent noise consisting of ambient noise and the residual ICI. The measurements on pilot subcarriers, denoted as ˇH n [m] = z n[m] s n [m], m S P, (4) can be used for channel estimation. Here, the underlying channel model is assumed to time-invariant as N p h n (τ) = A n,p δ(τ τ n,p ), (5) p From previous OFDM block Fig. 1. Channel Prediction Channel reestimation Pre-processing; set D = 0 Channel estimation Noise variance estimation ICI equalization Nonbinary LDPC decoding success or D = Dmax Yes Output decisions The n th OFDM block Progressive receiver Increase D; provide soft information No To the next OFDM block The progressive receiver for underwater acoustic OFDM systems. where N p denotes the number of paths, and A n,p and τ n,p are the amplitude and delay of the pth path at the nth OFDM block, respectively, such that N p H n [m] = A n,p e j2πτn,p(fc+m/t ). (6) p After channel estimation, data demodulation and decoding are carried out. A certain number of pilots are needed for the initialization step to have a reasonable performance. In our previous work [9], [10], one quarter of subcarriers are assigned as pilots for a blockwise initialization with the assumption that the UWA channel changes rapidly from block to block. B. Progressive Processing The motivation of the progressive reception is to adapt the OFDM receiver to different channel conditions in an automatic fashion, which progressively increases the ICI span during iterations. After the initialization, symbol estimates fed back from the channel decoder are available, which are used as additional pilots so that channel estimation can be carried out in the presence of ICI. Using a banded assumption H n [m, k] 0, m k >D, (7) with D denoting the ICI depth, the system model is correspondingly updated as z n [m] = k=m+d k=m D H n [m, k]s n [k]+v n [m], (8) where the value of D gradually increases as the iteration goes on; (Note that the index k is upper bounded by K/2 1 and

3 lower bounded by K/2 in (8)). The underlying channel is now time-varying, defined as N p h n (τ,t)= A n,p δ (τ (τ n,p a n,p t)), (9) p with a n,p denoting the Doppler rate of the pth path. The ICI coefficients H n [m, k] depend on the N p triplets {A n,p,τ n,p,a n,p }; the exact formulation was first derived in [8]. Compressive sensing techniques can be employed to reconstruct the channel coefficients {H n [m, k]} by explicitly estimating the N p triplets {A n,p,τ n,p,a n,p }. If decoding of the current iteration is not successful, the ICI depth in the system model will be increased to address a larger Doppler spread in the next iteration. In this paper, D is increased as 0,1,2,3 in the progressive steps after the initialization. III. THE PROPOSED INITIALIZATION METHOD To reduce the pilot overhead during the initialization phase, we exploit the channel correlation between adjacent OFDM blocks. The proposed initialization method involves two new elements: Channel iction. The receiver runs channel estimation again on the previous data block to obtain ˆH n 1 [m] based on the ICI ignorant model in (3) using all the estimated symbols of the previous block. Then it carries out a iction step to generate a set of artificial measurements { ˇH that could be used for channel estimation for the current block. Channel estimation. The receiver now has two sets of measurements: { ˇH n [m]} m SP on the pilots subcarriers and { ˇH based on iction from the previous block. These two sets of measurements have different reliability levels, especially the accuracy of iction depends on how fast the underlying channel varies. The proposed channel estimation algorithm judiciously combines these measurements, accounting for their measurement uncertainties. We next specify the details of these two steps. A. Channel Prediction We make the following assumptions on how the channel parameters are related from one block to the next: i) all paths undergo the same amplitude and phase fluctuations A n,p = γ n A n 1,p, p, (10) and ii) all paths have a common delay shift, τ n,p = τ n 1,p +Δτ n, p (11) where γ n = γ n e j γn is a complex scalar and Δτ n is the common delay shift; both need to be estimated. Once the estimates ˆγ n and Δˆτ n are available, the channel iction of the nth block is obtained as ˇH n n 1 [m] =ˆγ ˆH j2πm Δˆτn n n 1 [m]e T, m Sall. (12) Now we specify how to estimate γ n and Δτ n. Note that the same pilot subcarriers are available at all OFDM blocks in our system design. Denote the indices of S P pilots as {p 1,...,p SP }. We stack observations on pilot subcarriers in two adjacent OFDM blocks as z n = [ z n [p 1 ],z n [p 2 ],...,z n [p SP ] ] T (13) z n 1 = [ z n 1 [p 1 ],z n 1 [p 2 ],...,z n 1 [p SP ] ] T (14) The parameters γ n and Δτ n are obtained via {ˆγ n, Δˆτ n } = arg min z n γ n D(Δτ n )z n 1 2, (15) {γ n,δτ n} where D(Δτ n ) is a diagonal matrix with e j2πp kδτ n/t as its (k, k)th entry. For each tentative Δτ n, the estimate of γ n is available through the least-squares solution. Hence, a onedimensional search is needed to solve (15). The normalized mean-squared-error (NMSE) measures the iction accuracy NMSE(n) = z n ˆγ n D(Δˆτ n )z n 1 2 z n 2. (16) Remark: Using measurements on pilot subcarriers for phase compensation is a common practice in wireless OFDM systems. For example, in [13] a common phase shift due to residual carrier frequency offset is obtained by comparing measurements across two blocks. This corresponds to the formulation in (15) by setting Δτ n and γ n. in [14], a weighted least-squares approach is proposed to estimate the common phase shift due to carrier frequency offset and a frequency-dependent phase shift due to timing offset. This corresponds to the formulation in (15) by setting γ n. The difference from [14] is that the amplitude γ n is allowed to change across blocks, a situation proper for UWA channels. For underwater acoustic OFDM, frequency-dependent phase shift compensation was first proposed in [1], and applied in different settings, e.g., [6], [11], which corresponds to set γ n = 1 in (10) and search for a delay offset Δτ in (11). Parameter estimation in [1], [6], [11] was carried out by comparing the phase differences of the demodulated symbols before and after the decision device, within one OFDM block. As such the method in [1], [6], [11] does not require any pilots. B. Channel Estimation with Two Sets of Measurements The progressive receiver now has two sets of measurements to perform the initial channel estimation: { ˇH n [m]} m SP in (4) on the pilots subcarriers of the current block, and { ˇH in (12) based on iction from the previous block. Combining measurements with different origins is a well studied problem in the data fusion literature. To combine these measurements properly, the key is to evaluate the associated measurement uncertainties. With σs 2 denoting the energy of the pilot symbols, the variance of ˇH n [m] is calculated as σ1,n 2 = E{ ˇH n [m] H n [m] 2 } = E m S N { z n [m] 2 } σs 2. (17)

4 TABLE I SYSTEM AND ENVIRONMENTAL IN SPACE08 AND MACE10 Experiment name SPACE08 MACE10 Carrier frequency f c 13 khz 13 khz Bandwidth B 9.77 khz 4.88 khz No. subcarriers K No. pilots S P No. nulls S N Symbol duration T ms ms Subcarrier spacing Δf 9.54 Hz 9.54 Hz Guard interval T g 24.6 ms 25.2 ms Water depth m 15 m 80 m NMSE [db] No compensation Common phase Common delay Joint phase and delay Joint phase, delay and amplitude For the icted measurements, we approximate the uncertainly as σ2,n 2 = E{ E{ ˇH = ˇH n n 1 [m] H n[m] 2 } n n 1 [m] H n[m] 2 } E [ H n [m] 2 ] E [ H n [m] 2] NMSE(n)E [ ˇH n [m] 2], (18) Normalized by the corresponding uncertainties, the measurements are stacked into two vectors as y n (1) = 1 [ ˇHn [p 1 ],..., ˇHn [p SP ] ] T (19) σ 1,n y n (2) = 1 [ ] T ˇH σ n n 1 [ K/2],..., ˇH n n 1 [K/2 1] 2,n (20) Assuming that the maximum channel delay is T g, we sample the delay on a grid as { T τ 0, λk, 2T } λk,...,(n τ 1)T (21) λk where the time resolution is chosen as a fraction, 1/λ, ofthe baseband sampling time T/K, leading to N τ = λkt g /T tentative delays. Let ξ l be the complex amplitude for the lth path at delay τ l, and ξ denote the channel vector corresponding to N τ tentative delay points. Define A (1) amatrixofsize S P N τ having (k, l)th entry as e j2πp kτ l /T, and A (2) a matrix of size K N τ having (k, l)th entry as e j2πkτl/t.a sparse channel estimation [8] is then performed based on [ ] y ˆξ (1) [ ] 2 n A (1) =argmin ξ y n (2) A (2) ξ + ζ ξ 1 (22) where ζ controls the sparsity of the solution. Once ˆξ is obtained, the channel frequency response is calculated as in (6). If the information symbols cannot be successfully decoded with the current channel estimate, the progressive processing phase will be started. IV. EXPERIMENTAL RESULTS We use data recorded during the surface processes and acoustic communications experiment 2008 (SPACE08) and mobile acoustic communications experiment 2010 (MACE10), both of which were conducted off the coast of Martha s Vineyard, MA. In SPACE08, the transmitters and receivers were kept stationary. Three receivers, labeled as S1, S3 and S5, were 60 m, Block index Fig. 2. NMSE comparison with different channel iction methods in SPACE08, file id: F013 C0 S5. NMSE [db] No compensation Common phase Common delay Joint phase and delay Joint phase, delay and amplitude Block index Fig. 3. NMSE comparison with different channel iction methods in MACE10, file id: m and 1000 m away from the transmitter, respectively. One data burst was transmitted every two hours. For each transmission, there were 20 OFDM blocks with the parameters specified in Table I. In MACE10, the receive array was kept stationary and the transmitter was towed slowly during the experiment. There were two tows in MACE10, in which the OFDM signal was transmitted continuously every four minutes for the experimental duration with the parameters specified in Table I. In this paper, we present the results of tow 1 to illustrate the OFDM performance in the moving environment. The overall spectral efficiency (in bits/s/hz) is α = T (K S N S P ) r c log T + T g K 2 M, (23) where r c is the code rate, which is 1/2 in all settings, M is the constellation size. With bandwidth B, the data rate is R = αb bits per second. A. Comparison of Channel Prediction Methods We compare the following channel iction strategies: 1) No compensation: setγ n and Δτ n in (12). 2) Common phase compensation: a common phase shift is estimated by setting γ n and Δτ n in (15). 3) Common delay compensation: a common delay offset is estimated by setting γ n in (15).

5 pilot based hybrid pilot based pilot based hybrid 10 4 initialization initialization initialization hybrid (a) S1 (60 m) (b) S3 (200 m) (c) S5 (1000 m) Fig. 4. Performance of 16QAM in SPACE08, 12 phones are combined. Decoded BER Use icted measurements only Pilot only Hybrid Block index Hybrid Initialization Pilot based Fig. 5. Comparison of initialization methods, 64 pilots, 4 phones are combined,space08, fileid: F013 C1 S1. Dashed lines: genie-aided. Fig. 6. performance of 16QAM in MACE10, 1 phone used. 4) Joint phase and delay compensation: a common phase and a common delay are obtained with γ n in (15). 5) Joint phase, delay and amplitude compensation: the proposed solution in (15). From Figs. 2 and 3, we see that The joint phase, delay and amplitude compensation strategy outperforms other schemes uniformly in both SPACE08 and MACE10 testings. This justifies amplitude compensation in addition to phase compensation. With the joint phase, delay and amplitude compensation method, the NMSE in SPACE08 is around -9 db while it is around -15 db in MACE10. Hence, the channel in MACE10 is more stable to be icted. In the following, we adopt the joint phase, delay and amplitude method to report all the following results. B. Comparison of Initialization Methods During the initialization phase, the receiver has two sets of measurements: { ˇH n [m]} m SP and { ˇH. We compare the performance of the initialization step using (i) only the measurements on pilot subcarriers, (ii) only the icted measurements, and (iii) both sets of measurements. Fig. 5 depicts the decoded bit error rate (BER) at the end of the initialization phase, where genie-aided means that all the decoded symbols in the previous block are assumed correct. As expected, the performance of the pilot-only initialization is stable across the blocks, while that of using the icted measurements vary across blocks. The hybrid initialization is uniformly better than the alternatives. C. Performance: SPACE08 Fig. 4 shows the block error rate () performance for the progressive receiver with pilot-based and hybrid initialization strategies using different number of pilots in SPACE08 from Julian dates 295 to 302 averaged over more than 1500 OFDM blocks. As the available number of pilots decreases, the performance for both initialization methods deteriorates. However, the performance degradation for the hybrid initialization is much smaller than the pilot-based method. The pilot-based initialization needs 128 pilots to ensure a good receiver performance, while the hybrid method only needs 32 pilots in the tested S1, S3 and S5 settings. If 32 pilots were used instead of 256 pilots, the spectral efficiency with 16-QAM constellation and rate 1/2 coding would be 1.43 bits/s/hz instead of 1.07 bits/s/hz, a 33% improvement. D. Performance: MACE10 Fig. 6 shows the performance for the progressive receiver with pilot-based and hybrid initializations in MACE10.

6 Fig. 7. Fig. 8. Initilization = 0 = 1 = 2 = 3 Hybrid Pilot based phones performance, QPSK, N t, MACE10. Hybrid initilization = 0 = 1 = 2 = phones performance, QPSK, N t =4, MACE10. We can see that the system performance is robust with different number of pilots. With hybrid initialization, 94% and 99% OFDM blocks can be recovered when with 8 and 16 pilots, respectively. However, with pilot-based initialization, the performance degrades drastically when the number of pilots is reduced to 48, almost half OFDM blocks lost, while 96% of them can be decoded with 64 pilots. If 16 pilots were used instead of 128 pilots, the spectral efficiency with 16-QAM constellation and rate 1/2 coding would be 1.41 bits/s/hz instead of 1.06 bits/s/hz, a 33% improvement. V. EXTENSION TO MIMO OFDM The proposed hybrid initialization method can be easily extended to the progressive MIMO-OFDM [10]. After the initialization step, the same progressive processing is applied as in [10], where N t iterations among channel estimation, MIMO detection, and channel decoding are carried out for each system model with a particular ICI depth D. In the MIMO-OFDM, the total pilot subcarriers are divided into N t data streams evenly, i.e., each data stream has S p /N t pilot subcarriers. The overall spectral efficiency is N t times of that with single transmitter. We use the experimental data in MACE10, where the total number of pilots is S P = 128. Case 1: N t = 3. The number of pilots available per data stream is 128/3 = 42. The spectral efficiency with QPSK modulation and rate 1/2 coding is 1.59 bits/s/hz. Fig. 7 compares the performance with pilot-based and hybrid initializations. As the available number of pilots per transmitter is limited, the performance of the pilot-based initialization is poor. Significant performance improvement can be achieved with the hybrid initialization method. Case 2: N t =4. The number of pilots available per data stream is 128/4 = 32. The spectral efficiency with QPSK modulation and rate 1/2 coding is 2.12 bits/s/hz. Due to the limited available number of pilots, the pilot-based initialization method does not work. However, the hybrid initialization method still works well, as shown in Fig. 8. VI. CONCLUSIONS In this paper we developed a robust initialization scheme for the progressive underwater acoustic OFDM receivers, where channel estimation judiciously combines two sets of measurements with different reliabilities: one set of artificial measurements icted from the channel estimate of the previous block, and one set of measurements on pilot subcarriers of the current block. Extensive experimental results demonstrated robust performance with reduced number of pilots. For MIMO-OFDM systems, where the number of pilots is small per transmitter, the proposed hybrid initialization method enables dramatically improved receiver performance. 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