I Introduction
In recent years, there has been an increase in the demand for mobile communication systems and the evolution of these systems have focused, as a priority, on the increase in throughput. However, in scenarios predicted for the future generation of mobile communications, such as machinetomachine communication (M2M), Internet of Things (IoT), tactile Internet and wireless regional area networks (WRAN), there are characteristics that clearly go beyond the high data rates [1]. The challenges posed by these scenarios require: low power consumption, which makes it a problem for the synchronization of orthogonal frequency division multiplexing (OFDM) systems to maintain orthogonality between the subcarriers; short bursts of data, which prohibit the use of a cyclic prefix (CP) in all symbols due to low spectral efficiency; and the high outofband (OOB) emission of OFDM that is an issue for dynamic and opportunistic spectrum access.
Due to these requirements, Generalized Frequency Division Multiplexing (GFDM) [1] has been proposed for the air interface of 5G networks. The flexibility of GFDM allows it to cover CPOFDM as a special case. However, filtering of subcarriers results in nonorthogonal waveforms, intersymbol interference (ISI) and intercarrier interference (ICI). The Unique Word (UW) concept has been proposed for OFDM in [2] along with an optimized receiver concept. Since CP is random, its only function is to avoid the interference caused by the channel delay. The UW, being deterministic, if a non null UW is used, can be used also for synchronization and channel estimation. Many studies with UW have shown that a significant gain in bit error rate (BER) over OFDM can be obtained [2, 3, 8].
In this work, we propose the use of UW in GFDM systems which results in UWGFDM systems. We devise a signal model of a UWGFDM system considering a single UW and multiple UWs. We then develop an LMMSE receive filter for signal reception of the proposed UWGFDM system. Simulations show that the proposed UWGFDM system outperforms prior work. The paper is organized as follows: in Section II, a description of the signal model of the UWGFDM system is given; Section III describes the UWGFDM system design; the results of the simulations are presented in Section IV and in the Section V, some conclusions are drawn.
Ii Proposed Signal Model
In the proposed UWGFDM systems, the input to the system is a binary sequence organized in a vector
of length , where is the order of modulation, is the length of the data vector used in the GFDM subsymbol and is the number of time slots that make up one GFDM block.The first step is the mapper, where the binary sequence is mapped into a complex valued sequence , according to the mapping scheme adopted. In this work, we use the frequencyshift offset quadrature amplitude modulation (FSOQAM) [7] that can be exploited to address nonorthogonal conditions. Afterwards, the sequence of length obtained with the modulation of each group of bits is added to redundant subcarriers, so that , where is the number of subcarriers per GFDM subsymbol.
Then, the resulting sequence of length is reshaped by serialtoparallel conversion to a matrix with dimensions . To obtain interferencefree transmission, each element of the matrix is transmitted with its real and imaginary part using symmetric, realvalued, half Nyquist prototype filter with the offset of samples from each other and phase rotation of radians among adjacent subcarriers and subsymbols, given by
(1) 
where is the time index and .
The resulting GFDM signal can be described by
(2) 
Before transmitting the signal a UW with length or multiple UWs are added in order to preserve the circulant structure and to make frequency domain equalization possible at the receiver. Afterwards, the signal is converted to the analog domain and transmitted.
At the receiver, the received signal is described by
(3) 
where , denotes the impulse response of the channel, is the transmitted signal with addition of the UW, and is a additive white Gaussian noise.
At the receiver, the signal is converted from the analog to the digital domain, followed by the removal of the UW and equalized by
(4) 
The received data can be described by
(5) 
and,
(6) 
where denotes circular convolution with period , and represents or .
The received symbol vector is obtained by applying the parallel to serial converter, the Wiener smoothing operation and extracting the data part of the signal . After that, the data part of the signal is demapped into the detected bit vector . The block diagram of the proposed UWGFDM system is shown in fig. 1.
Iii Design of the UWGFDM System
In this section, we detail the design of UWGFDM systems [9]. The framing of UW is made by introducing a predefined sequence which shall form the tail of the data vector in the time domain . Therefore, the sequence assumes the form aiming to add the UW of length L in the time domain and to obtain [3].
In the first step, in order to get the vector structure in time domain, a reduction of the number of data subcarriers is made and a set of redundant subcarriers is added, in the frequency domain. In case of multiple UWs in GFDM systems, the matrix with data and redundant subcarriers, can be constructed as:
(7) 
where is a permutation matrix, and are the matrices of data and redundant subcarriers, respectively.
The GFDM and can be organized in a modulation matrices structured according to:
(8) 
where is a column vector containing the samples from with equal to or in (1).
The matrices and have dimensions x with an approximately diagonal block structure, according to:
(9) 
where .
With these observations, we can write each symbol of the transmitted GFDM block as:
(10) 
where
(11) 
Writing each result of with four submatrices , it is possible to write , where .
Due to the realorthogonality between the matrices and , i.e., , a code word can be obtained for each symbol of the GFDM block by
(12) 
where
is the identity matrix and
can be interpreted as a UW code generator matrix. Another interpretation is that introduces correlations in the vector of frequency domain samples of a GFDM block.In the second step, is added to the GFDM frame. The choice of (m) is made to optimize particular needs in GFDM systems, like synchronization, system parameter estimation purposes or BER gain. The symbols of can be placed in one or more symbols of a GFDM block, in a specific pattern, in order to optimize the UW autocorrelation properties. The UW sequences can be obtained by many ways, among which we highlight: the generalized Barker sequence[4] and a CAZAC sequence (Constant Amplitude, Zero Autocorrelation) [5] that are often used for channel estimation, frequency offset estimation and timing synchronization (not investigated in this work); or , which introduces a systematic complex valued block code structure within the sequence of subcarriers. Note that the gain due to the exploitation of correlations in frequency domain can be regarded as coding gain.
At the receiver, after performing the equalization and the timefrequency conversion, observing the influence of the UW on the received symbol, we can write the received vector as:
(13) 
where , and .
To eliminate the influence of the UW by subtracting from , we can consider that the channel matrix or at least an estimate of do such that , we can apply the Bayesian GaussMarkov theorem [10] to minimize the cost function , with , obtaining the LMMSE estimator for as given by
(14) 
with the noise covariance matrix , and with . Recalling that , the estimated data vector can be written as
(15) 
where represents a Wiener smoothing matrix given by
(16) 
The smoothing operation exploits the correlations between subcarrier symbols which have been introduced by (12) at the transmitter and act as a noise reduction operation on the subcarriers. Other interference cancellation techniques [11, 12, 13, 14, 15, 16, 17, 21, 23, 24, 19, 20, 22, 24, 25, 26, 27, 28, 31, 30, 31, 32, 33]. can also be examined for receive processing.
The design of the pulse shaping filter of GFDM strongly influences the spectral properties of the signal and the error rate. In this work, we use the Root Raised Cosine (RRC) with the Meyer auxiliary function proposed in [1] and described by
(17) 
where is a truncated function that is used to describe the rolloff area defined by in the frequency domain. The th subcarrier is centered at the normalized frequency and describes the overlap of the subcarriers. The function used here is the Meyer auxiliary function [6]. The use of this function as the argument of a RRC pulse shape defined in time improves spectrum properties [7].
Iv Simulations results
To validate the UWGFDM proposal, simulations were performed comparing its performance with the CPGFDM concept and with the UWOFDM and CPOFDM systems, whose performances are already widely known. In this work, we consider perfect synchronization, perfect knowledge of the channel by the receiver and . The simulations were performed with the parameters listed in Table I.
Systems  UWGFDM  CPGFDM 
Number of subcarriers [K]  64  64 
Data subcarriers []  48  64 
Redundant subcarriers []  16  0 
Length of UW and CP []  16  16 
Number of time slots [ M]  4  4 
Pulse shaping filter [G]  RRC  RRC 
Rolloff factor []  
Modulation subcarriers  FSOQAM  FSOQAM 
The CPOFDM and UWOFDM are simulated with the same parameters as CPGFDM and UWGFDM, respectively, except for the pulse shaping filter that is not used. The indexes of the 16 redundant subcarriers are chosen as in [8]. This choice, with an appropriately constructed matrix , provides minimum energy on the redundant subcarriers on average.
In the first example, we observe the performance in a channel that typically represents the WRAN scenarios [34]. These scenarios should be investigated for 5G systems. The channel has been modeled as a tapped delay line, whose power delay profile is ()[dB] for the delays ()[
s], each tap with Gaussian distribution, and is considered constant during a GFDM block period. In order to provide a simple way of equalization, the length of UW and the CP was set to
samples. In Fig. 2, we can observe that the curves UWGFDMall and UWOFDM show a similar performance and approximately 1.2 dB in better than CPOFDM and CPOFDM. It is also possible to observe that the use of a single UW in the first symbol of the GFDM block already reduces the required by approximately 0.5 dB for the same BER.In the second example, we can observe that the outofband (OOB) emission is not degraded by using the UW, and GFDM maintains its performance around 10 dB better than OFDM, as it had been observed in CPGFDM and shown in Fig. 3.
An important observation is that the peaktoaverage power ratio (PAPR) performance of UWGFDM is comparable to CPOFDM and CPGFDM systems using FSOQAM modulation.
In the last example, we compare the normalized throughput () of the systems, calculated by
(18) 
where is the block error rate. These comparisons allow us to observe how much the inclusion of redundant subcarriers affects the throughput in relation to the system with CP. Fig. 4 shows that the CPGFDM and UWGFDM have a comparable throughput (UWGFDM is slightly better for low values), and both are higher than CPOFDM. Observing the curves UWGFDMall and UWOFDM, we can conclude that the use of UW in all subsymbols of the GFDM block reduces the throughput significantly.
V Conclusions
In this work, we have introduced the concept of UW in GFDM systems. The guard interval is built by a UW instead of cyclic prefixes. This approach significantly reduces the noise on the subcarriers, maintaining the OOB obtained with the pulse shape filter in GFDM, and increases the throughput as compared to UWOFDM and CPOFDM, if applied to only one or a few block subsymbols. The use of UW in GFDM requires the application of a modulation that allows orthogonality between the subcarriers, and the possibility of the UW for synchronization and channel estimation purposes requires the use of a nonzero UW that is orthogonal to the subcarriers of the GFDM subsymbol. The proposed UWGFDM approach outperforms CPGFDM, UWOFDM and CPOFDM in all examples.
References
References
 [1] N. Michailow, M. Matthé, I. S. Gaspar, A. N. Caldevilla, L. L. Mendes, A. Festag, G. Fettweis, Generalized Frequency Division Multiplexing for 5th Generation Cellular Networks, IEEE Transactions on Communications,vol. 62, no. 9, pp. 3045  3061, Sep. 2014.
 [2] M. Huemer, A. Onic, C. Hofbauer, Classical and Bayesian Linear Data Estimators for Unique Word OFDM IEEE Transactions on Signal Processing, vol. 59, no. 12, Dec. 2011.
 [3] M. Huemer, A. Onic, Direct vs. TwoStep Approach for Unique Word Generation in UWOFDM Proceedings of the 15th International OFDM Workshop, Hamburg, Sep. 2010.
 [4] S. Golomb and R. Scholtz, Generalized Barker Sequences IEEE Transactions on Information Theory, Vol.11, No. 4, pp. 533 ? 537, Oct. 1965.
 [5] B.M. Popovic, Generalized Chirplike Polyphase Sequences with Optimum Correlation Properties IEEE Transactions on Information Theory, Vol. 38, No. 4, pp. 1406?1409, July 1992.
 [6] Y. Meyer, Ondelettes et op rateurs: Ondelettes ser. Actualités mathématiques. Paris, France: Hermann & Cie, 1990.
 [7] I. S. Gaspar, L. L. Mendes, N. Michailow, and G. Fettweis, A synchronization technique for generalized frequency division multiplexing EURASIP J. Adv. Signal Process., vol. 2014, no. 1, pp. 6776, May 2014.
 [8] M. Huemer, C. Hofbauer, J. B. Huber, NonSystematic Complex Number RS Coded OFDM by Unique Word Prefix IEEE Transactions on Signal Processing, vol. 60, no. 1, Jan. 2012.
 [9] J. T. Dias and R. C. de Lamare,“UniqueWord GFDM Transmission Systems,” in IEEE Wireless Communications Letters, vol. 6, no. 6, pp. 746749, Dec. 2017.
 [10] S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Englewood Cliffs, NJ: PrenticeHall, 1993.
 [11] R. C. de Lamare, R. SampaioNeto, “Adaptive MBER decision feedback multiuser receivers in frequency selective fading channels”, IEEE Communications Letters, vol. 7, no. 2, Feb. 2003, pp. 73  75.
 [12] A. Rontogiannis, V. Kekatos, and K. Berberidis,” A SquareRoot Adaptive VBLAST Algorithm for Fast TimeVarying MIMO Channels,” IEEE Signal Processing Letters, Vol. 13, No. 5, pp. 265268, May 2006.
 [13] R. C. de Lamare, R. SampaioNeto, A. Hjorungnes, “Joint iterative interference cancellation and parameter estimation for CDMA systems”, IEEE Communications Letters, vol. 11, no. 12, December 2007, pp. 916  918.
 [14] Y. Cai and R. C. de Lamare, ”Adaptive SpaceTime Decision Feedback Detectors with Multiple Feedback Cancellation”, IEEE Transactions on Vehicular Technology, vol. 58, no. 8, October 2009, pp. 4129  4140.
 [15] J. W. Choi, A. C. Singer, J Lee, N. I. Cho, “Improved linear softinput softoutput detection via soft feedback successive interference cancellation,” IEEE Trans. Commun., vol.58, no.3, pp.986996, March 2010.
 [16] R. C. de Lamare and R. SampaioNeto, “Blind adaptive MIMO receivers for spacetime blockcoded DSCDMA systems in multipath channels using the constant modulus criterion,” IEEE Transactions on Communications, vol.58, no.1, pp.2127, January 2010.
 [17] R. Fa, R. C. de Lamare, “MultiBranch Successive Interference Cancellation for MIMO Spatial Multiplexing Systems”, IET Communications, vol. 5, no. 4, pp. 484  494, March 2011.
 [18] R.C. de Lamare and R. SampaioNeto, “Adaptive reducedrank equalization algorithms based on alternating optimization design techniques for MIMO systems,” IEEE Trans. Veh. Technol., vol. 60, no. 6, pp. 24822494, July 2011.
 [19] P. Li, R. C. de Lamare and R. Fa, “Multiple Feedback Successive Interference Cancellation Detection for Multiuser MIMO Systems,” IEEE Transactions on Wireless Communications, vol. 10, no. 8, pp. 2434  2439, August 2011.
 [20] R.C. de Lamare, R. SampaioNeto, “Minimum meansquared error iterative successive parallel arbitrated decision feedback detectors for DSCDMA systems,” IEEE Trans. Commun., vol. 56, no. 5, May 2008, pp. 778789.
 [21] R. C. de Lamare and R. SampaioNeto, “ReducedRank Adaptive Filtering Based on Joint Iterative Optimization of Adaptive Filters”, IEEE Signal Processing Letters, Vol. 14, no. 12, December 2007.
 [22] R.C. de Lamare, R. SampaioNeto, “Minimum meansquared error iterative successive parallel arbitrated decision feedback detectors for DSCDMA systems,” IEEE Trans. Commun., vol. 56, no. 5, May 2008.

[23]
R. C. de Lamare and R. SampaioNeto, “Adaptive ReducedRank Processing Based on Joint and Iterative Interpolation, Decimation and Filtering”,
IEEE Transactions on Signal Processing, vol. 57, no. 7, July 2009, pp. 2503  2514.  [24] R.C. de Lamare and R. SampaioNeto, “Adaptive reducedrank equalization algorithms based on alternating optimization design techniques for MIMO systems,” IEEE Trans. Veh. Technol., vol. 60, no. 6, pp. 24822494, July 2011.
 [25] P. Li, R. C. de Lamare and J. Liu, “Adaptive Decision Feedback Detection with Parallel Interference Cancellation and Constellation Constraints for Multiuser MIMO systems”, IET Communications, vol.7, 2012, pp. 538547.
 [26] J. Liu, R. C. de Lamare, “LowLatency Reweighted Belief Propagation Decoding for LDPC Codes,” IEEE Communications Letters, vol. 16, no. 10, pp. 16601663, October 2012.
 [27] C. T. Healy and R. C. de Lamare, “Design of LDPC Codes Based on Multipath EMD Strategies for Progressive Edge Growth,” IEEE Transactions on Communications, vol. 64, no. 8, pp. 32083219, Aug. 2016.
 [28] P. Li and R. C. de Lamare, Distributed Iterative Detection With Reduced Message Passing for Networked MIMO Cellular Systems, IEEE Transactions on Vehicular Technology, vol.63, no.6, pp. 29472954, July 2014.
 [29] A. G. D. Uchoa, C. T. Healy and R. C. de Lamare, “Iterative Detection and Decoding Algorithms For MIMO Systems in BlockFading Channels Using LDPC Codes,” IEEE Transactions on Vehicular Technology, 2015.
 [30] R. C. de Lamare, ”Adaptive and Iterative MultiBranch MMSE Decision Feedback Detection Algorithms for MultiAntenna Systems”, IEEE Trans. Wireless Commun., vol. 14, no. 10, October 2013.
 [31] A. G. D. Uchoa, C. T. Healy and R. C. de Lamare, “Iterative Detection and Decoding Algorithms for MIMO Systems in BlockFading Channels Using LDPC Codes,” IEEE Transactions on Vehicular Technology, vol. 65, no. 4, pp. 27352741, April 2016.
 [32] Y. Cai, R. C. de Lamare, B. Champagne, B. Qin and M. Zhao, ”Adaptive ReducedRank Receive Processing Based on Minimum SymbolErrorRate Criterion for LargeScale MultipleAntenna Systems,” in IEEE Transactions on Communications, vol. 63, no. 11, pp. 41854201, Nov. 2015.
 [33] Z. Shao, R. C. de Lamare and L. T. N. Landau, “Iterative Detection and Decoding for LargeScale MultipleAntenna Systems with 1Bit ADCs,” IEEE Wireless Communications Letters, 2018.
 [34] H. Kim, J. Kim, S. Yang, M. Hong, and Y. Shin An Effective MIMO OFDM System for IEEE 802.22 WRAN Channels IEEE Transactions on Circuits and Systems, pp. 5558, August 2008.
Comments
There are no comments yet.