Patent Application
20100260276
The present invention relates generally to multiple access control (MAC) of communications networks, and more particularly to carrier allocation and transmission time sharing among multiple users in a wireless communications network that applies a MAC combing orthogonal frequency-division multiple-access (OFDMA) and time-division multiple-access (TDMA).
In orthogonal frequency-division multiplexing (OFDM) networks, a preamble is used for synchronization and channel estimation. In oversampled OFDM networks, the preamble used for time synchronization does not have an ideal autocorrelation function. The ideal function is the Dirac delta function, which represents an infinitely sharp peak bounding unit area. This is due to a guard band, which degrades the accuracy of symbol timing.
Oversampled OFDM is typical of most wireless standards that employ OFDM, such as IEEE 802.11, IEEE 802.16 and 3GPP-LTE. Because it is not possible to obtain and ideal preamble sequence in such cases, it is desired to provide an optimal preamble.
In an oversampled orthogonal frequency-division multiplexing (OFDM) orthogonal network, the preamble used for time synchronization does not have an ideal autocorrelation function due to guard bands, which degrade the accuracy of symbol timing. Therefore, a zero-correlation-zone (ZCZ) based preamble is used for time synchronization. A cross correlation function (CCF) used for time synchronization is forced to 0 within a certain region around a main lobe. The length of the ZCZ is guaranteed to be larger than a cyclic prefix length of OFDM data symbols to increase synchronization accuracy.
The embodiments of the invention provide a zero-correlation-zone (ZCZ) based preamble for time synchronization in oversampled orthogonal frequency-division multiplexing (OFDM) OFDM networks in URWIN. In particular, our preamble can force a cross correlation function (CCF) used for time synchronization to be 0 within a certain region around a main lobe. The length of the ZCZ is guaranteed to be larger than the cyclic prefix (CP) length of OFDM symbols. This increases the accuracy of synchronization. As used herein, the length (L) means a time duration. Throughout the disclosure we make reference to a specific design in which various parameters of the preamble are explicitly defined. We call this design URWIN (Ultra-Reliable Wireless Industrial Network) and provide the numerical quantities for the preamble design for exemplary purposes. The specific parameters for the URWIN along with specific preamble sequences are shown in Tables IV-VII in the Appendix.
Notations and Definitions
Convolution: The operator “*” denotes convolution of two sequences:
where zl is the convolution output of sequences x, l=0, 1, . . . , Lx−1, and yn, n=0, 1, . . . , Ly−1, min and max represent functions that return minimum and maximum values, respectively, and m is a summation variable whose limits are given in Equation (1).
Circular Convolution:
For the sequences x1 and yl with the same length L, the circular convolution output sequence Zl, l=0, 1, . . . , L−1, between these two sequences is well-known as
where ( )L denotes the modulus operation after division by L, and is the circular convolution operator.
Circular Cross Correlation Function (Circular CCF)
For the two sequences xl and yl with the same length L, the circular CCF between the two sequences is, denoted by ψxy(τ), is defined as
where ( )L denotes the modulus after division by L.
Vector Representation
Any sequence wl=0, 1, . . . Lw−1 can be written in a column vector form as w, (w0,w1, . . . ,wLw−1)T, where T denotes the transpose operator.
Eqs. (1) and (2) can be respectively rewritten as
z=x*y and z=xy.
Preamble Structure and Transmission Model
Table I lists parameters for the OFDM/OFDMA network. The URWIN network has specific parameters. Our preamble is derived as a general approach for various OFDM parameters. Moreover, the parameters defined in Table I are for OFDM data symbols.
The OFDM symbols in the preamble can differ from the OFDM data symbols, e.g., the CP length for some symbols differ when the OFDM symbols in the preamble have a different structure. This is explicitly noted.
As shown in
The first symbol of the preamble is used for signal detection (SD), automatic gain control (AGC), and frequency offset estimation (FOE). Because the CP is not an essential component for signal detection, AGC, and frequency offset estimation, we do not use the CP for the first symbol. The 11.2 μs length of the first symbol is longer than the length specified in the 802.11 standard for signal detection and AGC.
The second preamble symbol 102 is used for symbol synchronization, which has a CP with 1a length of 2Tg. We use a longer length for the CP of the second symbol because the ZCZ length is longer than the CP length of the data symbols.
The third symbol 103 is used for channel estimation, and has a CP with the same length as data symbols. The functions and parameters for the three symbols of preamble are summarized in Table II.
Transmitted and Received Signal Model
With the above structure, the transmitted preamble signal in discrete time, can be denoted by Φn, which is a piecewise function expressed as
where fn, sn and cn denote the first, second, and third OFDM symbols in the preamble, respectively. The variables Ng, Ns, and N are defined in Table I, and n=0 corresponds to the beginning of the useful part of the second symbol, as shown in
More specifically, we can express the time domain sequences, fn, sn and cn through the Fourier relationship to the frequency domain symbols Fk, Sk, and Ck. Doing so we obtain the explicit expression for each preamble component as follows.
where j is the imaginary number √{square root over (−1)}, k, indexes the subcarriers of the OFDM symbol, n indexes the time/sample of the corresponding time domain representation of the preamble symbols, Fk, Sk, and Ck, are the frequency-domain values (complex-valued) on the kth subcarrier for the first, second, and the third symbol, respectively, in the preamble. Since we only focus on the useful subcarriers, Eqs. (6)-(8) can be rewritten as
where k(u) maps 0, . . . , U−1 to the real subcarrier indices k as
The received preamble is
r
n
=φ
n
*h
n+σn, (12)
where hn, n=0, 1, . . . , Dmax−1, is the channel impulse response, and σn is the additive white Gaussian noise (AWGN) with power spectrum density (PSD) N0. We assume that the CP length of normal data OFDM symbols is larger than the maximum delay caused by the channel. Thus, we have L≦Ng.
Designs of the First and Third OFDM Preamble Symbols
Third Preamble Symbol
The third symbol 430 is to be used for channel estimation. An essential requirement for a high quality channel estimation sequence is a uniform-power across the frequency domain so that all subcarriers are sounded with equal power. Another general requirement is to minimize the peak-to-average-ratio (PAPR). To fulfill the uniform power constraint, we set the normalized magnitude of the power for Ck(u) to 1 for all subcarriers u. The third symbol Ck(u) uses quadrature phase-shift keying (QPSK) to simplify the implementation. Then, we have
C
k(u)
=e
jφ′
, (13)
where the phase φ′k(u)ε{π/4; 3π/4; 5π/4; 7π/4} is selected as follows.
We randomly generate many {φ′k(u)}u=0U by using a random-number-generator 410, such that we can get many realizations of {Ck(u)}u−0U. Among these realizations, we select the one with the minimum PAPR 420. The selected sequence Ck(u) 430 is shown in Table IV, under which the obtained PAPR is 5 dB (as listed in Table III).
First Preamble Symbol
The OFDM symbol used for signal detection and AGC needs to be periodic with a relatively short period. To satisfy this constraint, we set the first symbol Fk(u) 440
where θ is a positive integer, and U(θ) is the number of subcarriers satisfying (k(u) mod (θ)=0. Using equation (9), we see that the time domain representation of the first symbol, fn, has a period equal to Tb=0. In the URWIN network, we set θ=16 based on the following reasons. Using θ=16, for the first OFDM symbol, we obtain 16 periods, each with 16 samples, comparable to 802.11 OFDM networks. This duration is long enough for fast frequency offset estimation. Moreover, the power is uniformly distributed to 24 subcarriers. The spacing between two adjacent subcarriers is to 16=Tb=1.43 MHz.
Because the coherence bandwidth is a few megahertz, the above setting can achieve full frequency diversity in signal detection. Note that the θ can be adjusted meet other requirements.
CCF Analyses of the Second Preamble Symbol
The time-domain signal sn usually needs to be a pseudo-random waveform, such that its autocorrelation function (ACF) is close to a single pulse with a single peak, which can be used to indicate the accurate timing. To achieve the single-peak waveform, the receiver can pass the signal through an matched filter with a response of s*n.
The ACF of an ideal synchronization signal should be a delta function. With this property, the output of the matched filter is exactly the same as the channel impulse response. Other preferable properties include constant amplitude in the time domain, and uniform power in the frequency domain.
A constant amplitude in the time-domain yields the lowest PAPR, while a uniform power in the frequency domain is fair for all subcarriers to combat frequency-selective fading. For the ACF to be a delta function, the power must be uniform power for all subcarriers.
However, in practice, OFDM designs allocate a portion of the total bandwidth 210 as a guard band 220-222 one at each end of the frequency spectrum such that the sampling rate of an OFDM signal is always higher than the useful bandwidth. We call such a network an oversampled OFDM network. Each guard band 220-222 contains a number of sub-carriers 231. The number of sub-carriers in one guard band can be different from the other. The carriers in the usable band 221 are further divided into groups 240. One sub-carrier is dedicated as a pilot sub-carrier 230 in each group 240. In the oversampled OFDM network, uniform power across the frequency domain is impossible, and thus the perfect autocorrelation property is not achievable, which motivates us to design new synchronization signal for oversampled OFDM system and the URWIN network specifically.
Usually, the signal for synchronization is periodic. Therefore, we assume that the second OFDM preamble symbol is periodic with a period equal to
N/α, where α2ε{1, 2, 4, . . . , (log2 N)−1,
which forces
S
k(u)=0 for α≠1 and (k(u) mod α)≠0; ∀n. (16)
At the receiver, we pass the signal through a local correlator denoted by {tilde over (s)}n, n=0,1, . . . ,N/α−1. Then, the output of the correlator is the convolution between {tilde over (s)}n and sn, which is
r
n
*{tilde over (s)}
−n*=(φn*hn+σn)*{tilde over (s)}−n*. (17)
If we set {tilde over (s)}n=sn, then the correlator is a matched filter. The matched filter maximizes the received SNR. However, the output is not necessarily a sharp and accurate timing metric. We provide an alternative {tilde over (s)}n for accurate timing.
By, applying the periodic property of sn, we obtain
r
n
*{tilde over (s)}
−
*=s
n
*{tilde over (s)}
−n
**h
nσn*{tilde over (s)}−n*=ψs{tilde over (s)}((n)N/α)*hn+σn*{tilde over (s)}−n*,
if nε[−2Ng,−2Ng+1, . . . ,(α−1)N/α].
Using Eqn. (3), we further derive
ψs{tilde over (s)}(τ)=Σsm{tilde over (s)}(m−τ)
which can be simplified to
Equation (19) can be rewritten in vector form as
ψs{tilde over (s)}=Ω(α)μ(α), (20)
where ψs{tilde over (s)} is an N/α-dimensional column vector
where μ(α) is a U(α)-dimensional column vector, and Ω(α) is a (N(α) by U(α)) matrix. U(α) denotes the number of subcarriers with k(u) mod α=0. More specifically, Ω(α) and μ(α) are constructed from an N by U matrix Ω, and a U by 1 vector μ, respectively, which are
Then, we construct the new matrix Ω(α) and vector μ(α) by the following steps
As shown in the above equations, the correlator output can be written in the form of the circular CCF between sn and {tilde over (s)}n. To obtain a sharp metric to indicate the time synchronization, we determine μ(α) such that ψs{tilde over (s)}=(1, 0, . . . ,0)T. However, note that the equation
ψs{tilde over (s)}=Ω(α)μ(α)=(1,0, . . . ,0)T (23)
is inconsistent, implying that we cannot find such a vector μ. Therefore, we provide a zero-correlation-zone (ZCZ) based preamble.
ZCZ Based Preamble
Because the perfect correlation property can not be achieved because a solution to Equation (23) is not possible), we design the preamble such that the circular CCF ψs{tilde over (s)} has a zero correlation zone. The ZCZ has been used in CDMA networks.
However, how to apply ZCZ sequences in an oversampled OFDM network has neither been well understood, nor thoroughly studied. We apply the ZCZ sequences into the preamble design to enable more efficient and reliable time synchronization.
Main Lobe
The peak amplitude of ψs{tilde over (s)}(τ) is at τ=0. The main lobe covers a small region around τ=0. The main lobe width, denoted by WM (number of samples), is as small as possible to obtain good time resolution for synchronization. We set WM=2M+1 for M≧0.
Zero Correlation Zone
On the left-hand side of the main lobe, we ψs{tilde over (s)}(τ)=0 if τε[−WL−M, −M−1]. Note that ψs{tilde over (s)}(τ) can be treated as a periodic signal with period equal to N/α). The interval [−WL−M, −M−1] is the left ZCZ 302. A similar interval [M+1, WR+M] of length WR, within which ψs{tilde over (s)}(τ)=0 holds, is on the right-hand side of the main lobe and is the right ZCZ 302. The left and right ZCZs form the ZCZ.
In order to better acquire the delay feature of the channel impulse response (CIR) for accurate time synchronization, given CIR h(τ), we expect the convolution between the main lobe of ψs{tilde over (s)}(τ) and h(τ) to be in the ZCZ. Following this principle, WL and WR are larger than the maximum delay spread. Because the CP length of the data symbol is longer than the maximum delay spread, WL and WR are larger than Ng, i.e., WL, WR≧Ng. We set WL=WR.
Side Lobe
All other regions of ψs{tilde over (s)}(τ) belong to the side lobe. We suppress the peak to side-lobe ratio (PSR) between the peak of |ψs{tilde over (s)}(τ)| and the maximum amplitude of the side lobe. However, there is a tradeoff among the PSR, main lobe width, and ZCZ length. Generally, a smaller main lobe width and/or longer ZCZ degrade the PSR in an oversampled OFDM network.
Determining μ
The CCF ψs{tilde over (s)}(τ) is
To obtain above vector, we guarantee that μ is orthogonal to the vector space spanned by
Θ={ΩM+1T(α), . . . ,ΩM+W
where ΩiT(α) is the 1th row vector of matrix Ω(α). Such a μ(α) can be determined using the procedure below.
and
The second step can be performed by Gram-Schmidt orthonormalization, or a singular value decomposition (SVD). The third makes the vector S orthogonal to all vectors in Θ. By inserting μ(α)=S into Eqn. (20), we obtain the ZCZ for Eqn. (24).
Method to Determine Sk(u) and {tilde over (S)}k(u)
By applying Eqn. (16), we obtain the U×1 vector μ, form which we will determine {tilde over (S)}k(u) and {tilde over (S)}k(u). When using the matched filter, μ, becomes a real-valued vector (|Sk(0)|2,|Sk(1)|2, . . . , |Sk(U−1)|2)T. However, for the desired ψs{tilde over (s)}, the expected vector μ(α) can be complex-valued. Therefore, we modify the matched filter with phase as
{tilde over (S)}
k(u)
=S
k(u)
e
jφ
∀u=0,1,2, . . . ,U−1, (26)
which results in
μ=(|Sk(0)|2ejφ
based on Eqn. (22).
The disturbing phase φk(u) is obtained from μ. According to Eqns. (26) and (27), we obtain amplitudes |Sk(u)| and |{tilde over (S)}k(u)| as
|Sk(u)|=|{tilde over (S)}k(u)|=√{square root over (μ)} ∀u=0,1,2, . . . ,U−1.
The power loss during peak detection, due to phase disturbance, is negligible, see the last column of Table III. Our technique has the following advantages. We maintain the same amplitude property in the frequency domain as compared to the matched filter. The original phase of Sk(u) do not affect the amplitude or the phase of μ. Thus, we can minimize the PAPR by setting the phase of Sk(u) independently.
The phase of Sk(u) requires that the following properties hold. 1 ) The preamble should appear as a pseudo-random waveform in the time-domain 2 the sequence should have as low a PAPR as possible. Eqns. (26)-(28) can only the guarantee the preamble sequence has a ZCZ, but not the pseudo-random time-domain signal. Therefore, we apply a pseudo-random scrambling phase sequence ξk(u) (the phase uniformly distribution in [0, 2π) to the amplitude |Sk(u)|
S
k(u)
=|S
k(u)
|e
jξ
. (29)
The PAPR varies with the selection ξk(u). To achieve a low PAPR, we examime random phase sequences, and select the one with the lowest PAPR for randomizing.
Parameter Selection
Initialization of S
The vector S is initialized as the least square solution to
where {circumflex over (Ω)}(α) 460 denotes the psudeo-inverse of Ω(α).
Selection of Main Lobe Width and ZCZ Length
Given the main-lobe width and ZCZ length, we determine the corresponding OFDM symbol as described above. We select the length that can maximize the PSR to improve synchronization. Before searching for the optimal parameter set, we identify the domain of parameters M, WR, and WL 450. The selection of the main-lobe width (2M+1) satisfies
(2M+1)+Dmax−1≦Ng. (32)
where Dmax is the maximum delay spread of the channel, and Ng is the CP length. This constraint guarantees that the convolution-output length between the main lobe of ψs{tilde over (s)}(τ) and h(τ) does not exceed Ng.
For the ZCZ length, we require that
WR=WL≧Ng, (33)
which guarantees that the ZCZ length is long enough to acquire the time-domain channel features.
Because the rank of Ω(α) is equal to 2└U/2α┘, the maximum WR is limited such that
2WR≦2└U/2α┘−1. (34)
If the above condition is violated, the number of independent vectors in Θ becomes 2└U/2α┘, the algorithm in
Although the invention has been described with reference to certain preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the append claims to cover all such variations and modifications as come within the true spirit and scope of the invention.
