- Open Access
Non-maximally decimated filter bank-based single-carrier receiver: a pathway to next-generation wideband communication
© Chen et al.; licensee Springer. 2014
- Received: 22 November 2013
- Accepted: 17 March 2014
- Published: 8 May 2014
We present the design of a wideband digital modem based on non-maximally decimated filter bank (NMDFB) with perfect reconstruction (PR) property. The PR-NMDFB contains an analysis filter bank (AFB) and a synthesis filter bank (SFB) whose efficient polyphase forms are named as polyphase analysis channelizer (PAC) and polyphase synthesis channelizer (PSC). The waveform being processed is the legacy square root Nyquist-shaped quadrature amplitude modulation (QAM). In contrast to orthogonal frequency division multiplexing (OFDM) systems, the shaped QAM transmission has much superior performance properties in throughput, peak-to-average power ratio (PAPR), and synchronization. We will show the PR-NMDFB is capable of efficiently performing several key tasks of a digital receiver with dramatic workload reduction. This includes digital filtering, carrier recovery, and symbol timing recovery. Moreover, the nature of NMDFB allows the signal processing to operate a significantly reduced sample rate, which is a desired characteristic for replacing current FIR implementation in wideband systems.
- Filter bank
- Single-carrier transmission
- Perfect reconstruction
- Non-maximally decimated filter bank
The wireless technology has experienced significant growth in the past decades; and we have seen generations of wireless communication systems increasing their bandwidth and data rates by more than an order of magnitude per generation. Current systems offer 100-Mbps data rates in 20-MHz bandwidth links. We can expect future generation wireless systems to offer 1 Gbit/s data rates with 500-MHz bandwidth links. As the demands for high data rate communication grows, the conventional methods, i.e., shaped quadrature amplitude modulation (QAM), become seemingly incapable of dealing with highly dispersive channels in a cost-effective manner. The legacy receivers often require building several time offset overlapped finite impulse response (FIR) filters operating in parallel to perform synchronization, matched filtering, as well as channel equalization. As the signal bandwidth grows comparable to the hardware's clock rate, any FIR filtering becomes extremely expensive. Meanwhile, the frequency-selective channel requires very sophisticated equalizers, which further increases the difficulty in fitting the legacy QAM waveform into today's communication systems. To overcome this problem, many broadband techniques such as spread spectrum and multicarrier transmission were introduced. Although the orthogonal frequency division multiplexing (OFDM) technique suffers from problems such as high peak-to-average power ratio (PAPR), sensitivity to carrier frequency offset, and time and frequency guard spans, it has become dominant because of its simple equalizer structure for highly frequency-selective channels. An unappreciated advantage of OFDM is its fast Fourier transform (FFT)-based block processing nature, which not only takes advantage of FFT's efficiency but also reduces the hardware processing speed, due to the serial/parallel conversion at the transmitter and receiver.
Several authors have studied the FBSC from equalization perspectives and have shown the equalization task is closely related to subband adaptive filtering (SAF). The authors in show the preliminary examples on FB-based channel identification. The authors in demonstrated the design of fractionally spaced equalizer (FSE) via NMDFBs (oversampled FBs). The authors in this paper address the design of FBSC from the synchronization perspective. In particular, we will introduce the recently proposed PR-NMDFB-based digital filtering concept which allows us to carry out much more rigorous performance analysis towards FBSC compared to the past works[11–14]. Note that the PR-NMDFB in practice will become near-perfect reconstruction (NPR) due to practical realization; however, the bounds on reconstruction errors require arithmetic with sufficient bit width to support the stop-band attenuation levels.
We will present the NMDFB-based carrier frequency recovery, symbol timing recovery, and matched filtering (MF) process. These independent tasks were not discussed in the past works on FBSC. The novelty of this paper is as follows: (1) we present the PR-NMDFB filtering-based formulation for FBSC and (2) propose the synchronization techniques for FBSC in the FB-transformed domain. To our best knowledge, these topics were not presented before or studied in depth.
The organization of this paper is as follows: Section 2 introduces the PR-NMDFB and its filtering property, Section 3 presents the carrier frequency recovery technique, Section 4 solves the symbol time recovery problem, Section 5 performs the complexity analysis, Section 6 presents the simulation results, and Section 7 draws the conclusion.
The basic building blocks of FBSC modems are based on oversampled or non-maximally decimated FBs with PR support, which are in general considered well studied[17–19] and have numerous variations[20–24]. The implementation of FBSC can be viewed using FB to perform digital filtering in the channelizer domain; filtering is achieved by altering the gain and phase over each spectral span presented at analysis filter bank (AFB) outputs. In order to accomplish this FB-based filter task, several restrictions on FB need to be met: (1) it must have PR or near-PR property. (2) The aliasing cancelation should not involve other channels; as a counter example, the cosine-modulated filter bank (CMFB) requires adjacent channels to cancel aliasing thus generally cannot be used in communication systems. (3) Efficient polyphase implementation must exist, preferably with fixed channel size M and adjustable decimation factor D (D < M). One filter bank design that meets these conditions is proposed by Karp, in Figure nine of under the name 'DFT polyphase realization,’ which serves as an intermediate step to derive the polyphase implementation of modified DFT (MDFT)[20, 25].
2.1 Background on PR-NMDFB
and is the total transfer function (TF) for the M-path, decimated by D, AFB, and SFB. is the desired signal TF, whereas is the undesired aliasing TF. We require the NMDFB to have PR property[20, 25]. This condition translates to (1) zero aliasing TF and (2) distortionless signal TF, A(Z) G(Z) = HNYQ(Z), where HNYQ(Z) is any Nyquist pulse.
2.2 The filtering property of PR-NMDFB
The PR-NMDFB-based filtering is discussed intensively in; here, we briefly review its concept and establish our notation. Given the discrete time Fourier transform (DTFT) of a target spectrum S(ω) and its finite time duration or truncated impulse responses s(n), n = 0, 1, … Nmax, the goal is to synthesize or approximate it via an M-path PR-MNDFB.
In practice, as detailed in, this filter can be designed by using a windowed (i.e., Kaiser) sinc function.
Note that, if γs,m ≤ Bε,m, the phase distortion is from - π to π. However, this also implies the target spectrum S(ω) has significant attenuation at ω m and the signal around frequency ω m may not have significant value, i.e., in the stop-band of the target spectrum.
where is the residue CFO and phase offset after down-conversion and τ is the sampler time offset. Note, we do not consider the multipath channel effects in this paper. The equalization for FBSC is treated in; it can be easily shown from PR-NMDFB filtering property that setting IPE as the linear equalizer response is equivalent to an FIR linear equalizer.
3.1 CFO correction in filter -bank-transformed domain
3.2 CFO detection in FB-transformed domain
The CFO detection is based on a pair of BE filters centered on the left and right of the received signal's transition bands. They can be efficiently integrated in the NMDFB structure via spectral shaping IPEs. As shown in, the target spectrum of the two BE filters is the frequency derivative of the SRRC shaping filter's left and right transition bands. To synthesize an NMDFB-based BE filter, one simply sets the target spectrum S(ω) to be the ideal BE filter spectrum with IPE gain K m = S(ω m ). Unlike the conventional time domain implementation (Figure 5b) in which suboptimal, symmetrically extended BE filters have to be built to avoid designing sharp filter transition bands, the PR-NMDFB-based filter allows us to directly synthesize the ideal BE filter spectrum and produce near-optimal frequency response as shown in Figure 5a. We will further demonstrate this in the simulation section.
Serving as the error detector within a PLL, the input signal to the BE filter must already be frequency-shifted or error-compensated as shown in Figure 4. Re-examine Equation 12 and consider a non-trivial IPE, i.e.,, Equation 12a corresponds to filter the input data and then deliver the heterodyned output, whereas Equation 12b maps to first heterodyne the input signal and then apply the filtering. Clearly, the arrangement in Equation 12b matches the requirement of a loop control system. Therefore, the NMDFB implementation requires the analysis LPPF to be a low-pass filter and synthesis LPPF to be any Nyquist pulse, i.e., Figure 7. Another detail which is worth noting is that the conventional BE design produces an oversampled filter (see Figure 5). The oversampling ratio is related to the SRRC filter's transition bandwidth or the roll-off factor. Mapping to the NMDFB implementation, this means only a certain group of entries of BE filter's IPE matrix is non-zero. Equivalent of saying, only a portion of FB channels are needed to synthesize a BE filter. Therefore, M′-path, reduced size PSC is used to only synthesize the FB channels that fall into the signal's left or right transition bands. This saves computational resources and increases the efficiency of the proposed architecture.
Often, the tanh(.) function is replaced by its small signal approximation tanh(x) ≈ x for low signal-to-noise ratio (SNR) and tanh(x) ≈ sign(x) for high SNR. The authors in proposed full digital timing recovery techniques based on polyphase FB and have shown various timing error detection (TED) methods via FBs. In this paper, we adopt the TED formed by taking the product between the MF output and the derivative MF output, i.e., Figure ten of. The derivative MF is produced by taking the derivative to the time domain SRRC impulse response; this should not be confused with BE filter which is formed by taking the frequency domain derivative of the SRRC spectra.
4.1 Timing error correction in FB-transformed domain
The digital timing error correction requires building a fractional delay filter (FDF). The FDF is conventionally implemented in the time domain either via Farrow structure which is a polynomial-based interpolator or via polyphase interpolators. In this section, we introduce the NMDFB-based FDF.
From the spectral approximation point of view, the problem becomes using M spectral samples to approximate complex sinusoid up to half a cycle. In the case of straight line approximation and M = 64 , we use Equations 7 to 9 to determine the maximum magnitude error to be -70 dB and maximum phase distortion to be 3.012 × 10-4 rad. It is clear that the spectral approximation provides a very good FDF with only 64-path filter banks.
4.2 Timing error detection in FB-transformed domain
Examining Figure 9, the FBSC receiver contains one M-path PAC, two M-path PSC, two reduced size M′-path PSC, five M-entry IPEs, and two reduced size M′-entry IPEs. Let all LPPFs have L taps (real coefficient) per polyphase arm, i.e., the LPPF length for M-path PAC (or M-path PSC) is M × L and the LPPF length for M′-path PSC is M′ × L. Take the M-path, decimation by D, PAC for example: a block of D pieces of data enter the PAC, and its LPPF operates once, and so does its M-point FFT. Therefore, the workload in terms of the number of multiplies per input complex (I-Q pair) sample, for an M-path, decimation by D, PAC is calculated as, where 〈M Pnt∘FFT〉 denotes the number of multiplies required for an M-point FFT processing complex inputs. In addition, the workload for an M-entry complex coefficient IPE is.
where N is the number of taps of SRRC filter.
We now assign practical parameters to Equations 14 and 15 to make further comparison. A 65-tap, i.e., N = 64, SRRC filter with 25% roll-off factor is used for time domain implementation. Therefore, based on Equation 15, the conventional FIR approach costs 520 real multiplies per complex input. In the FBSC solution, we use M = 240, M′ = 42, and, triangular-shaped PR-NMDFB with LPPF length L = 8, and our observation shows it can well equalize multipath channels with normalized RMS delay spread τrms/T = 5. The 240-point and 42-point complex FFT cost 1,100 and 152 real multiplies, respectively,. Plugging in those parameters into Equation 14, we find the workload count for FBSC receiver is 270 real multiplies per complex input. Those numbers show the PR-NMDFB-based FBSC solution offers 48% workload reduction only for the synchronization part, and this workload reduction did not account for the linear equalization which is required in the conventional FIR approach; notice that, on the other hand, the equalization task has already been included in Equation 14. Furthermore, as will be shown in the simulation section, the 65-tap SRRC only gives 43-dB stop-band performance; however, the PR-NMDFB offers 100-dB dynamic range, an improvement by 56 dB.
This section presents the simulation results of the proposed FBSC receiver. We shall first examine the PR-NMDFB-implemented filters and compare them with the FIR-based designs. Then, we will demonstrate the behaviors of the proposed CFO recovery loop and symbol timing recovery loop.
6.1 PR-NMDFB-implemented filters
6.2 CFO recovery results
6.3 Symbol timing recovery results
We have proposed the complete receiver structure for FBSC transmission with emphasis on receiver filters and synchronization. We applied the PR-NMDFB-based filtering property in designing the wideband carrier and symbol timing synchronization. This allows us to concurrently design BE filters and fractional delay filters within the entire FB-based receiver structure. The complexity analysis shows the proposed approach offers 48% workload reduction when only the synchronization tasks are considered, and further reduction in computation is expected if equalization is considered. Moreover, in contrast to the conventional FIR approach, which requires the hardware clock to run on many times of the input sample rate, the proposed FBSC receiver allows all the filtering tasks to operate on deeply decimated sample rate, which is a highly desired characteristic for the hardware implementation of fully digital receivers.
- Ariyavisitakul S, Falconer D, Adachi F, Sari H: Guest editorial - wireless broadband techniques. IEEE J. Select. Areas Commun. 1999, 17(10):1709-1710.View ArticleGoogle Scholar
- Richard VN, Prasad R: OFDM Wireless Multimedia Communication. Artech House, Boston; 2000.Google Scholar
- Benvenuto N, Dinis R, Falconer D, Tomasin S: Single carrier modulation with nonlinear frequency domain equalization: an idea whose time has come—again. Proc. IEEE 2010, 98(1):69-96.View ArticleGoogle Scholar
- Tomasin S, Benvenuto N: Iterative design and detection of a DFE in the frequency domain. IEEE Trans. Commun. 2005, 53(11):1867-1875. 10.1109/TCOMM.2005.858666View ArticleGoogle Scholar
- Huang G, Nix A, Armour S: Feedback reliability calculation for an iterative block decision feedback equalizer, in 2009 IEEE 70th Vehicular Technology Conference Fall (VTC 2009-Fall). Piscataway, IEEE; 2009:1-5.Google Scholar
- Magarini M, Barletta L, Spalvieri A: Efficient computation of the feedback filter for the hybrid decision feedback equalizer in highly dispersive channels. IEEE Trans. Wireless Commun. 2012, 11(6):2245-2253.View ArticleGoogle Scholar
- Zhang C, Wang Z, Pan C, Chen S, Hanzo L: Low-complexity iterative frequency domain decision feedback equalization. Vehicular Technol. IEEE Trans. 2011, 60(3):1295-1301.View ArticleGoogle Scholar
- Ihalainen T, Ikhlef A, Louveaux J, Renfors M: Channel equalization for multi-antenna FBMC/OQAM receivers. IEEE Trans. Veh. Technol. 2011, 60(5):2070-2085.View ArticleGoogle Scholar
- Caus M, Perez-Neira AI: Transmitter-receiver designs for highly frequency selective channels in MIMO FBMC systems. Trans. Sig. Proc. 2012, 60(12):6519-6532.MathSciNetView ArticleGoogle Scholar
- Ihalainen T, Stitz TH, Rinne M, Renfors M: Channel equalization in filter bank based multicarrier modulation for wireless communications. EURASIP J. Appl. Signal Process 2007, 2007: 140-140.View ArticleMATHGoogle Scholar
- Yang Y, Ihalainen T, Rinne M, Renfors M: Frequency-domain equalization in single-carrier transmission: filter bank approach. EURASIP J. Adv. Signal Process 2007, 2007: 1-6.MATHGoogle Scholar
- Weiss S, Dooley SR, Stewart RW, Nandi AK: Adaptive equalization in oversampled subbands. Electron Lett. 1998, 34(15):1452-1453. 10.1049/el:19981085View ArticleGoogle Scholar
- Yang Y, Stitz TH, Rinne M, Renfors M: Mitigation of narrowband interference in SC transmission with filter bank equalization. In IEEE Asia Pacific Conference on Circuits and Systems, 2006. APCCAS 2006. IEEE, Piscataway; 2006:748-751.View ArticleGoogle Scholar
- Yang Y, Ihalainen T, Renfors M, Rinne M: Noise predictive turbo equalization for a filter bank based receiver in a SC transmission system. In IEEE 65th Vehicular Technology Conference, 2007. VTC2007-Spring. IEEE, Piscataway; 2007:2389-2393.View ArticleGoogle Scholar
- Farhang-Boroujeny B: Adaptive Filters: Theory and Applications. Wiley, Chichester; 1998.MATHGoogle Scholar
- Chen X, Harris FJ, Venosa E, Rao BD: Non-maximally decimated analysis/synthesis filter banks: applications in wideband digital filtering. IEEE Trans. Signal Process. 2014, 62(4):852-867. doi: 10.1109/TSP.2013.2295549MathSciNetView ArticleGoogle Scholar
- Bolcskei H, Hlawatsch F: Oversampled cosine modulated filter banks with perfect reconstruction. IEEE Trans. Circuits and Systems II 1998, 45(8):1057-1071. 10.1109/82.718813View ArticleMATHGoogle Scholar
- Cvelkovic Z, Vetterli M: Oversampled filter banks. IEEE Trans. Signal Process 1998, 46(5):1245-1255. 10.1109/78.668788View ArticleGoogle Scholar
- Bolcskei H, Hlawatsch F, Feichtinger HG: Frame-theoretic analysis of oversampled filter banks. IEEE Trans. Signal Process 1998, 46(12):3256-3268. 10.1109/78.735301View ArticleGoogle Scholar
- Karp T, Fliege NJ: Modified DFT filter banks with perfect reconstruction. IEEE Trans. Circuits and Systems II 1999, 46(11):1404-1414. 10.1109/82.803480View ArticleMATHGoogle Scholar
- de Haan JM: Filter bank design for subband adaptive filtering. PhD dissertation. Department of Telecommunications and Signal Processing, University of Karlskrona and Ronneby, Sweden; 2001.Google Scholar
- Harris FJ, Chen X, Venosa E, Rao BD: Wideband 160-channel polyphase filter bank cable TV channeliser. Signal Proc. IET 2011, 5(3):325-332. 10.1049/iet-spr.2010.0031View ArticleGoogle Scholar
- Harris FJ, Venosa E, Chen X, Rao BD: Polyphase analysis filter bank down-converts unequal channel bandwidths with arbitrary center frequencies. Analog Integr. Circ. S. 2012, 71(3):481-494. 10.1007/s10470-011-9746-yView ArticleGoogle Scholar
- Nguyen T: Near-perfect-reconstruction pseudo-QMF banks. IEEE Trans. Signal Process 1994, 42(1):65-76. 10.1109/78.258122View ArticleGoogle Scholar
- Fliege NJ: Multirate Digital Signal Processing. Wiley, Chichester; 1994.MATHGoogle Scholar
- Harris FJ: Multirate Signal Processing for Communication Systems. Prentice Hall, Upper Saddle River; 2004.Google Scholar
- Harris FJ, Venosa E, Chen X, Dick C: Band edge filters perform non data-aided carrier and timing synchronization of software defined radio QAM receivers. In 2012 15th International Symposium on Wireless Personal Multimedia Communications (WPMC). IEEE, Piscataway; 2012:271-275.Google Scholar
- Dick C, Harris FJ, Rice M: Synchronization in software radios. Carrier and timing recovery using FPGAs. In 2000 IEEE Symposium on Field-Programmable Custom Computing Machines. IEEE, Piscataway; 2012:195-204.Google Scholar
- Harris FJ, Rice M: Multirate digital filters for symbol timing synchronization in software-defined radios. IEEE J. Sel. Areas Commun. 2001, 19(12):2346-2357. 10.1109/49.974601View ArticleGoogle Scholar
- Franks LE: Carrier and bit synchronization in data communication: a tutorial review. IEEE Trans. Commun. 1980, 28(8):1107-1121. 10.1109/TCOM.1980.1094775View ArticleGoogle Scholar
- Harris FJ: Performance and design of Farrow filter used for arbitrary resampling. Proc. 13th Int. Conf. DSP 1997, 2: 595-599.Google Scholar
- Burrus CS, Parks TW: DFT/FFT and Convolution Algorithms: Theory and Implementation. Wiley, New York; 1984.MATHGoogle Scholar
- Shafik R, Rahman S, Islam AR: On the extended relationships among EVM, BER and SNR as performance metrics. In International Conference on Electrical and Computer Engineering, 2006. ICECE '06. IEEE, Piscataway; 2006.Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.