Out-of-Band Emission Reduction Technique for OFDM and MC-CDMA Systems

In this paper, we introduce a method for out-of-band power reduction of multicarrier communication systems. Recent years MC systems possess a dominated role in wireless access due to ability to achieve high data rates and simultaneously high robustness to multipath and fading. Despite all advantages, MC transmission produces an essential out-of-band interference. The OOB radiation leads to the wastage of scarce spectral resources and severe threats to adjacent wireless channels. We propose a novel technique for reducing OOB radiations in OFDM and MC-CDMA systems. To reduce the OOB emissions in the MC-CDMA system, we propose analytical criterion for spectrum efficiency estimation as far as low complexity algebraic algorithm for the proper waveform selection. The structure of selected waveform provides suppression for radiation outside the signal necessary bandwidth. Being implemented in the OFDM system, proposed algorithm is used for calculation of phases of cancellation carriers suppressing most powerful OOB sidelobesin transmitted signal. In the final part of document we consider primer of the simple precoding procedure for OFDM systems which by 10 dB or more reduces the OOB power at the cost of inessential decrease of the information data rate. 1


Introduction
Recently multicarrier (MC) signals became the focal point in the wireless systems development. Digital broadcasting, wireless access and communication systems which include Wi-Fi, WiMAX, LTE/4G cellular -this is not a complete list of their applications. The key idea of MC transmission is to transform broadband frequency-selective channel in a group of parallel non-selective narrow-band channels. Its 1 Part of this paper was presented at the 10th Int. Symposium on Electromagnetic Compatibility, York, UK, Sep. 26-30, 2011. advantage over single-carrier schemes is their ability to cope with severe channel conditions such as frequency-selective fading caused by multipath and narrowband interference.
Orthogonal frequency division multiplexing (OFDM) has attracted great interest in the last decade for its ability to transmit a high rate data stream splitting it to a number of orthogonally-spaced slower data streams. The division of the available spectrum into a number of orthogonal subcarriers makes the transmission system robust to multipath channel fading [1]. These features have led to the adoption of OFDM as a standard for digital audio broadcasting (DAB), broadband local and metropolitan wireless area networks [2], mobile broadband wireless access (MBWA) [3]. OFDM provides high computational efficiency by using FFT techniques in modulation/demodulation functions and perfect coexistence with current and future wireless systems.
Multicarrier code-division multiple-access (MC-CDMA) modulation scheme benefits from the advantages of both multicarrier and CDMA techniques: multiple access capability with the high flexibility and spectral efficiency, robustness in frequency selective channels with low-complexity at receiver considering simple one-tap equalization and narrow-band interference rejection [1].
Despite all benefits, a potential drawback of both systems is high out-of-band (OOB) power due to the sidelobes of the subcarriers. The OOB spectrum decreases slowly according to a sinc function. Even for a large number of subcarriers as 256, where it goes down rapidly in the beginning, the bandwidth on the −40 dB level is almost four times exceeds the −3 dB bandwidth. Both systems produce a substantial amount of OOB interference which may disrupt communications in adjacent wireless channels. Conventional disabling a set of OFDM subcarriers on the left and right side of its spectrum sometimes is not sufficient to avoid interference.
Several approaches to mitigate this source of interference are known [4]. One way is using conventional filters to reduce the out-of-band spectrum. But digital filter requires at most a few multiplications per sample, so filtering can increase the system complexity and introduce long delays.
The second way is windowing -a convolution of spectrum with a set of impulses at the carrier's frequencies (for those samples which fall into the roll-off region). A commonly used is the raised cosine window type. Only a few percent of the samples are in the roll-off region, therefore windowing is an order of magnitude less complex than filtering.
The third approach is sidelobe suppression via spectral compensation, where the total number N of subcarriers to be transmitted divided into two sets: a set of K information subcarriers and a setof S compensation subcarriers. Using properly chosen tones as compensation subcarriers leads to a more compact spectral mask. Spectral compensation does not require any shaping-related processing at the receiver: simple tone-wise equalization is possible since the orthogonality of the received basis functions is preserved [5]. Consequently, such technique conforms to any standard.
Known methods of compensation include subcarrier weighting [6], use of interference cancellation carriers [7], and multiple-choice sequences (MCS) [8]. First approach referred to as subcarrier weighting is based on weighting the individual subcarriers in a way that their sidelobes cancel each other. The other, cancellation carriers (CCs) is a promising technique which inserts carriers with optimized amplitudes and phases on the reserved positions (usually at the left and right edges of spectrum) in order to cancel the sidelobes of the transmitted signal. These carriers do not carry any data and are calculated to cancel out the OOB interference. Sidelobes are reduced significantly at the expense of a slightly increased bit error rate or a reduced throughput. Thirdly, with the multiple choice sequences method, the transmitted symbol is mapped into multiple equivalent transmit sequences and the one with the lowest sidelobe power is transmitted.
In this paper, we consider a simple algebraic criterion which provides us with a basis for selection sequences with the low spectrum power sidelobes within the MCS method as well as low complexity algorithm for determining of subcarriers phases within the CC S method.
The rest of this paper is organized as follows. In Section II, we consider a multicarrier data transmission scheme concept discussing the similarities and differences of MC-CDMA and OFDM air interfaces. Then we examine spectral properties of multicarrier signals depending on their phase structure. The spectrum efficiency criterion for MC waveform is introduced in Section III. In Section IV, we consider a simple precoding algorithm for OFDM system. The spectrum efficient sequences existence as well as their number is studied in Section V. The paper is concluded with a summary in Section VI.

Spectral Properties of Multicarrier Signals
The conceptual scheme of multicarrier data transmission is depicted in the Fig.1.
Main difference between the OFDM and MC-CDMA schemes is that in the first most of the coefficients cn represent data symbols (excluding subcarriers on reserved positions) while in the second one they describe the spreading code. Therefore, in the OFDM system the choice of the waveform is limited. In general case coefficients ci which describe amplitudes and phases of subcarriers are complex. Note the QPSK (or QAM) signal can be represented by the sum (weighted sum) of binary signals which phases are in quadrature. Therefore its spectrum is a superposition of independent binary signals spectra. That is why the binary case is the most appropriate for studying.
Let the N-carrier signal be represented as where U(t)=1, 0 ≤ t < TMC is a rectangular pulse envelope and TMC is the symbol duration. For MC-CDMA system di is a ith data symbol, cn=±1 is N-chip binary spreading code sequence. For OFDM, cn is a data vector(n=1,2,..N) and di is set to 1. Cyclic frequency ω n =ω 0 +Ω n of the n-thsubcarrier is equal to the sum of the carrier ω 0 and the n-th cyclic subcarrier Ω n =n⋅Ω 1 , where Ω 1 =2π/T MC is basic cyclic frequency of spectrum and 1/T MC is a frequency separation between any two adjacent subcarriers. The spectrum of signal (1) near the baseband can be representedas Maximums of its sidelobes moduli are reached where the sinus argument is equal to ±π/2 − namely, in discrete points of the frequency axis Ω q =qΩ 1 +π. Assuming T MC =1 for simplicity, one can consider In the points q* of maximum spectrum sidelobe moduli (at cyclic frequencies Ω*=π(2q*+1)/T DS ) we have Since T MC =NT DS , the corresponding points on the frequency axis are q=N⋅q*+N/2. As far as q>>n, the value of (q−n+1/2) −1 gradually less depends of n, showing constant behavior. From (2) we obtain the asymptotic expression That is why

A New Criterion for OOB Spectrum Suppression
Let us consider the next part of (2) expanding it so as (q−n+1/2) −1 =q −1 +o(∆ 1 ), where ∆ 1 =q −1 is the first term of the OOB-emission, which decreases proportionally to 1 st degree of frequency offset (its power decreases in proportion to the 2 nd degree of the frequency offset). The second element o(∆ 1 ) is always a small value compared to ∆ 1 . Then where m ≤ P, come true, then P out-of-band components of multicarrier signal decreasing proportionally to 1/q, 1/q 2 , ... 1/q P (proportionally to 1/q 2 , 1/q 4 , ... 1/q 2P in terms of power) will be compensated due to the special phase relationships between subcarriers. For P=1, 2 and 3 respectively, we have Let us refer to (6) as to the compactness criterion of the MC signal spectrum. Then c n is a "spectrum-efficient" code (SE-code) of the order P. The normalized right side of power spectra of single carrier and multicarrier signals are shown in Fig. 2 (we consider MC-CDMA system with N=8 subcarriers and three different spreading codes). Here ∆Ω=2π⋅∆F is the width of a frequency band, which is necessary for undistorted transmission of the signal. Curve "1" depicts the spectrum of single carrier rectangular pulse, "2" − the spectrum of the multicarrier signal with the "bad" code sequence (P=0), "3" − spectrum of signal based on the "average" code with a "random" properties, "4"− spectrum of the "best" waveform where only about 0,05% of signal power is OOB-radiated: Fig. 3 shows the power spectra of multicarrier (N=16) signals with different waveforms. Here curve "1" depicts the spectrum of signal having "random" properties (P=0), the other corresponds to signals based on SE-codes (P=2, P=3 and P=4). The last, {1,−1,1,1,1,1,−1,1,−1,1,−1,−1,1,−1,1,1} provides the lowest level of OOB emission (99.996% of its total radiated power falls within the necessary band ∆F=N/T MC ). For N=16 the average OOB power is about 2.5%, maximal -almost 45% from the total radiated power. In other words, the best waveform almost 50 times reduces OOB power compared to "average" and little less than a thousand timescompared to the "worst" one. For the frequency offset ∆f=∆F (from the edge of the necessary band) the decrease in signal power spectral density is about 35 dB for P=2, 50 dB for P=3 and almost 60 dB for P=4. On the contrary, the least spectral effective waveform increases the OOB emission relative to "average" waveform on 15 dB or even more.

Spectrally Efficient Coding for OFDM Systems
The basic idea of spectrally-efficient encoding is similar to CCs method [7], where a few subcarriers which do not carry any data themselves are inserted on both sides of the OFDM spectrum to cancel out a certain part of the OOB emissions. If the source data rate is equal to or less than N dataMAX =log 2 (Q N ) symbols per OFDM signal interval, then the transmitted data block can always be mapped onto some SE MC waveform. However when N is large, random nature of the transmitted data flow leads to high complexity of the mapping algorithm.
Let us consider a simple OFDM mapping scheme where a fixed number of frequency positions reserved for subcarriers which do not used for data allocation. Let there N be the FFT window size; K is the number of data subcarriers (which is equal to the number of information bits in data block to be transmitted); S is thenumber of the cancellation subcarriers in the data block, S=N−K; M=K/2 is the number of data subcarriers in the even/odd "semiblock" to be transmitted; L=S/2 is the number of the cancellation subcarriers in the any semiblock, L=N/2-M.
Suppose, α and β are weights of odd and even semiblocks consisted from additive group symbols c n ∈{0;1}. There always will be a loss in data rate caused by the fact that a certain amount of the signal power spent on the CCs and is not available for data transmission. So a rational trade-off between the data throughput and interference mitigation must be considered. We illustrate performances of a some flexible data allocation scheme by plotting P OOB versus number of data subcarriers K and total number of subcarriers N (so R=K/N is the relative information data rate). The instant transmission rate depends on the current data configuration. Fig. 4 shows that the cancellation scheme provides the OOB power level control at the expense of reasonable reduction of data rate. For comparison, in a WiMAX system with 256 subcarriers 55 are disabled (28 subcarriers on the left side and 27 on the right side) in order to provide guard bands and limit OOB radiations [4].
The performance of the proposed method was investigated. For N=2048 the average transmission rate in system with 1 st order of OOB spectrum suppression is about 0,93. Using more sophisticated waveform selection and mapping techniques, the required number of cancellation carriers can be reduced in exchange for an increase in system complexity (instead of that, additional complexity can be used to further reduce a sidelobe power). An optimal CCs scheme achieves R≈0,995.
The system performance is compared with a conventional OFDM system without any suppression scheme. Fig. 5 shows the effect of proposed technique in OFDM power spectrum. It depicts the OOB emissions in OFDM spectra with and without inserting cancellation carriers. The curve no. 1 represents the original spectrum with uncontrolled OOB radiation level, while curves 2, 3 and 4similar spectra after CCs insertion. Curve no. 2 depicts OOB emissions of typical "first order" spectrum, 3 -the minimal one (achieved by using the selection stage), 4 -highest OOB level for spectra after the CC insertion. The sidelobe reduction produced by proposed CCs alghorithm is within 10 -20 dB.

Synthesis and the Number of SE-Codes
According to (6) the weight of even symbols of SE-code (which is assumed to be any code with P≥1) is equal to weight of its odd symbols. Actually this is a simple rule to construct a complete set of codes having 1st order spectrum compactness. The number of SE-codes of length N is The total number of SE-codes for some of N≤1024 defined according to (7) is given in the 3 rd column of the Table 2. From the 4 th column of the table it's clear that the SE-code family is an essential part of the binary code set (2 N different codewords). For data transmission one can use SE-waveforms only at the expense of insignificant data rate reducing. Say, if we use 1/64 part from total set of 1024-subcarrier binary waveforms (so reducing the number of data carriers for 6), we'll tenfold decrease the power level of OOB emissions.
To synthesize selectively SE-codes for P≥2, we solve a system of P−1 equations where i 1 , i 2 , … i N/2 is a set of indexes of all positive symbols in the waveform and B k denote Bernoulli numbers [10] which for integer k≥1 can be found by recursion Within this work, we obtained the complete solution of (8) when P=2. For P≥3 the common approach for that still wasn't found except the direct computer search. Instead, we had some partial solutions for several special cases for N=2 P ⋅k as well as N=2 P−1 ⋅(2k+1), k=1,2,… . The total numbers of SE-codes for N≤36 for the different P are given in the Table 3.