Iterative scatteredbased channel estimation method for OFDM/OQAM
 Chrislin Lélé^{1}Email author
https://doi.org/10.1186/16876180201242
© Lélé; licensee Springer. 2012
Received: 23 February 2011
Accepted: 22 February 2012
Published: 22 February 2012
Abstract
This article deals with channel estimation (CE) in orthogonal frequency division multiplexing (OFDM)/OQAM. After a brief presentation of the OFDM/OQAM modulation scheme, we present the CE problem in OFDM/OQAM. Indeed, OFDM/OQAM only provides real orthogonality therefore the CE technique used in cyclic prefixOFDM cannot be applied in OFDM/OQAM context. However, some techniques based on imaginary interference cancelation have been used to perform CE in a scatteredbased environment. After recalling the main idea of these techniques, we present an iterative CE technique. The purpose of this iterative method is to use the imaginary interference at the receiving side in order to improve CE.
Keywords
1. Introduction
Nowadays, in the presence of multipath channels, multicarrier modulations such as orthogonal frequency division multiplexing (OFDM) are more and more used since they provide a good tradeoff between higher bit rate and complexity. A cyclic prefix (CP) longer than the maximum delay spread of the channel is generally used with OFDM to preserve the orthogonality. This CPOFDM modulation transforms a frequency selective channel into a bunch of several flat fading channels, leading to a one tap zeroforcing (ZF) equalization per subcarrier. Moreover, compared to singlecarrier systems, multicarrier systems permit a better use of the channel frequency diversity. The large popularity of CPOFDM, which is now present at the physical layer of many transmission standards such as ADSL or IEEE802.11a and specifications, mainly comes from its two most attractive features. Firstly, OFDM corresponds to a modulated transform that can be easily implemented using fast algorithms. Secondly, the equalization problem is simply solved with OFDM thanks to the addition of the CP. However, the CP leads to a loss of spectral efficiency as it contains redundant information. Moreover, the prototype filter used in CPOFDM is the window one which leads to a poor (sinc(x)) behavior in the frequency domain. This poor frequency localization makes it difficult for CPOFDM systems to respect stringent specifications of spectrum masks. Null subcarriers are inserted at the frequency boundaries of CPOFDM systems in order to avoid interferences with close systems in frequency. Null subcarriers also means loss of spectral efficiency. To overcome these drawbacks, OFDM/OQAM seems to be a good alternative. Firstly, because OFDM/OQAM does not use any CP and secondly, because it offers the possibility to use different prototype filters. Indeed, for a given type of timefrequency transmission lattice, the orthogonality constraint for OFDM/OQAM is relaxed being limited to the real field while for OFDM it has to be satisfied in the complex field. Thus, there is more degree of freedom for OFDM/OQAM prototype filters. However, real orthogonality has considerable impact on channel estimation (CE) which is quite simple in CPOFDM. In [1], an interference cancelation method was presented in other to perform CE in scattered environment for OFDM/OQAM. In this article we present the drawback of this method. Then, the iterative CE in [2] is presented by providing the different decoding structures. Comparison of both methods is made. Section 2 recalls some details about OFDM/OQAM and presents the problem of CE in OFDM/OQAM. Section named imaginary interference cancelation is about the method described in [1]. The following section presents the iterative CE method while providing the advantages of this method. It also gives the simulation results in a DVBT2 [3] context. Let us have some notations:

x or X represents scalar x or X

x or X represents the module of the complex scalar x or X

$\underset{}{x}$ is the column vector $\underset{}{x}$

${\underset{}{x}}^{T}$ is the transpose of the vector $\underset{}{x}$

$\u2225\underset{}{x}\u2225$ is the norm 2 of the vector $\underset{}{x}$

$\underset{}{X}$ is the matrix $\underset{}{X}$

E{x} mean or expectation value of the random value x
2. The OFDM/OQAM system
with M = 2N an even number of subcarriers, ${F}_{0}=1/{T}_{0}=1/2{\tau}_{0}$ the subcarrier spacing, g the prototype function assumed here to be a realvalued and even function and ν_{ m,n } an additional phase term such that ${\nu}_{m,n}={j}^{m+n}{e}^{j{\varphi}_{0}}$ where ${\varphi}_{0}$ can be chosen arbitrarily. The transmitted data symbols a_{ m,n } are realvalued. They are obtained from a 2^{2K}QAM constellation, taking the real and imaginary parts of these complexvalued symbols of duration ${T}_{0}=2{\tau}_{0}$, where ${\tau}_{0}$ denotes the time offset between the two parts [4–7].
where ${\delta}_{m,p}=1$ if m = p and ${\delta}_{m,p}=0$ if m ≠ p. For brevity purpose, we set ${\u27e8g\u27e9}_{p,q}^{m,n}=j\u27e8{g}_{m,n}{g}_{p,q}\u27e9$, with $\u27e8{g}_{m,n}{g}_{p,q}\u27e9$ a pure imaginary term for (m, n) ≠ (p, q).
The prototype filter has to satisfy the orthogonality conditions or at least must be nearly orthogonal. It can be derived directly in continuoustime, as it is the case for instance in [4] with the isotropic orthogonal transform algorithm (IOTA). Naturally, the resulting prototype filter has to be truncated and discretized to be implemented. The IOTA prototype filter used in this article is of length L = 4M and it is denoted by IOTA4. Prototype filters can also be directly derived in discretetime with a fixed length, see e.g., [7]. This is the case of the time frequency localization (TFL) [7, 8] prototype filter. In this article, it is taken of length L = M and denoted by TFL1. Before being transmitted through a channel the baseband signal is converted to continuoustime. Thus, in the rest of this article, we present an OFDM/OQAM modulator that delivers a signal denoted s(t), but keeping in mind that the modulator corresponds to the one in Figure 1.
and we also define ${\mathrm{\Omega}}_{\mathrm{\Delta}m,\mathrm{\Delta}n}^{*}={\mathrm{\Omega}}_{\mathrm{\Delta}m,\mathrm{\Delta}n}\left\{\left(0,0\right)\right\}$.
We talk about "pseudopilot" for ${b}_{{m}_{0},{n}_{0}}$ because ${a}_{{m}_{0},{n}_{0}}^{\left(i\right)}$ is not transmitted but it is created at the receiver side. For clarity purpose, when in OFDM/OQAM we talk about real data transmitted at a given position (m, n), we refer to it by a_{ m,n } . However, when it is a real transmit pilot in a given position (m, n), we refer to it by p_{ m,n } .
Thus the channel is easily estimated. Having the same estimation process in OFDM/OQAM implies performing some processing at the transmitter side. The purpose of the processing is to cancel ${a}_{{m}_{0},{n}_{0}}^{\left(i\right)}$ at the receiver side. Let us call these processing methods as imaginary interference cancelation.
3. Imaginary interference cancelation
3.1 Imaginary interference cancelation: principle
Ideally, one would like to transmit eight random real data d_{ k } at the eight distinct positions, k = 0, 1 . . . 7, and to get ${a}_{{m}_{0},{n}_{0}}^{\left(i\right)}=0$.That is naturally not possible in general.
3.1.1 Method 1
It is worth saying that using two real positions (the pilot position and the i_{7} position) for CE in OFDM/OQAM is similar to use only one complex position in CPOFDM. ^{ a } The drawback of using high power suggests that we should look for an other method.
3.1.2 Method 2
we have, $\underset{}{a}=\underset{}{Cd}$. At the receiver side, to ensure the reconstruction of $\underset{}{d}$from $\underset{}{a},\phantom{\rule{2.77695pt}{0ex}}\underset{}{C}$ must be a nonsingular matrix, thus $\underset{}{d}={\underset{}{C}}^{1}\underset{}{a}$. However it is important to choose $\underset{}{C}$ orthonormal for two main reasons:

$\underset{}{C}$orthonormal implies that $\left\right\underset{}{d}\left\right\phantom{\rule{2.77695pt}{0ex}}=\phantom{\rule{2.77695pt}{0ex}}\left\right\underset{}{a}\left\right$, because an orthonormal matrix preserves the norm.

At the receiver side, the noise will be multiplied by ${\underset{}{C}}^{1}$ which is also orthonormal. Using an orthonormal matrix prevents the noise power being increased while multiplying by${\underset{}{C}}^{1}$.
 (1)
Introduce a real pilot at that position;
 (2)
Replace the data around the pilot position by other data resulting from the product of $\underset{}{C}$ with the initial data;
 (3)
Modulate and transmit the overall data.
Using interpolation techniques [14], an estimate of the channel over all the positions (m, n) can be derived. Then, using (8), we obtain an estimate of the real transmitted data. Around the pilot position, the transmitted data were obtained after multiplying the initial data by $\underset{}{C}$. To have an estimate of the initial data, we must multiply these estimates of a_{ k } by ${\underset{}{C}}^{1}$. This method indeed enables CE without increasing the power use for CE.
However, it implies one matrix computation at each pilot position this at the transmitter and receiver. Thus, it increases the complexity.
3.2 Performance of the imaginary interference cancelation method
Let us look at the performance of the interference cancelation method using the matrix cancelation process previously presented. We use the approximation in (12). Our simulations have been carried out with the following channel profile and parameters:

Sampling frequency f_{ s }= 9.14 MHz;

Number of paths: 6;

Power profile (in dB) :− 6.0, 0.0, − 7.0, − 22.0, − 16.0, − 20.0;

Delay profile (μ s):3, 0, 2, 4, 7, 11. We denote by Δ the maximum delay spread of the channel (Δ=11μ s);

Guard interval composed of 130 samples(14.22μ s);

QPSK and 16QAM modulations;

FFT size M = 1024; Let denote by T_{ u }the useful CPOFDM symbol duration:${T}_{u}=\frac{M}{{f}_{s}}$

Convolutional channel coding (K = 7with generators g 1 = (133)_{ o },g 2 = (171)_{ o }, in octal form and code rate$=\frac{1}{2}$);

Frame structure of DVBT2 standard [3];

The velocity is 5 km/h;

The zero forcing equalization technique is used;

Prototype filter used: IOTA4 and TFL1;
Thus, by considering the approximation of ${a}_{{m}_{0},{n}_{0}}^{\left(i\right)}$ for Δm = 5 the result for TFL1 should be better.
In this section, the purpose has been to cancel the imaginary interference at pilots positions in order to achieve a simple equalization. How about using this interference term at the receiver side to improve the CE?
4. Iterative CE method
4.1 The iterative CE method: principle
 (1)
OFDM/OQAM demodulation;
 (2)
A CE is performed at the pilot position using (22), with ${\xe2}_{{m}_{0},{n}_{0}}^{\left(i\right)}={a}_{{m}_{0},{n}_{0}}^{\left(i\right)}$. Then, using an interpolation technique, an estimate of the whole channel is derived in every timefrequency position;
 (3).
Then the equalization of the demodulated signal can be performed. By taking the real part (block R) of the equalized signal, we obtain an estimate of the real data;
 (4).
The block R→C in Figure 7, reconstructs the complex symbol from the two real data, then the demapping operation generates the soft bits;
 (5).
The decoding operation generates two kinds of information:

The decoded bits which are the estimates of the transmitted bits.

The soft or hard (soft/hard) coded bits which are the metric values that are generally used for the iterative process [15].

Then, the process should be reiterated and a new CE can be performed using (22) with this new "pseudopilot" estimation value. Then, the bits recovering block gives new decoded bits and soft/hard coded bits. The process can be repeated n times.
4.2 Advantages of the iterative CE method
There are two main advantages with the iterative CE method.
The power of the transmitted pilot denoted by P^{2}, is taken similar in OFDM/OQAM and in CPOFDM, i.e., $E\left\{{p}_{{m}_{0},{n}_{0}}{}^{2}\right\}={P}^{2}\ge {\sigma}_{c}^{2}=2{\sigma}_{a}^{2}$, with ${\sigma}_{a}^{2}$ the power of the real data a_{ m,n } and ${\sigma}_{c}^{2}$the power of the complex data as in CPOFDM. Let us recall that, the power of the transmitted pilot is greater than ${\sigma}_{c}^{2}$ when boosting is used. In [16], we show that $E\left\{{a}_{{m}_{0},{n}_{0}}^{\left(i\right)}{}^{2}\right\}\approx {\sigma}_{a}^{2}$. Therefore,
showing that its power is greater than in CPOFDM. This virtual boosting in OFDM/OQAM is due to the interference term ${a}_{{m}_{0},{n}_{0}}^{\left(i\right)}$, which is added in a constructive way to the transmit pilot. This implies that the CE should be better in OFDM/OQAM than in CPOFDM, leading to potentially better performance for OFDM/OQAM.
Second advantage: The second advantage with this OFDM/OQAM CE is that the transmit pilot in OFDM/OQAM is a "realbased" symbol and not a "complexbased" one as in CPOFDM. Therefore, the percentage of the overhead pilots with this CE method should be half the one required for CPOFDM. As an example, in DVBT2 standard [3], we have about 8.33% of pilots into the CPOFDM frame. For OFDM/OQAM, this CE method leads to an overhead of 4.16%. This leads to a gain in spectral efficiency, because we can transmit a real data information symbol each time we transmit a real pilot. However, in order to have a fair comparison in terms of transmit power between CPOFDM and OFDM/OQAM, the power P^{2} of the pilot has to be split in OFDM/OQAM between the transmitted pilot and the extra data. So in OFDM/OQAM, if we add an additional real data each time we transmit a pilot, the pilot power should be ${P}^{2}{\sigma}_{a}^{2}$ and the additional real data power being ${\sigma}_{a}^{2}$. Thus the power of ${b}_{{m}_{0},{n}_{0}}$ becomes: $E\left\{{b}_{{m}_{0},{n}_{0}}{}^{2}\right\}\approx {P}^{2}$; Leading to no gain in terms of CE when compared to CPOFDM.
4.3 Simulations
We have performed simulations and made comparisons, using the system and channel parameters defined in Section 3. We have evaluated the performance of both receivers, i.e., either by implementing or not the decoding into the iteration process (IP). IOTA4Bound (Resp. TFL1Bound) corresponds to the case where we assume that the term ${a}_{{m}_{0},{n}_{0}}^{\left(i\right)}$ is perfectly known by the receiver at the pilot position. IOTA4n iter (Resp. TFL1n iter) corresponds to the case where we implement the presented algorithm with n iterations. n = 1 corresponds to a noniterative case. When considering channel decoding inside the IP, IP, as shown in Figure 8, we have used a hard decoding procedure.
4.3.1 Performances with decoding inside the IP process
4.3.2 Performances without decoding inside the IP process
5. Conclusion
In this article, we have shown that the CE in OFDM/OQAM cannot be performed in the same way as in CPOFDM modulation. The imaginary interference cancelation method provides a mean to estimate in a similar way the channel as in CPOFDM and its performances are closer to CPOFDM ones. The article has presented an iterative CE method, which uses the imaginary interference at the receiver side to improve the CE. This is done by an iterative estimation of the imaginary interference using either the decoding block inside or not the IP. Comparisons with CPOFDM show indeed that when the decoding block is used inside the IP the performances of OFDM/OQAM modulation outperform CPOFDM ones as long as both modulations have the same transmitted pilot power. Iterative CE method suggests that the imaginary interference can be used positively, how about trying to use it in order to improve the data estimation process?
Endnote
^{ a } The two real positions can be viewed as the real and imaginary parts of a complex position.
Declarations
Authors’ Affiliations
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