Iterative MMSE-DFE Equalizer for the High Data Rates HF Waveforms in the HF Channel Mahmoud A. Elgenedy 1 , Essam Sourour 2 and Mohammed Nafie 3 1 Varkon Semiconductors, Egypt 2 Alexandria University, Egypt 3 Cairo University, Egypt melgenedy@varkonsemi.com, sourour@ieee.org, mnafie@ieee.org Abstract—several researches investigate the performance of the conventional adaptive equalizers for the medium data rates HF waveforms (up to 8 PSK) and show that they are suitable for mitigating the HF channel. However, the performance of these types of equalizers is very bad for the high data rates HF waveforms (up to 64QAM). Most of the later researches in the high data rates HF waveforms are based on the soft turbo equalizers which are very complicated. In this paper, we try to design the lowest complex equalizer can mitigate the HF channel for the high data rates waveforms. We investigate the performance of the minimum mean square error decision feedback equalizer (MMSE-DFE) indirectly adaptive through channel estimation based on least square estimation (LS). We show that the basic performance of the MMSE-DFE cannot satisfy the standard requirements, and then we introduce two additional enhancements. First, an effective channel estimation technique (double estimation) is proposed. The new estimator shows a clear performance enhancement over simple least square estimation with linear interpolation (about 3 dB gain at 1e-5 BER for the 64QAM). The second enhancement is to use the iterative structure through decoder using the same conventional equalizer and decoder and this gives another 3 dB gain at 1e-5 BER for the 64QAM. Iterative structure is less complicated than turbo equalizers for sure, as turbo equalizers require a lot of changes in the equalizer, decoder and demapper blocks to be SISO modules. Final equalizer model satisfies all the strict requirements of both (STANAG 4539 annex B) and (MIL- STD-188-110B app. C) standards under the ITU-R Poor channel conditions. In addition, we compare our performance with two different vendors of HF modems and other different research and show that our performance is very competitive. Keywords-MMSE; DFE; Iterative Equalization; HF; LS; I. INTRODUCTION The HF band is defined as the frequency range of 3 to 30 MHz in which there are two basic modes of propagation: ground waves and sky waves. As their names imply, ground waves travel along the surface of the earth, while sky waves “bounce” back to earth hundreds or thousands of miles away. Depending on frequency, time of day, and atmospheric conditions, a signal can bounce several times before reaching a receiver. Using sky waves can be tricky, since the ionosphere is constantly changing. Therefore, the mitigation process is difficult in these channel conditions, especially when high data rates waveforms are used. HF waveform standards, produced by either STANAG (published by NATO) or the MIL-STD (published by US DoD), are three main types: Frequency shift keying FSK, Parallel-tone waveforms and Serial-tone waveforms. FSK is inefficient in terms of power as well as bandwidth. The authors in [1] show that the basic performance of the serial- tone waveform and parallel-tone waveform standards is similar, but the ECC used in the serial-tone waveform standards performs better than used in the parallel-tone waveform standards. For this reason, serial-tone waveforms have gained popularity. For an unknown and time-varying channel, equalizer requires a specific algorithm to update the equalizer coefficients and track the channel variations. There are two basic approaches for adaptation structures: separate channel estimation and equalization and direct adaptation of the filter coefficients. For the separate channel estimation and equalization, the channel estimation is done first (separately), and then provides equalizer with estimates of the channel impulse response. When training symbols have been transmitted, they can be of course used in the estimation. Between the training sequences, when data symbols have been transmitted, hard- decided symbols generated from the output of the equalizer are often used as an input signal to the channel estimator, in which case error propagation will degrade the performance of the receiver. If the channel is slowly varying, it may suffice to update the channel estimate only once per block of received symbols (i.e.: no need to use the hard-decided symbols). In this case, the channel estimate can either be kept constant between the training sequences, or interpolation can be used to generate a channel estimate which also varies between the training sequences. The second approach, direct adaptation, is to use an algorithm for adaptive filtering to adapt the equalizer coefficients directly. Use of various types of direct adaptation equalizers based on Kalman-DFE for medium data rate HF waveforms were proposed in [2-5]. For filter- based equalizers, direct adaptation is simpler to implement than separate channel estimation, but the ability to track ,((( $VLORPDU channel variations is worse, for two reaso n number of parameters estimated by the ad a generally larger because the length of the equ a few times larger than the length of the CIR f o to p erform well. Secondly, channel variation i jumps) and slower than filter coefficients an can be expected. The fact that separate cha n outperforms direct adaptation in HF commun i was demonstrated by [6] and [7]. Decision feedback equalizers DFE applications where the channel distortion is t o linear equalizer to handle, and are commonpl a wireless systems. For the DFE equalizers, m o errors result from the bad reliability of har d equalizer output, which affect the adaptation p r The main idea behind iterative or turbo s exchange the information (hard or soft infor m the decoder and the equalizer iterativel y interleaver). A returned data from decoder reliable than equalizer output hard decisions with iterations. The main difference betwee n turbo (in this paper) is the type of data exc h information is used, we call this Iterative, b expression Turbo is used with soft informatio n In the case of the iterative structure, we equalizers and decoders as in conventional main difference as explained previously is t o returned from decoder instead of hard decisio output. Returned data from decoder shoul d interleaver again then encoder and finally to Iterative structure enhances the estimated er r for channel estimation. In case of Deci equalizers, use of good quality decoder output equalizer output decisions enhances the ISI ca n structure of turbo equalizer is quite similar t structure exce p t exchanging soft values (L L hard decisions. Exchanging soft values r modifications for both equalizer and decod them should accept soft information at its in p soft information as output (SISO modules). Linear MMSE using a priori information [8]. In [9], the author proposes the Linear M M ISI cancellation in a turbo equalization str u medium data rate standard and extends the r data rates in [10] with some tweaking in t h order for the iterative procedure to conve r equalization for the high data rates is also p r 12] with less details about the design. Iterati v directional Kalman-DFE is used to mitigate t h for the high data rates HF in [13]. How e p erformance does not meet the standard requi r higher constellations. The authors show a limitation even with increasing the number of limitation is due to the direct adaptation s t limits the number of equalizer taps. n s: Firstly, the a ptive filter is a lizer must be a o r the equalizer s smoother (no d the behavior n nel estimation i cation systems are used in o o severe for a a ce in practical o st of equalizer d decisions of r ocess. s tructures is to m ation) between y (through an is much more and improved n iterative and h anged. If hard b ut the famous n . e use the same receivers. The o use the data ns of equalizer d pass on the the modulator. r or signal used sion feedback data instead of ncellation. The t o the iterative L R) instead of r equires some er, as both of p ut and provide is proposed in M SE with soft u cture for HF r esults for high h e algorithm in r ge. The turbo r oposed in [11- v e structure bi- h e HF channel e ver, the final r ements fo r the a performance iterations. This t ructure which In this paper, we investigat e MMSE-DFE equalizer where t h LS estimation during the train i interpolation to get the estim a effective enhancement for th proposed by re-estimating the c h using LS from hard decisions f o operation (double estimation). W structure model instead of using t structure. Finally, we show that all performance requirements i n very competitive results when c o and researchers. The rest of the paper is orga n section presents the system m o performance of the MMSE-D F p resents the enhancement for th e double estimation. In Section V proposed. Finally, we draw out o u II. SYSTE M A. Transmitter The transmitter structure for H is defined in Annex B of STAN A C of MIL-STD-188-110B [15 ] p uncturing techniques shall b e convolutional code to produce a the same length as the inter-leave then scrambled and input to modulation types used are QPS K and 64QAM. An 8PSK training within the data frames. Frame str u Fig. 1: The HF frame B. Channel Model In an ionospheric HF co m transmitter and receiver are not m relative to the wavelength), whil e reflected by a large number of r a suggests that the Doppler shift h as was verified experimentally Gaussian Doppler spectrum can b e the performance of the h e channel estimation uses i ng sequences then linear a tes during the data. An e channel estimation is h annel at the data symbols llowed by moving average W e also propose the iterative t he more complicated turbo the proposed model meets n the standards and gives o mpared with other vendors n ized as follows. The next o del. In section III, basic F E is shown. Section IV e channel estimation using V the iterative structure is u r conclusions. M MODEL H igh data rate serial tone HF A G 4539 [14] and Appendix ] . The full-tail-biting and e used with a rate 1/2 rate 3/4 block code that is r. The inte r -leaver output is modulation block. The K , 8PSK, 16QAM, 32QAM symbols are then inserted u cture is shown in fig. 1. structure. [15] m munication system, the m oving (or moving slowly e the radio waves are being a ndomly moving ions. This h as a Gaussian distribution, by Watterson i n [16]. A b e writte n as ࡿ ሺ ߥ ሻ ൌ ඨ ʹ ߨࣰ ௗ ଶ ݁ ିଶఔ మ ࣰ మ ǡ (1) where ࣰ ୢ is the Doppler spread. There has been a problem that the fading spectra of different channel simulators are slightly different, such that the modem performances reported by different vendors cannot be compared directly. Furman and Nieto in [17] address this problem and proposed a strict definition on how to generate the tap gains. We follow all of these conditions in our simulations. The ITU-R Poor channel shall consist of two independent but equal average power Rayleigh fading paths with a fixed 2 ms delay between paths and with a fading two sigma bandwidth of 1 Hz. III. MMSE-DFE For a DFE equalizer, the MMSE optimal filter coefficients are normally calculated assuming that the past symbol decisions ሾሿ are correct. For a given channel impulse response ݄ and noise variance ɐ ୬ ଶ , the MMSE- optimal filter coefficients for forward filterሾሿ ሾሿൌ൫Ȟ ୟ ሾ ሿ ɉ ୟ Ȟ ୟ ୌ ሾ ሿ ɐ ୬ ଶ Ǥ ାଵ ൯ ିଵ Ǥ ୟ ሾሿ, (2) where ୌ denotes the complex conjugate transpose, Ȟ ୟ is a ሺ ୟ ͳ ሻ ൈሺ ୟ ሻ channel convolution matrix, N a is the forward filter length, ୟ is the ሺ ୟ ͳ ሻ column ofȞ ୟ , and ɉ ୟ is a ሺ ୟ ሻൈሺ ୟ ሻ diagonal matrix where the first ሺ ୟ ͳሻ diagonal elements are 1 and the remaining ሺെͳሻ diagonal elements are 0. The corresponding coefficients of the feedback filterሾሿ is given by ሾሿൌെȞ ୠ ୌ ሾሿǤሾሿ, (3) where Ȟ ୠ is ሺ ୟ ͳሻൈ ୠ matrix in the form of (4), N b is the backward filter length Ȟ ୠ ሾሿൌ ۏ ێ ێ ێ ێ ۍ ͲͲǥͲͲ ڭ ڭͲ ିଵ Ͳڭ ڭ ିଵ ଶ ڭڰ ଵ ଶ ǥ ିଵ ͲǥͲ ے ۑ ۑ ۑ ۑ ې ୬ (4) Finally, the equalizer soft output can be calculated by ොሾሿൌ ୌ ሾሿǤሾሿ ୌ Ǥ ሾሿ, (5) whereሾሿൌሾ ሾ ୟ ሿ ǥ ሾ ͳ ሿ ሾ ሿ ሿ is the equalizer input, and ሾሿൌሾሾെͳሿǥሾെ ୠ ሿሿ . A very good approximation used in our simulation is to update the filter coefficients each amount of symbols (not symbol by symbol). In all simulations we update the filter coefficients each 16 symbol (i.e.: we compute the matrix inversion only 16 times each data frame instead of 256 times), and each one of these estimations is used for 8 previous symbols and 8 next symbols. Assuming known perfect channel knowledge, the performance of the MMSE- DFE is shown in fig. 2. For channel of length, assume the system equation during the training symbols of a length ୲୰ is Ʌ ൌȦǤ , (6) where ɅൌሾɅሾͲሿɅሾͳሿǥɅሾ ୲୰ െͳሿሿ is the channel output during training sequence, andൌሾ ଵ ǥ ିଵ ሿ , and Ȧ is a ୲୰ ൈ training symbols convolution matrix. It is also preferable to neglect the first instances from the output signal Ʌ as we don't know complete information about them, and then neglect first rows from matrixȦ. The least square estimation for the channel h is ൌሺȦ ୌ Ȧሻ ିଵ Ȧ ୌ Ʌ . (7) Note that MMSE requires information about channel second statistics, i.e., noise varianceɐ ୬ ଶ , but we notice from the simulation that it is possible to fix it to a constant value for each data rate. Fig.3 shows the BER performance using LS channel estimation with linear interpolation during data symbols for 64QAM at different filter lengths. We note from fig. 3 that increasing the filter taps always enhances the performance and this is the main advantage for the indirectly adaptive equalizer over the directly adaptive one. This fact is very clear when comparing with the results of Kalman-DFE used in [13] where the authors show from simulation that the optimum number of taps is eleven for the forward filter and five for the backward. Fig. 4 shows the BER performance for the Kalman-DFE used in [13] and we can notice the big loss in the performance when compare it with the indirectly adapted MMSE-DFE. Fig. 2. MMSE-DFE performance for known channel, Decision directed mode, 72 frame interleaver size, ୟ =40, ୠ =5, Poor channel. Fig. 3. MMSE-DFE performance for Unknown channel, Decision directed mode, 64QAM, 72 frame interleaver size, ୠ =5, Poor channel. Fig. 4. Forward Kalman-DFE performance, Decision directed mode, 72 frame interleaver size, ୟ =11, ୠ =5, Poor channel. [13] IV. PROPOSED CHANNEL ESTIMATION ENHANCEMENT (DOUBLE ESTIMATION) In case of poor channel, the linear interpolation is not a good assumption for channel variation in some cases (like the case appears in fig. 5). The proposed enhancement is to repeat the channel estimation again from the output hard decisions of the equalizer using LS channel estimation with a moving window of length 25 symbols and updated each symbol. The estimated channel then smoothed using moving average filter. Finally, we compare the mean square error MSE for the two equalized sequences and choose the equalized sequence with minimum MSE. The MSE is calculated between the equalizer output and corresponding hard decisions. The enhancement for the estimate after each step is shown in fig. 5. The BER for 64QAM using double estimation is shown in fig. 6 where the performance gain is about 3dB at 1e-5 BER. Fig. 5. Real component of first path of the fading channel. Fig. 6. MMSE-DFE performance for unknown channel, Double estimation Vs Linear interpolation, 64QAM, ୟ =45, ୠ =5, Poor channel. V. I TERATIVE MMSE-DFE The main task of the iterative structure is to enhance the unreliable hard decisions feedback data which are the main reason for performance degradation in the decision feedback equalizers. Another task here for the iterative structure is to enhance the channel estimate from the data returned back from the decoder iteratively. Fig. 7 shows the performance improvement with iteration for the case of 64QAM (we can notice ~3 dB gain after 3 iterations). In the final design, we combine the iterative and the double estimation enhancements, i.e., the first time equalization (zeroth iteration) uses double estimation. The final design of the iterative MMSE-DFE (using 3 iterations and Na=56) is compared with two different HF modems by two different vendors: Harris RF-5710A modem [18] and RapidM RM6 modem [19]. We notice that the overall performance of our equalizer is better than the two modems performances (neglecting the implementation loss). The comparison between the different HF equalizers is summarized in Table 1. VI. CONCLUSIONS In this paper we present the MMSE-DFE iterative equalizer as a solution for the HF high data rates wave form standards in the poor channel conditions. An effective enhancement for the channel estimation is proposed and we show that proposed technique has about 3 dB performance gain than simple LS with linear interpolation only. Another important enhancement is to use the iterative structure through decoder which is less complicated than soft turbo equalization. The iterative equalizer enhances the performance with about 3 dB at 1E-5 BER for the 64 QAM after three iterations. The performance of the final model satisfies all the performance requirements in the Annex B of STANAG 4539 and Appendix C of MIL-STD-188-110B with competitive margins when compared to other vendors and researches. Fig. 7. Iterative MMSE-DFE performance with iteration, 64QAM, 72 frame interleaver size, ୟ =45, ୠ =5, Poor channel. Table. 1. Comparison between different HF equalizers with respect to average SNR (dB) for BER not to exceed 1.0E-5 under ITU-R Poor channel conditions and 72 frames interleaver size. Equalizer (A): Iterative MMSE-DFE with Iterative Double Channel Estimation (3 iterations – Na=56), Equalizer (B): [13], Equalizer (C): [18], and Equalizer (D): [19]. Rate bps Average SNR [dB] for coded BER not to exceed 1E-5 Eq. (A) Eq. (B) Eq. (C) Eq. (D) MIL_ST D_ 110B (App. C) STANAG 4539 (Annex B) 3200 11.9 13.21 13.3 12.7 15 15 4800 15.5 17.35 17.3 17.3 20 21 (DO:18) 6400 18.75 22.93 20.5 20.3 24 24 8000 22.75 28.95 23.9 23.9 28 28 (DO:25) 9600 27.8 35.36 27.5 27.6 33 32 (DO:29) DESIGN OBJECTIVE (DO), REFLECTING THE PERFORMANCE THAT IS KNOWN TO BE ACHIEVABLE . VII. R EFERENCES [1] J .Nieto, "Does modem performance really matter on HF channels? An investigation of Serial-Tone and Parallel-Tone Wareforms," sixth Nordic HF conference, HF 01, Fårö, Sweden, 2001. [2] E. Eleftheriou and D. D. Falconer, "Adaptive Equalization Techniques for HF Channels," IEEE Journal on Selected Areas in Communications, vol. 5, pp. 238 - 247, Feb 1987. [3] D. Falconer, A. U. H. Sheikh, E. Eleftheriou, and M. Tobis, "Comparison of DFE and MLSE Receiver Performance on HF Channels," IEEE Transactions on Communications, vol. 33, pp. 484- 486, May 1985. [4] F. M. Hsu, A. A. Giordano, H. E. Depedro, and J. G. Proakis, "Adaptive equalization techniques for high-speed transmission on fading dispersive HF channels," National Telecommunications Conference, vol. 3, pp. 58.1.1-58.1.7, November 1980. [5] F. M. Hsu, "Square root Kalman filtering for high-speed data received over fading dispersive HF channels " IEEE Transactions on Information Theory, vol. 28, pp. 753 - 763, Sep 1982. [6] S. A. Fechtel and H. Meyr, "An investigation of channel estimation and equalization techniques for moderately rapid fading HF- channels," IEEE International Conference on Communications, ICC '91, vol. 2, pp. 768-772, Jun 1991 . [7] P. K. Shukla and L. F. Turner, "Channel-estimation-based adaptive DFE for fading multipath radio channels," IEE Proceedings In Communications, Speech and Vision, vol. 138, pp. 525-543, Dec. 1991 . [8] M. Tüchler, A. C. Singer, and R. Koetter, "Minimum Mean Squared Error Equalization Using A Priori Information," IEEE Transactions on Signal Processing, vol. 50, pp. 673-683, Mar 2002 . [9] R. Otnes, "Improved receivers for digital High Frequency communications: Iterative channel estimation, equalization, and decoding," Ph.D. thesis, Department of Telecommunications, Norwegian University of Science and Technology, Trondheim, Norway, 2002. [10] R. Otnes and N. Bauer, "Evaluation of turbo equalization for the high- rate HF waveforms of STANAG 4539," Ninth International Conference on HF Radio Systems and Techniques, pp. 114-119, June 2003. [11] J. Nieto, "Iterative decoder-aided equalization of STANAG 4539 high data rate waveforms," Ninth International Conference on HF Radio Systems and Techniques, pp. 42-47, June 2003. [12] J. Nieto, "Investigating the benefits of iterative equalization and decoding of STANAG 4539 HF waveforms," The Institution of Engineering and Technology 11th International Conference on Ionospheric radio Systems and Techniques, pp. 1-5, April 2009. [13] Mahmoud A. Elgenedy, Essam Sourour and Magdy Fikri "Iterative Bi-directional Kalman-DFE Equalizer for the High Data Rate HF Waveforms in the HF Channel," The First International Conference on Communications, Signal Processing, and their Applications ICCSPA’13, Sharjah, February 2013. [14] STANAG, "STANAG 4539: Technical Standards for Non-Hopping HF Communications Waveforms," ed: STANAG, 2000. [15] DOD, "MIL-STD-188-110B: Interoperability and Performance Standards for Data Modems," ed. USA: US Department of Defense, 2000. [16] C. C. Watterson, J. R. Juroshek, and W. D. Bensema, "Experimental Confirmation of an HF Channel Model," IEEE Transactions on Communication Technology, vol. 18, pp. 792-803, December 1970. [17] W. N. Furman and J. Nieto, "Understanding HF channel simulator requirements in order to reduce HF modem performance measurement variability," Sixth Nordic HF Conference, HF 01, 2001. [18] J. W. Nieto, "Performance Testing of MIL-STD-188-11OB High Data Rate HF Waveforms," Eighth International Conference on HF Radio Systems and Techniques, pp. 107 – 111, Guildford, July 2000. [19] RapidM, RM6: HF Data Modem & ALE Controller, Pretoria, South Africa. . the performance of these types of equalizers is very bad for the high data rates HF waveforms (up to 64QAM). Most of the later researches in the high data rates HF waveforms are based on the. researches investigate the performance of the conventional adaptive equalizers for the medium data rates HF waveforms (up to 8 PSK) and show that they are suitable for mitigating the HF channel. . equalizers which are very complicated. In this paper, we try to design the lowest complex equalizer can mitigate the HF channel for the high data rates waveforms. We investigate the performance