BLIND CARRIER FREQUENCY OFFSET ESTIMATOR BASED ON SINGLE-OFDM-SYMBOL PN RANGING CODE IN MULTI-USER OFDMA UPLINK

Abstract

A blind carrier frequency offset estimator is based on a single-OFDM-symbol training sequence in multi-user OFDMA uplink. Through multiple access interference modeling and analysis, a virtual user is employed that occupies the all null sub-carriers. By minimizing the energy leakage on the virtual user in term of tentative frequency offsets, the estimator can approach the real frequency offset. The estimator performs only on frequency-domain, simplifies interference calculations, and lowers the rank of the matrix. An iterative computation method is used to approach the real frequency offset.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

The aforementioned and other features and objects of the present invention and the manner of attaining them will become more apparent and the invention itself will be best understood by reference to the following description of a preferred embodiment taken in conjunction with the accompanying drawings, wherein:

FIG. 1( a) is a diagram of an initial ranging method;

FIG. 1( b) is a diagram of a periodic ranging method according to the prior art;

FIG. 2 is a diagram of a single-user signal model according to the present invention;

FIG. 3 is a multi-user signal model according to the present invention;

FIG. 4 is a plot of the cost function vs. the tentative CFO according to the present invention;

FIG. 5 is a flow chart of an iterative computational method according to the present invention; and

FIG. 6 is a diagram of an OFDMA system incorporating the method of the present invention.

DESCRIPTION OF THE INVENTION

Prior to the introduction of the CFO estimator, we shall develop a base-band signal model for the interleaving OFDMA uplink. Starting by constructing a single-user signal model, we will deduce a multi-user signal model with CFO and a time-variant frequency-selective channel.

An equivalent base-band single-user transmitter/receiver 200 is illustrated in FIG. 2. FIG. 2 illustrates a single-user base-band signal model of an interleaving OFDMA system. The out-modem part of the transmitter, such as randomization, channel coding, etc, is simplified as a modulator 202, and the receiver part is simplified as a de-modulator 204 respectively. The OFDM Framing/DeFraming block 206, 208 is used for constructing/deconstructing the standard compatible OFDMA transmission frame. Also the IFFT transformation 210 converts the frequency-domain signal into time-domain and the CP is appended 212 to each OFDM symbol after IFFT transformation 210. On the receiver side, FFT transformation 214 and CP removal block 216 are implemented for inverse operation as a transmitter part.

Focusing on frequency offset estimation, we can safely simplify the outer-modem part of the transmitter as a (de-)modulator. Define complex-valued vector S_M×1=[s(0), s(1), s(2), . . . , s(M−1)]^T as the signals from the modulator to be transmitted in one OFDM symbol. Then, the M signals are to be mapped onto one frequency-domain OFDM symbol vector (a complex vector of length of N×1) by a set of pre-defined index. The remaining (N−M) entries are set to be zeros. The mapping relationship can be realized by a position index (sc(0), sc(1), . . . , sc(M−1)), that is, s(i) is mapped at the sc(i)-th entries of the frequency-domain OFDM symbol vector. Define a position matrix PN×M=[ε_sc(0), ε_sc(1), . . . , ε_{sc(M−1)], where i is (N×}1) zeros vector but with its j-th entry being 1. Thus, the frequency-domain OFDM symbol signal can be expressed as P·S. IFFT operation can be realized by left-multiplication of a (N×N) IFFT matrix W^H. The (k,l) entry of W is defined as

$N^{-\frac{1}{2}}·{}^{-j\frac{2\pi ·k·l}{N}}.$

The CP (cyclic prefix) operation is also represented by a left multiplication of the matrix CP_(Ncp+N)×N=[[O_{Ncp×(N−Ncp)}I_Ncp×Ncp]^T I_N×N]^T, where Ncp is length of CP. Finally, the transmitted signal vector X_(N+Ncp)×1 is:

X _{(N+N CP )×1} =CP _{(N CP +N)×N} ·W _N×N ^H ·P _N×M ·S _M×1  Equation 1

The signal vector X is sequentially transmitted through a time-varying frequency selective channel. This continuous channel distortion can be modeled as:

$\begin{array}{cc}\begin{array}{c}y\left(t\right)={}^{j2\pi F_0t}·h\left(\tau ,t\right)\otimes x\left(t\right)+n\left(t\right)\\ ={}^{j2\pi F_0t}{\int }_0^{{\tau }_{\max }}h\left(\tau ,t\right)x\left(t-\tau \right)\tau +n\left(t\right)\end{array}& \mathrm{Equation}2\end{array}$

where h(τ, t) is channel impulse response simplified to h(τ) during one OFDM symbol; F₀ is CFO; n(t) is AWGN noise; τ_max is the maximum excess delay. Discrete-time equivalent of Equation 2 by replacing t with i/F_s, (F_s is the sampling frequency), is:

$\begin{array}{cc}y\left(i\right)={}^{\mathrm{j2\pi }f_0}\sum _{l=0}^{N_{\max }-1}h\left(l\right)x\left(i-l\right)+n\left(i\right)& \mathrm{Equation}3\end{array}$

where N_max=τ_max·F_s, f₀=F₀/F_s is the normalized CFO. If N_max<N_CP, no ISI (inter-symbol-interference) occurs, so the received time-domain signal vector is:

Y _N×1 =e ^{j2πf 0 ·N CP} ·diag(g(f₀))_N×N·W_N×N^H·P_N×M·diag(h)_M×M·S_M×1  Equation 4

where g(f)=[e^j2π·f·0, f^j2π·f·1, . . . , e^{j2π·f·(N−1)}], and h=[H(sc(0)), H(sc(1)), . . . , H(sc(M−1))] (H(i) is designated for the channel frequency response at the i-th sub-carrier). The received frequency-domain signal can be expressed by left multiplications of a FFT matrix W and position matrix p^T:

R _M×1 =e ^{j2πf 0 N CP} P ^T ·W·diag(g(f₀))·W^H·P·diag(h)·S_M×1  Equation 5

Equation 5 is the base-band signal transmission model of the inner-modem part. If f₀=0, i.e. no CFO presents, because the matrix diag(g(f₀))=I_N×N. And with W·W^H=I_N×N and P^T·P=I_M×M, we can rewrite R:

R _M×1 =e ^{j2πf 0 N CP} ·diag(h)·S_M×1  Equation 6

Apparently, f₀=0 gives rise to no interference between sub-carriers.

An equivalent base-band multi-user transmitter/receiver 300 is illustrated in FIG. 3. FIG. 3 illustrates a multi-user based band signal model for an interleaving OFDMA system. The out-modem part of transmitter, such as randomization, channel coding, etc, is simplified as a modulator 302, and the receiver part is simplified as a de-modulator 304, respectively. The OFDM Framing/DeFraming block 306, 308 is used for constructing/deconstructing the standard compatible OFDMA transmission frame. Also, the IFFT transformation 310 converts the frequency-domain signal into time-domain and the CP is appended 312 to each OFDM symbol after IFFT transformation 310. On the receiver side, FFT transformation 314 and CP removal block 316 are implemented for inverse operation as a transmitter part.

Comparing with the single user model, the user De-Mux block 318 is implemented on the receiver side to extract each single user data from its location within the OFDMA transmission frame.

In order to give out a multi-user signal model, we denote the superscript (•)^(k) as the assignment to the k-th user. Since one OFDM symbol is shared by several users without collision (overlapping), we have:

$\begin{array}{cc}{\left(P^{\left(k\right)}\right)}^T·\left(P^{\left(l\right)}\right)=\{\begin{array}{cc}{I}_{M^{\left(k\right)}\times M^{\left(l\right)}}& k=l\\ O_{M^{\left(k\right)}\times M^{\left(l\right)}}& k\ne l\end{array}& \mathrm{Equation}7\end{array}$

And

$\sum _{k=0}^{N_{\mathrm{user}}-1}M^{\left(k\right)}\le N-N_{\mathrm{left\_guard}}-N_{\mathrm{right\_guard}}.$

Thus, the received time-domain signal can be a sum of those of individual users:

$\begin{array}{cc}\begin{array}{c}{Y}_{N\times 1}=\sum _{k=0}^{N_{\mathrm{user}}-1}Y_{N\times 1}^{\left(k\right)}\\ =\sum _{k=0}^{N_{\mathrm{user}}-1}{}^{j2\pi f_0^{\left(k\right)}N_{\mathrm{CP}}}·\mathrm{diag}\left(g\left(f_0^{\left(k\right)}\right)\right)·\\ W^H·P^{\left(k\right)}·\mathrm{diag}\left(h^{\left(k\right)}\right)·S^{\left(k\right)}\end{array}& \mathrm{Equation}8\end{array}$

Similarly, the received frequency-domain of the k-th user is:

$\begin{array}{cc}{R}_{M^{\left(k\right)}\times 1}^{\left(k\right)}={{}^{\mathrm{j2\pi }f_0^{\left(k\right)}N_{\mathrm{CP}}}\left(P^{\left(k\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f_0^{\left(k\right)}\right)\right)·W^H·P^{\left(k\right)}·\mathrm{diag}\left(h^{\left(k\right)}\right)·S_{M^{\left(k\right)}\times 1}^{\left(k\right)}+\underset{l\ne k}{\sum _{l=0,}^{N_{\mathrm{user}}-1}}{{}^{\mathrm{j2\pi }f_0^{\left(l\right)}N_{\mathrm{CP}}}\left(P^{\left(k\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f_0^{\left(l\right)}\right)\right)·W^H·P^{\left(l\right)}·\mathrm{diag}\left(h^{\left(l\right)}\right)·S_{M^{\left(l\right)}\times 1}^{\left(l\right)}& \mathrm{Equation}9\end{array}$

The first term on the right-hand side of Equation 9 is the received signal from the k-th user. If f₀^(k)≠0, the sub-carrier interference presents, denoted as self-interference. The second term on the right-hand side of Equation 9 includes the signals from the other users. If f₀^(l)=0, ∀l,l≠k, the sum of the second term is zero because of Equation 7; otherwise, it introduces the interference from other users, denoted as MAI.

In order to design a blind CFO estimator, we shall introduce a concept of a “virtual user”. As its name suggests, UL PUSC of IEEE802.16e system, one of the mandatory transmission structure, uses some of the sub-channels, that is, some sub-channels are deliberately set to zeros. These null sub-channels are uniformly distributed on the overall band in a given permutation way to separate different users. In a practical system, about 60%˜75% sub-channels are used, while the remainders are null sub-channels against the MAI. Thus, despite the presence of the interferences due to the existing CFOs, their influence from one user on another user would greatly diminish along with the increasing of the sub-carrier distances between the two users.

Another issue is sectorization. Like other cellular systems, IEEE802.16e system sectorizes its cell. All of the available sub-channels, excluding the null sub-channels, are grouped into three segments. Each segment is assigned to a sector's usage. Concurrently, three sets of directional transmitter/receiver antenna arrays are installed at the BS for the sectors. Therefore, in a given sector, the signal energies (or interferences) from the neighboring sectors can be low enough to be considered as white noise. Accordingly, the sub-channels of the other segments can be regarded as null sub-channels too.

Taking into account the two points above, there are a number of null sub-channels in OFDMA uplink. These null sub-channels can be regarded as a special user that transmits only zero signals without CFO. We denote this null sub-channel set as “virtual user.” Logically, it contributes no interferences on the other users; whereas the other users present interferences on it. Equation 10 expresses this relationship:

$\begin{array}{cc}{R}_{M^{\left(\mathrm{null}\right)}\times 1}^{\left(\mathrm{null}\right)}=N_{M^{\left(\mathrm{null}\right)}\times 1}+\sum _{l=0.}^{N_{\mathrm{user}}-1}{\left(P^{\left(\mathrm{null}\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f_0^{\left(l\right)}\right)\right)·W^H·P^{\left(l\right)}·\mathrm{diag}\left(h^{\left(l\right)}\right)·S_{M^{\left(l\right)}\times 1}^{\left(l\right)}& \mathrm{Equation}10\end{array}$

where the superscript (•)^(null) is designated for the assignment to the virtual user. The mapping relationship of the virtual user can be realized by a position index (null(0), null(1), . . . , null(M^(null)−1)). And a null position matrix P_N×M=[ε_null(0), ε_null(1), . . . , ε_null(M−1)].

In an ideal synchronous system, i.e., ω₀^(l)=0, ∀l, the virtual user only transmits the white noise; otherwise, the MAI from other users leaks on the virtual user's band. We name this MAI as “signal energy leakage.”

Due to the fact that CFO gives rise to the signal energy leakage that augments the signal energy on the virtual user's band, we design a CFO estimator that minimizes the energy.

Ranging can be regarded as a specific user. Denote the superscript (•)^(ranging) as the assignment to the ranging user. Define a joint position index of the virtual user and the ranging user as ((null+ranging)(0), (null+ranging)(1), . . . , (null+ranging) (M^(null)+M^(ranging)−1))=(null(0), null(1), . . . , null(M^(null)−1))∪(sc^(ranging)(0), sc^(ranging)(1), . . . , sc^(ranging)(M^(ranging)−1)). The joint position matrix of the virtual user and the ranging user is:

$\begin{array}{cc}{P}_{N\times \left(M^{\left(\mathrm{null}\right)}+M^{\left(\mathrm{ranging}\right)}\right)}^{\left(\mathrm{null}+\mathrm{ranging}\right)}=\lfloor \begin{array}{c}{\varepsilon }_{\left(\mathrm{null}+\mathrm{ranging}\right)\left(0\right)},{\varepsilon }_{\left(\mathrm{null}+\mathrm{ranging}\right)\left(1\right)},\dots ,\\ {\varepsilon }_{\left(\mathrm{null}+\mathrm{ranging}\right)\left(M^{\left(\mathrm{null}\right)}+M^{\left(\mathrm{ranging}\right)}-1\right)}\end{array}\rfloor & \mathrm{Equation}11\end{array}$

The observed frequency-domain joint signal of the virtual user and the ranging user is:

$\begin{array}{cc}{R}_{\left(M^{\left(\mathrm{null}\right)}+M^{\left(\mathrm{ranging}\right)}\right)\times 1}^{\left(\mathrm{null}+\mathrm{ranging}\right)}={{}^{\mathrm{j2}\pi f_0^{\left(\mathrm{ranging}\right)}N_{\mathrm{CP}}}\left(P^{\left(\mathrm{null}+\mathrm{ranging}\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f_0^{\left(\mathrm{ranging}\right)}\right)\right)·W^H·P^{\left(\mathrm{ranging}\right)}·\mathrm{diag}\left(h^{\left(\mathrm{ranging}\right)}\right)·S_{M^{\left(\mathrm{ranging}\right)}\times 1}^{\left(\mathrm{ranging}\right)}+\underset{l\ne \mathrm{ranging}}{\sum _{l=0,}^{N_{\mathrm{user}}-1}}{{}^{\mathrm{j2\pi }f_0^{\left(l\right)}N_{\mathrm{CP}}}\left(P^{\left(\mathrm{null}+k\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f_0^{\left(l\right)}\right)\right)·W^H·P^{\left(l\right)}·\mathrm{diag}\left(h^{\left(l\right)}\right)·S_{M^{\left(l\right)}\times 1}^{\left(l\right)}& \mathrm{Equation}12\end{array}$

Assuming that the other users have already been synchronized with the BS, that is, f₀^(l)=0, ∀l,l≠k, the second term of the right hand side of Equation 12 turns to zeros:

$\begin{array}{cc}{R}_{\left(M^{\left(\mathrm{null}\right)}+M^{\left(\mathrm{ranging}\right)}\right)\times 1}^{\left(\mathrm{null}+\mathrm{ranging}\right)}={{}^{\mathrm{j2}\pi f_0^{\left(\mathrm{ranging}\right)}N_{\mathrm{CP}}}\left(P^{\left(\mathrm{null}+\mathrm{ranging}\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f_0^{\left(\mathrm{ranging}\right)}\right)\right)·W^H·P^{\left(\mathrm{ranging}\right)}·\mathrm{diag}\left(h^{\left(\mathrm{ranging}\right)}\right)·S_{M^{\left(\mathrm{ranging}\right)}\times 1}^{\left(\mathrm{ranging}\right)}& \mathrm{Equation}13\end{array}$

Multiple R^{(null+ranging)} by correction matrixes in term of a tentative CFO f^(ranging), and extract the signal of the virtual user:

$\begin{array}{cc}{R}_{M^{\left(\mathrm{nll}\right)}\times 1}^{\prime \left(\mathrm{null}\right)}={\left(P^{\left(\mathrm{null}\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f^{\left(\mathrm{ranging}\right)}\right)\right)·W^H·P^{\left(\mathrm{ranging}+\mathrm{null}\right)}·R^{\left(\mathrm{nll}+\mathrm{ranging}\right)}& \mathrm{Equation}14\end{array}$

Replace Equation 13 into Equation 14:

$\begin{array}{cc}{R}_{M^{\left(\mathrm{nll}\right)}\times 1}^{\prime \left(\mathrm{null}\right)}={}^{j2\pi f_0^{\left(\mathrm{ranging}\right)}N_{\mathrm{CP}}}·{\left(P^{\left(\mathrm{null}\right)}\right)}^T·W·\mathrm{diag}\left(g\left(f^{\left(\mathrm{ranging}\right)}+f_0^{\left(\mathrm{ranging}\right)}\right)\right)·W^H·P^{\left(\mathrm{ranging}\right)}·\mathrm{diag}\left(h^{\left(\mathrm{ranging}\right)}\right)·S_{M^{\left(\mathrm{ranging}\right)}\times 1}^{\left(\mathrm{ranging}\right)}& \mathrm{Equation}15\end{array}$

Equation 15 indicates that R′^(null) is the signal leakage from the ranging user that is corrected by a tentative CFO f^(ranging). Define a correct matrix C^(ranging)(f)=(P(null))^T·W·diag(g(f^(ranging))·W^H·P^{(null+ranging)}. We re-write (14):

$\begin{array}{cc}{R}_{M^{\left(\mathrm{nll}\right)}\times 1}^{\prime \left(\mathrm{null}\right)}=C^{\left(\mathrm{ranging}\right)}\left(f\right)·R^{\left(\mathrm{nll}+\mathrm{ranging}\right)}& \mathrm{Equation}16\end{array}$

We can introduce a cost function in terms of the signal energy of R′^(null):

$\begin{array}{cc}\begin{array}{c}{J}^{\left(\mathrm{ranging}\right)}\left(f\right)={\left(R_{M^{\left(\mathrm{nll}\right)}\times 1}^{\prime \left(\mathrm{null}\right)}\right)}^H·R_{M^{\left(\mathrm{nll}\right)}\times 1}^{\prime \left(\mathrm{null}\right)}\\ ={\left(R^{\left(\mathrm{null}+\mathrm{ranging}\right)}\right)}^H·{\left(C^{\left(\mathrm{ranging}\right)}\left(f\right)\right)}^H·\\ C^{\left(\mathrm{ranging}\right)}\left(f\right)·R^{\left(\mathrm{null}+\mathrm{ranging}\right)}\end{array}& \mathrm{Equation}17\end{array}$

To explain why the estimated CFO minimizes the cost function J^(ranging)(f), we note that in Equation 15 f^(ranging)+f₀^(ranging)=0 leads to diag(g(f^(ranging)+f₀^(ranging)))=I_N×N, i.e. R′^(null)=0. Thus, relying on the cost function, the CFO estimator is given by:

${\stackrel{⋒}{f}}_0^{\left(\mathrm{ranging}\right)}=\underset{f}{\arg \min }J^{\left(\mathrm{ranging}\right)}\left(f\right)$

FIG. 4 shows the cost function in terms of tentative CFO.

As noted above, the CFO estimator is based on signal energy detection on the virtual user. However, the generation of the correction matrix C^(ranging)(f) is high complex operation to be performed once f^(ranging) is updated. To address the simplification of the CFO estimator, we start by analyzing MAT property in OFDMA uplink.

From Equation 9, the interference from the 1-th user on the k-th user due to the CFO of the 1-th user can be modeled as:

MAI(k,l,f_o^(l)))=e^j2πf0(l)NCP(P^(k))^T·W·diag(g(f₀^(l)))·W^H·P^(l)·R_M(l)×1^(l)  Equation 18

Define a MAI function m(k,l,f)=(P^(k))^T·W·diag(g(f))·W^H·P^(l), so the interference is re-written as:

MAI(k,l,f_o^(l)))=e^j2πf0(l)NCP·m(k,l,f₀^(l))·R_M(l)×1^(l)  Equation 19

To investigate the MAT property, we discard the term e^j2πf0(l)NCP, for it only causes the phase rotation. Without loss of generality, we can investigate MAI property by studying m(k,l,f). The function m(k,l,f) returns a M^(k)×M^(l) matrix, the (u,v) entry of which is

$I\left(u,v\right)=\left(1/N\right)·\sum _{n=0}^{N-1}{}^{j2\pi \left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)n/N}.$

It equals:

$\begin{array}{cc}I\left(u,v\right)=\frac{\sin \pi \left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)}{N\sin \frac{\pi }{N}\left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)}·{}^{-\mathrm{j\pi }\left(1-\frac{1}{N}\right)\left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)}& \mathrm{Equation}20\end{array}$

Noting that for a large N:

$\begin{array}{cc}\underset{N->\infty }{\lim }\frac{\sin \pi \left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)}{N\sin \frac{\pi }{N}\left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)}=\sin c\left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)& \mathrm{Equation}21\end{array}$

the normalized power of I(u, v) decreases dynamically with the increase of the distance |sc^(l)(u)−sc^(k)(v)| (it is an integer) for different f (f≠0). It can be concluded that the interference from the u-th sub-carrier of the l-th user has the influence only on its limited neighboring sub-carriers. In the case of f=0, sinc(sc^(l)(u)−sc^(k)(v))≡0 if and only if |sc^(l)(u)−sc^(k)(v)|≠0.We introduce an interference influence factor d to express the “effective” interference limitation:

$\begin{array}{cc}I\left(u,v\right)=\{\begin{array}{cc}\sin c\left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)·{}^{-\mathrm{j\pi }\left(1-\frac{1}{N}\right)\left(f+{\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\right)}& {\mathrm{sc}}^{\left(l\right)}\left(u\right)-{\mathrm{sc}}^{\left(k\right)}\left(v\right)\le d\\ 0& \mathrm{else}\end{array}& \mathrm{Equation}22\end{array}$

With Equation 22, we can lower the rank of the correction matrix C^(ranging)(f) by discarding those null sub-carriers from which the distances to the nearest ranging sub-carriers are greater than a pre-defined distance d. Re-define null sub-carrier position index:

{sc^(null′)(l)εnull∥sc^(null)(l)−sc^(ranging)(m)|≦d, m=0,1, . . . M^(ranging)}

And the (u, v) entry of C^(ranging)(f) is I(u, v) in Equation 22 where sc^(l)(u)=sc^(null′)(u), sc^(k)(v)=sc^(ranging)(v), and f=f^(ranging).

The cost function of J^(ranging)(f) is illustrated in FIG. 5. Knowing that f₀^(ranging)ε(f₁, f₂), we can use iterative computation to reach the estimated f^(ranging):

• • 1. f^(ranging)=f₁, J₀=+∞; (step 502)
  • 2. Calculate C^(ranging)(f^(ranging)) with Equation 22; (step 504)
  • 3. Calculate

$R_{M^{\left({\mathrm{nll}}^{\prime }\right)}\times 1}^{\prime \left({\mathrm{null}}^{\prime }\right)}$

based on Equation 16; step (506)

• • 4. From

$R_{M^{\left({\mathrm{nll}}^{\prime }\right)}\times 1}^{\prime \left({\mathrm{null}}^{\prime }\right)},$

calculate J^(ranging)(f^(ranging)) with Equation 17, and J₁=J^(ranging)(f^(ranging)); (step 518)

• • 5. If J₁>J₀, go to end and return f^(ranging); (decision 508)
  • 6. f^(ranging)=f^(ranging)+Δf_step, if f^(ranging)>f₂, go to end and estimate failure, otherwise J₀=J₁ and go to step 2; (steps 510, 512, and 516)
  • 7. End.

The flow chart of the iterative method of the present invention is shown in FIG. 5. The flow chart of FIG. 5 also includes step 518. Step 518 denotes J as J1 for the next step comparison and iteration. The flow chart also includes decision diamond 514 that ends the method of the present invention if the upper end of the carrier frequency offset is reached. The iterative method of the present invention can be enhanced if desired. For instance, Δf_step can be adjusted according the ΔJ=J₁−J₀; a LMS (least Mean Square) algorithm can also be proposed to improve better tracking performance.

The minimum value of the cost function is determined during the iterative method of the present invention, as is shown in FIG. 4. For the first time iteration, it is impossible for J1 to be greater than J0 (positive infinity), and in step 512 J1 is denoted as J0, so for the next step, the new frequency resulted cost function value is compared with J0, which has the same value of J1 (not positive infinity). By successive iterations, the method of the present invention is continued until the minimum value of cost function is found.

Referring now to FIG. 6, an entire OFDMA system 600 is shown, including all of the blocks previously described. In addition, system 600 includes a CFO estimator block 620 incorporating the method of the present invention as was previously described. In addition, system 600 includes a frequency offset corrector block 622, which compensates for the frequency offset estimated by the CFO estimator block 620.

As is known in the art, the entire system 600, and blocks 620 and 622 in particular, can be implemented in an integrated circuit using DSP technology to realize all of the various mathematical steps and transformations in the method of the present invention.

While there have been described above the principles of the present invention in conjunction with specific components, circuitry and bias techniques, it is to be clearly understood that the foregoing description is made only by way of example and not as a limitation to the scope of the invention. Particularly, it is recognized that the teachings of the foregoing disclosure will suggest other modifications to those persons skilled in the relevant art. Such modifications may involve other features which are already known per se and which may be used instead of or in addition to features already described herein. Although claims have been formulated in this application to particular combinations of features, it should be understood that the scope of the disclosure herein also includes any novel feature or any novel combination of features disclosed either explicitly or implicitly or any generalization or modification thereof which would be apparent to persons skilled in the relevant art, whether or not such relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as confronted by the present invention. The applicants hereby reserve the right to formulate new claims to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

The following Abbreviations used herein are listed in Table I:

AWGN  Additive White Gaussian Noise
BS    Base Station
CDMA  Code Division Multiple Access
CFO   Carrier Frequency Offset
CP    Cyclic Prefix
FFT   Fast Fourier Transform
ICI   Inter-Channel-Interference
IFFT  Inverse Fast Fourier Transform
LS    Least Square
ISI   Inter Symbol Interference
LMS   Least Mean Square
MAI   Multiple Access Interference
ML    Maximum Likelihood
OFDM  Orthogonal Frequency Division Multiplexing
OFDMA Orthogonal Frequency Division Multiple Access
PN    Pseudo Noise
PUSC  Partial Used Sub Channel

The following Parameters are used herein in Table II:

M            number of the available sub-carriers
N            OFDM modulation size
S(k)         complex data vector of user k
Sc(k)        position index of user k
P            position matrix
εj           N × 1 zero vector but with its j-th entry being 1
CP           cyclic prefix matrix
Ncp          length of CP
WH           IFFT matrix
W            FFT matrix
X            transmitted signal vector
h(τ, t)      channel impulse response
n(t)         AWGN noise
τmax         maximum excess delay
Fs           sampling frequency
F0           CFO
f0           normalized CFO, F0/Fs
Y            received time-domain signal vector
I            identity matrix
Nleft-guard  left virtual guard size
Nright-guard right virtual guard size
R            received frequency-domain signal vector
R′           corrected received frequency-domain signal vector
C            correction matrix
J            cost function in term of the signal energy
m(k, l.f)    MAI function

Claims

1. A method for estimating a carrier frequency offset for an interleaved OFDMA uplink receiver comprising: initializing a carrier frequency offset;initializing a cost function value;calculating a correction matrix on a current frequency value;calculating a cost function using a calculated correction matrix value;comparing the calculated value of the cost function to the initial value of the cost function;if the calculated value of the cost function is greater than the initial value of the cost function, then the method is terminated and the initial carrier frequency offset is returned as the estimated carrier frequency offset;if the calculated value of the cost function is less than the initial value of the cost function, then the present calculated value is set as a new initial carrier frequency offset value;incrementally increasing the frequency offset value; andrepeating the correction matrix and cost function calculations until an estimated carrier frequency offset is returned, or until the range of the carrier frequency offset is exceeded.

2. The method of claim 1 wherein initializing the carrier frequency offset comprises initializing the carrier frequency offset within a predetermined range of frequency offset values.

3. The method of claim 1 wherein initializing the cost function value comprises initializing the cost function value at a predetermined high value.

4. The method of claim 1 wherein the estimated carrier frequency offset is found at a minimum cost function value.

5. The method of claim 1 wherein the correction matrix is calculated using the formula:

6. The method of claim 1 wherein the correction matrix is calculated using the formula:

7. The method of claim 1 further comprising a virtual user that occupies all null sub-carriers.

8. The method of claim 1 wherein the method is performed only in the frequency-domain.

9. The method of claim 1 wherein the method is performed without knowing a transmitted CDMA ranging code.

10. The method of claim 1 further comprising lowering the rank of a correction matrix by discarding null sub-carriers from which the distances to the nearest ranging sub-carriers are greater than a pre-defined distance.

11. An OFDMA uplink receiver comprising a CP removal block, an FFT block, a CFO estimator block, a frequency offset corrector, an OFDM DeFraming block, a user demux block, and a demodulator, the CFO estimator block employing a method for estimating a carrier frequency offset, the method comprising: initializing a carrier frequency offset;initializing a cost function value;calculating a correction matrix on a current frequency value;calculating a cost function using a calculated correction matrix value;comparing the calculated value of the cost function to the initial value of the cost function;if the calculated value of the cost function is greater than the initial value of the cost function, then the method is terminated and the initial carrier frequency offset is returned as the estimated carrier frequency offset;if the calculated value of the cost function is less than the initial value of the cost function, then the present calculated value is set as a new initial carrier frequency offset value;incrementally increasing the frequency offset value; andrepeating the correction matrix and cost function calculations until an estimated carrier frequency offset is returned, or until the range of the carrier frequency offset is exceeded.

12. The OFDMA receiver of claim 11 wherein initializing the carrier frequency offset comprises initializing the carrier frequency offset within a predetermined range of frequency offset values.

13. The OFDMA receiver of claim 11 wherein initializing the cost function value comprises initializing the cost function value at a predetermined high value.

14. The OFDMA receiver of claim 11 wherein the estimated carrier frequency offset is found at a minimum cost function value.

15. The OFDMA receiver of claim 11 wherein the correction matrix is calculated using the formula:

16. The OFDMA receiver of claim 11 wherein the correction matrix is calculated using the formula:

17. The OFDMA receiver of claim 11 further comprising a virtual user that occupies all null sub-carriers.

18. The OFDMA receiver of claim 11 wherein the method is performed only in the frequency-domain.

19. The OFDMA receiver of claim 11 wherein the method is performed without knowing a transmitted CDMA ranging code.

20. The OFDMA receiver of claim 11 further comprising lowering the rank of a correction matrix by discarding null sub-carriers from which the distances to the nearest ranging sub-carriers are greater than a pre-defined distance.