System and/or method for channel estimation in communication systems

System and/or method for channel estimation in communication systems

This patent application claims priority to U.S. Provisional Application No. 60/645,526, filed January 20, 2005, entitled "MIMO Channel Estimation using Complimentary Sets of Sequences in Multiuser Environments," assigned to the assignee of this application.

The subject matter of this application relates to communication.

It would be desirable for the communication system to have the ability to perform channel estimation as in a MIMO communication system.

The subject matter of the invention will be specifically pointed out and distinctly claimed at the end of the specification. However, the claimed subject matter, both with respect to its scheme and method of operation, together with its objects, features and advantages, will be best understood when taken in conjunction with the accompanying drawings with reference to the following detailed description.

1A and 1B are frame structures of training blocks for a MIMO system according to an embodiment.

2 is a schematic diagram illustrating one embodiment of a filter structure that may be utilized in a communication system.

3 is a schematic diagram illustrating one embodiment of a channel estimator that may be utilized in a communication system.

4 is a schematic diagram illustrating one embodiment of a communication system for channel estimation.

5 is a graph illustrating performance results simulated using various embodiments of a channel estimation method.

6 is a graph illustrating performance results simulated using various embodiments of a channel estimation method.

In the following detailed description, numerous specific details will be set forth in order to provide a thorough understanding of the claimed subject matter. However, it will be apparent to one of ordinary skill in the art that the claimed subject matter may be practiced without these specific details. In other instances, well-known methods, procedures, components, and/or circuits have not been described in detail herein so as not to obscure the claimed subject matter.

Some portions of the detailed description that follow are presented using computational algorithms and/or symbolic representations for data bits and/or binary digital signals stored within a computing system, such as a computer and/or computing system memory. These algorithmic content and/or representations are techniques used by those skilled in the art to convey their work to others skilled in the art. An algorithm is generally considered to be a self-consistent sequence of operations and/or similar processing to arrive at a desired result. Calculations and/or processing may involve physical processing of physical quantities. Typically, though not necessarily, these quantities may take the form of electrical and/or magnetic signals capable of being stored, transmitted, combined, compared, and/or otherwise manipulated. It has proven convenient at times, principally for the pretext of common usage, to refer to these signals as bits, data, values, elements, symbols, characters, terms, numbers, numbers, etc. It should be understood, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels.

The term "one embodiment" throughout this specification means that a particular configuration, structure, or feature disclosed in connection with the embodiment is included in at least one embodiment of the claimed subject matter. Thus, the appearances of the phrase "in one embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment. In addition, particular configurations, structures, and/or features may be combined in one or more embodiments.

Unless specifically stated otherwise, from the discussion below, discussions using the terms "compute", "determining", etc. throughout this specification refer to the processors, memories, registers, and/or other Computing, such as a computer or similar electronic computing device, that manipulates and/or transforms data expressed as physical, electronic and/or magnetic quantities and/or other physical quantities within information storage, transmission, reception and/or display devices. It will be appreciated to mean actions and/or processes that may be performed by the platform. Accordingly, a computing platform means a system or device having the ability to process and/or store data in the form of signals. Accordingly, a computing platform in this context may comprise hardware, software, firmware and/or any combination thereof. In addition, unless otherwise specifically described, processes described herein with reference to flowcharts or the like may also be executed and/or controlled in whole or in part by a computing platform.

Although the following discussion details several possible embodiments, these are merely examples and are not intended to limit the scope of the claimed subject matter. As another example, one embodiment may be on hardware, such as implemented to operate on a device or combination of devices, while another embodiment may be on software. Likewise, an embodiment may be implemented via firmware, hardware, software, and/or any combination of firmware and the like. As such, although the scope of the claimed subject matter is not limited in this respect, one embodiment may include one or more items, such as a storage medium or storage media. Instructions may be stored on such a storage medium, such as one or more CD-ROMs and/or disks, which instructions are executed by a system such as a computer system, computing platform, or other system, such as the embodiments described above. One such embodiment may be an embodiment of a method in accordance with the practice of the claimed subject matter. Embodiments may be utilized on a variety of possible communication devices including, for example, cell phones, personal digital assistants (PDAs), laptop computers, media players, and the like. Of course, claimed subject matter is not limited to these examples.

Utilization of antenna arrays in a wireless communication system may result in spatial diversity within the system. For example, a multiple input, multiple output (MIMO) system may use multiple antenna arrays as transmitters and/or receivers. Spatial diversity may provide an increase in the achievable capacity of the system and/or the stability of the system. In wireless communication systems that use antenna arrays, channel state information (CSI) may be desired. However, since CSI may not be available, it will be estimated for one or more channels of the system. Typical system models for a MIMO system may rely on known or predetermined estimation of CSI. For example, GJ Foschini and MJ in Wireless Personal Commun., Volume 6, pages 311-335, 1998. Gans's "On Limits of Wireless Communications in a Fading Environment" (hereafter referred to as refusal [1]), or IEEE J. Select. Reference may be made to "A simple transmit diversity technique for wireless communications" by SM Alamouti in Areas Commun, vol. 16, pages 1451-1458 (hereafter referred to as reference [2]). However, in practical applications, it may be desirable to estimate the CSI using one or more estimation schemes.

At least two general types of estimation schemes may provide a CSI estimation function. Blind estimation may include, for example, channel estimation, which may be performed based on the structure of a received signal. Blind estimation can be complex and can affect the performance of a wireless communication system or the like. Training-based estimation may include providing one or more training signals, such as during a training period of the system. Training signals may be provided from one or more transmitters of a wireless communication system to one or more receivers. The training signals may be perceived by the receiver and may be embedded in the signal, such as embedded in a frame. Training-based estimation may reduce complexity and/or improve performance of a wireless communication system or the like. Certain guidelines for designing training signals may be utilized when designing a training-based estimation scheme. For example, "How much training is needed in multiple-antenna wireless links?" by B. Hassibi and BM Hochwald in IEEE Trans.Inform, Theory vol. 49, pages 951-963, 2003, IEEE Trans. (hereinafter referred to as chamjeung [3]) or IEEE Trans. "Lower bound on training-based channel estimation error for frequency-selective block-fading Rayleigh MIMO channels" by O. Simeone and U. Spagnolini in Signal Processing, Vol. 52, pp. 3265-3267 (hereafter referred to as Ref. [4]). ) can be referred to. In addition, the design of the training signals of the training-based channel estimation method may involve consideration of the PAPR (Peak-to-Average-Power-Ratio) of the communication system, and the like. For example, "Optimal training for MIMO fading channels with time- and frequency-selectivity" by L. Yang, X. Ma, and GB Giannakis, during the ICASSP'04 conference in Montreal, Canada (hereinafter referred to as 'Camp [5]') can refer to

Without loss of generality, training signals are given to the receiver and will contain training blocks, which blocks will contain a series of sequences. However, it is worth noting that claimed subject matter is not limited in this respect. 1A shows a plurality of transmit antennas;<img file="KR20080098485A_D0001.tif" />It exemplifies the blocks of the frame format for . As illustrated in FIG. 1A , the training blocks include binary training blocks, or in other words, a two-sided structure such as one frame with a preamble and a postamble. and may include one or more gaps. Although not shown, the training blocks may include three or more side training blocks, for example, one or more midambles in at least one embodiment. In addition, FIG. 1B illustrates a frame structure of a training block that may be implemented in a MIMO system such as, for example, a MIMO-ISI system. The sequences illustrated in FIG. 1B may include sets of cyclic prefixed (CP) orthogonal complementary sequences, such as including at least a preamble a and a postamble b.

The training signal design for training-based channel estimation may use design models such as a Hadamard matrix and/or Golay complementary sequences. For example, in 1961 IEEE Trans. MJE Goay's "Complementary series" in Inform, Theory, Vol. 7, pages 82-87 (hereinafter referred to as Reference [6]), and IEEE Vehic, Birmingham, Arizona. Technol. Conf. Among K. Niu, S, -Q. Reference may be made to "A novel matched filter for primary synchronization channel in W-CDMA" by Wang et al. (hereinafter referred to as reference [7]). However, the claimed subject matter is not limited with respect to the referenced design models and the like.

When designing training signals for training-based channel estimation, it may be desirable to consider a merit factor such as the merit factor specified in reference [8] and/or Cramer-Rao Lower Bound (CRLB). Alternatively, implementation of a training scheme for frequency estimation may use circular convolution and/or fast Fourier transform (FFT), although claimed subject matter is not limited with respect to a particular method of implementing the schemes disclosed herein. , it will be appreciated that numerous other computational schemes and/or techniques may be used in embodiments of the claimed subject matter.

In one embodiment of the claimed subject matter, one scheme of channel estimation may be applied to a MIMO communication system with Inter-Symbol Interference (ISI). However, claimed subject matter is not so limited. For example, at least some of the schemes disclosed herein may be implemented in MIMO communication systems with frequency selective channels, frequency selective fading channels, and/or other types and/or categories of channels not detailed herein. can As mentioned above, training-based estimation schemes can reduce estimation errors and/or reduce the complexity of other estimation schemes, such as blind estimation. Such an approach may include, for example, MIMO-UWB (Ultra Wide Band), MIMO-OFDM (Orthogonal Frequency Division Multiplexing) compliant systems, and/or other systems that may utilize MIMO that currently exist or will be developed in the future. It can be utilized in multi-user systems and other systems that can utilize channels.

Consider a MIMO frequency selective channel in a MIMO communication system. In this embodiment, the channel may include block fading. In other words, CSI will not change within one block of a MIMO channel, but may change from block to block. For example, an indoor MIMO system may include such characteristics due, at least in part, to the mobility characteristics of the indoor MIMO system. For example, "Indoor MIMO channels: A parameter correlation model and experimental results" by S. Wang et al. during the Samoff'04 conference in Princeton, New Jersey can be referred to. In this example<img file="KR20080098485A_D0002.tif" />Let n contain the discrete-time channel impulse response (CIR) of the MIMO frequency selective channel. here<img file="KR20080098485A_D0003.tif" />may be given as the matrix below as the l-th tap of the MIMO CIR:

<maths num="1"><df><img file="KR20080098485A_D0004.tif" /></df></maths>

here, <img file="KR20080098485A_D0005.tif" />is the n of the MIMO communication system<sb>r</sb> th receiver antenna and n<sb>t</sb> It is the l-th tap of the CIR between the th transmit antennas. In this embodiment, an assumption can be made that one or more sub-channels of the system have unit power, or it can be shown as follows:

<maths num="2"><df><img file="KR20080098485A_D0006.tif" /></df></maths>

from above <img file="KR20080098485A_D0007.tif" />may be an expectation operator.

The received signal corresponding to the training block may additionally be rewritten as follows:

<maths num="3"><df><img file="KR20080098485A_D0008.tif" /></df></maths>

X will be given by the following matrix:

<maths num="4"><df><img file="KR20080098485A_D0009.tif" /></df></maths>

<img file="KR20080098485A_D0010.tif" />am.

<maths num="5"><df><img file="KR20080098485A_D0011.tif" /></df></maths>

In this embodiment, <img file="KR20080098485A_D0012.tif" />is n<sb>t</sb> It will contain the training signal given by the second transmit antenna. The training signal may include, for example, a plurality of training blocks that may be complementary. The training signal will be given at time n,<img file="KR20080098485A_D0013.tif" />is n at time n<sb>r</sb><sb></sb>It may include a signal received through the th reception antenna. <img file="KR20080098485A_D0014.tif" />silver <img file="KR20080098485A_D0015.tif" /> Additional noise components may be included, and SNR includes the signal-to-noise ratio.

As another option, X may be given as a matrix:

<maths num="6"><df><img file="KR20080098485A_D0016.tif" /></df></maths>

<img file="KR20080098485A_D0017.tif" />am.

<maths num="7"><df><img file="KR20080098485A_D0018.tif" /></df></maths>

Forward-shift permutation matrix of order N<img file="KR20080098485A_D0019.tif" />can be shown as:

<maths num="8"><df><img file="KR20080098485A_D0020.tif" /></df></maths>

<img file="KR20080098485A_D0021.tif" />, and the matrix of Equation 8 can be rewritten as follows:

<maths num="9"><df><img file="KR20080098485A_D0022.tif" /></df></maths>

Design of training sequences for training-based channel estimation schemes may include designing sets of sequences with special characteristics. For example, sets of sequences include complementary sequence sets, sets of uncorrelated periodic complimentary sequences, and/or sets of orthogonal periodic complimentary sequences with only a few sets of sequences. Examples may be included. It should be noted, however, that these sequence sets are listed by way of example only, and claimed subject matter is not limited in this respect. In one embodiment, complementary sequence sets may be designed and/or constructed according to design, definition and/or construction criteria.

For example, one can consider the following criteria for defining a set of complementary sequences:

<img file="KR20080098485A_D0023.tif" />to contain the sequence of ones and -1s, <img file="KR20080098485A_D0024.tif" />is the sequence<img file="KR20080098485A_D0025.tif" />contains irregular autocorrelation of a set of sequences<img file="KR20080098485A_D0026.tif" />Is, <img file="KR20080098485A_D0027.tif" />If , include complementary sequences. In one embodiment, sequences with the same length N will be considered, where<img file="KR20080098485A_D0028.tif" />am. Further discussion can be found, for example, in the 1972 IEEE Bulletin Inform. In "Complimentary sets of sequences" by CC Tseng and CL Liu (hereafter referred to as reference [11]) in Theory, Vol.

In one embodiment, the length is N=2<sp>n</sp>, Golay complementary sequence pairs with n1 can be constructed according to the following inductive approach:

<maths num="10"><df><img file="KR20080098485A_D0029.tif" /></df></maths>

here, <img file="KR20080098485A_D0030.tif" />is, <img file="KR20080098485A_D0031.tif" />am. This is a set of complementary sequences of length N<img file="KR20080098485A_D0032.tif" />Wow <img file="KR20080098485A_D0033.tif" />It will provide a.

In another embodiment, periodic complementary sequence sets may be designed and/or constructed according to design and/or construction criteria. The periodic complementary sequences may be orthogonal and/or decorrelated periodic sequences in one or more embodiments. For example, one can consider the following criteria to define a set of complementary sequences:

<img file="KR20080098485A_D0034.tif" />to include a sequence of 1s and -1s, <img file="KR20080098485A_D0035.tif" />is the sequence <img file="KR20080098485A_D0036.tif" />will include periodic decorrelation of set of sequences<img file="KR20080098485A_D0037.tif" />Is <img file="KR20080098485A_D0038.tif" />, it is a periodic complement. In one embodiment, sequences with period N may be considered, where<img file="KR20080098485A_D0039.tif" />am. Again, further discussion can be found, for example, in the 1972 IEEE Bulletin Inform. In "Complimentary sets of sequences" by CC Tseng and CL Liu (hereafter referred to as reference [11]) in Theory, Vol.

However, a set of different sequences <img file="KR20080098485A_D0040.tif" />is the periodic complement, <img file="KR20080098485A_D0041.tif" />and at this time <img file="KR20080098485A_D0042.tif" /> back side <img file="KR20080098485A_D0043.tif" />silver <img file="KR20080098485A_D0044.tif" />will respond to

Additionally, a collection of periodic complementary sequence sets <img file="KR20080098485A_D0045.tif" />is mutually uncorrelated when every two sets of complementary sequences in this collection correspond to each other. A discussion of the corresponding sequence sets will be further discussed, for example, in reference [11].

In another embodiment, the length <img file="KR20080098485A_D0046.tif" />, <img file="KR20080098485A_D0047.tif" />An ingolay complementary sequence pair can be constructed as follows:

<maths num="11"><df><img file="KR20080098485A_D0048.tif" /></df></maths>

At this time <img file="KR20080098485A_D0049.tif" />am. In this embodiment,<img file="KR20080098485A_D0050.tif" />contains the complex number of the unit amplification degree. After n rounds of interaction, a pair of complementary sequences<img file="KR20080098485A_D0051.tif" />class <img file="KR20080098485A_D0052.tif" />It can be created with this length N. Other than that,<img file="KR20080098485A_D0053.tif" />class <img file="KR20080098485A_D0054.tif" />is complementary Also, if (a, b) is a complementary set<img file="KR20080098485A_D0055.tif" />becomes a corresponding set, leading to a general conclusion, which can also be called a pair. As an example, based on Equations 10 and 11, when N = 16,

<img file="KR20080098485A_D0056.tif" />

<img file="KR20080098485A_D0057.tif" />may include, for example, two singbo-type sequence sets.

In at least one embodiment, the maximum number of complementary sequence sets will not be defined. However, in the binary case there are two decorrelation sets when each set has only two sequences, which will limit applications to MIMO systems. However, this problem can be addressed by taking one or more of the following binary case approaches:

1) Assigning sequences to pairs of transmit antennas with different phases.

2) Expansion of the number of sequences in each complementary set (see eg reference [11]).

3) Construct more sequences with zero correlation window (ZCW) based on complementary sets.

It should be noted, however, that these are merely typical approaches and that claimed subject matter is not limited thereto.

The design of training sequences for training-based channel estimation schemes may incorporate design criteria. For example, maximum likelihood estimation (MLE), least-square estimation (LSE), and/or linear minimum mean-square error (LMMSE) may be used as a design criterion. For example, Equation 3 can be rewritten as:

<maths num="12"><df><img file="KR20080098485A_D0058.tif" /></df></maths>

here <img file="KR20080098485A_D0059.tif" />is the Kronecker product, <img file="KR20080098485A_D0060.tif" />ego, <img file="KR20080098485A_D0061.tif" />is the sum of all the columns of the independent variables (arguments) in one column vector (stack). In this example, e is a complex AWGN vector containing the unit variance for each component. In this embodiment, the MLE of h may be reduced to the LSE of H. This will be given as:

<maths num="13"><df><img file="KR20080098485A_D0062.tif" /></df></maths>

In addition, the covariance of the matrix and <img file="KR20080098485A_D0063.tif" />MSE of each <img file="KR20080098485A_D0064.tif" /> and <img file="KR20080098485A_D0065.tif" />am. In one embodiment,<img file="KR20080098485A_D0066.tif" />The MSE of the training sequences is <img file="KR20080098485A_D0067.tif" />It will be the minimum when the condition is satisfied. If this condition is satisfied in this embodiment, the MLE of h may have a variance that achieves a reduced Cramer-Rao lower bound (CRLB). For example, the reduced CRLB may be obtained by constructing two binary training blocks that satisfy the following equation.

<maths num="14"><df><img file="KR20080098485A_D0068.tif" /></df></maths>

Also, the LMMSE of H will be given as:

<maths num="15"><df><img file="KR20080098485A_D0069.tif" /></df></maths>

<img file="KR20080098485A_D0070.tif" />The covariance matrix of and MSE are respectively<img file="KR20080098485A_D0071.tif" /> and <img file="KR20080098485A_D0072.tif" />this can be <img file="KR20080098485A_D0073.tif" />Minimizing the MSE of <img file="KR20080098485A_D0074.tif" />It may be accompanied by the satisfaction of the condition. If this condition is satisfied, the training sequence of one or more antennas of the MIMO system will be substantially orthogonal, for example.

The channel estimation algorithm may be designed based, at least in part, on one or more of the aforementioned criteria. In this embodiment,<img file="KR20080098485A_D0075.tif" />class <img file="KR20080098485A_D0076.tif" />Assuming that is orthogonal to each other, <img file="KR20080098485A_D0077.tif" />presuppose that Also, in this example,<img file="KR20080098485A_D0078.tif" />Wow <img file="KR20080098485A_D0079.tif" />are each transmit antenna <img file="KR20080098485A_D0080.tif" />Wow <img file="KR20080098485A_D0081.tif" />contains the preamble of In addition,<img file="KR20080098485A_D0082.tif" />class <img file="KR20080098485A_D0083.tif" />are each transmit antenna <img file="KR20080098485A_D0084.tif" />Wow <img file="KR20080098485A_D0085.tif" />includes the postamble of In this embodiment,<img file="KR20080098485A_D0086.tif" />, so the LSE of H is,

<maths num="16"><df><img file="KR20080098485A_D0087.tif" />, which can be rewritten as follows based on the preamble and postamble assignments:</df></maths>

<maths num="17"><df><img file="KR20080098485A_D0088.tif" /></df></maths>

In another embodiment, <img file="KR20080098485A_D0089.tif" />are assumed to be uncorrelated with each other. also,<img file="KR20080098485A_D0090.tif" />is assumed to be an even number. A transmit antenna for a set of complementary sequences (a, b)<img file="KR20080098485A_D0091.tif" />The following assignments can be made to:

<maths num="18"><df><img file="KR20080098485A_D0092.tif" /></df></maths>

from above <img file="KR20080098485A_D0093.tif" />may periodically shift the sequence x to the left by 1 element. also,<img file="KR20080098485A_D0094.tif" />If is odd, the following assignment may be made:

<maths num="19"><df><img file="KR20080098485A_D0095.tif" /></df></maths>

Also, additionally, the last antenna <img file="KR20080098485A_D0096.tif" />can be assigned a pair of different complementary sequences as follows:

<maths num="20"><df><img file="KR20080098485A_D0097.tif" /></df></maths>

For example, the condition <img file="KR20080098485A_D0098.tif" />When this is satisfied, inter-pathe interference is substantially reduced or eliminated. Also, by showing the expression below,

<maths num="21"><df><img file="KR20080098485A_D0099.tif" /></df></maths>

The LSE of H may appear as:

<maths num="22"><df><img file="KR20080098485A_D0100.tif" /></df></maths>

When the above assignments are utilized, they may appear as follows.

<maths num="23"><df><img file="KR20080098485A_D0101.tif" /></df></maths>

Thus, the LMMSE estimate of H can be expressed as:

<maths num="24"><df><img file="KR20080098485A_D0102.tif" /></df></maths>

One embodiment for a channel estimator may utilize a filter structure. For example, reference may now be made to FIG. 2 , in which a filter structure 102 is shown. The filter structure 102 can be mathematically modeled by taking a Z transform on both sides of Equation (10). It can lead to the following results:

<maths num="25"><df><img file="KR20080098485A_D0103.tif" /></df></maths>

here, <img file="KR20080098485A_D0104.tif" />am.

As another option, the filter structure shown in FIG. 2 may be built on a plurality of antennas of a MIMO system. This will allow for parallel processing, which will, for example, improve the speed of performing the estimation function. In one embodiment, the postamble processing may use a last in first out (LIFO) scheme on the received data to enable the same filter used for the preamplifier process. In addition, an efficient Golay correlator (EGC) may be used. For example, 1999 Electorn. Lett., vol. 35, pp. 1427-1428, BM Popovic's "Efficient Golay Correlator" (hereafter referred to as 'Efficient Golay Correlator') may be referred to.

In one embodiment, one training sequence may be defined as A. A is<img file="KR20080098485A_D0105.tif" />may include, in which case <img file="KR20080098485A_D0106.tif" />includes the received signal, <img file="KR20080098485A_D0107.tif" />contains a training block, such as one or more training blocks described above. For example, in one embodiment,<img file="KR20080098485A_D0108.tif" />can be a circulant matrix. In this embodiment,<img file="KR20080098485A_D0109.tif" />can be efficiently implemented through FFT. For example, suppose C is a cyclic matrix. In this example, C is<img file="KR20080098485A_D0110.tif" />In Fourier Transform Matrix <img file="KR20080098485A_D0111.tif" />is diagonalized by <img file="KR20080098485A_D0112.tif" />can appear as

<maths num="26"><df><img file="KR20080098485A_D0113.tif" /></df></maths>

The implementation of training blocks in a MIMO system will be described in more detail with reference to FIG. 3 . 3 illustrates a fast Fourier implementation of a channel estimator according to at least one embodiment. In this embodiment, the number of FFT operation points will be N, where N is the period of the sequences. A switch may be used to select an estimation method. For example, when the switch is open, the LM can be used, and when the switch is closed, the LMMSE can be utilized. Of course, claimed subject matter is not limited in this respect.

In this embodiment, n of the MIMO system<sb>r</sb>second antenna<img file="KR20080098485A_D0114.tif" />can be defined as:

<maths num="27"><df><img file="KR20080098485A_D0115.tif" /></df></maths>

O is a Hadamard product, and * means a conjugate. Even columns can be defined as:

<maths num="28"><df><img file="KR20080098485A_D0116.tif" /></df></maths>

<img file="KR20080098485A_D0117.tif" />The odd columns of can be defined as:

<maths num="29"><df><img file="KR20080098485A_D0118.tif" /></df></maths>

<img file="KR20080098485A_D0119.tif" />The even columns of can be defined as:

<maths num="30"><df><img file="KR20080098485A_D0120.tif" /></df></maths>

In one embodiment, the channel estimation scheme may be used in an orthogonal frequency division multiplexing (OFDM) system, such as a MIMO-OFDM system. In this embodiment, channel estimation may be performed, at least in part, based on time domain estimation and/or frequency domain estimation. An implementation of one channel estimation scheme can be shown in FIG. 4 . 4 shows an implementation example of a channel estimation scheme, where a frequency domain channel impulse response may be derived from an FFT transform. Of course, claimed subject matter is not limited to this aspect.

In one embodiment where each set of complementary sequences includes p periodic complementary sequences, the received signal corresponding to the i-th training block can be illustrated as follows:

<maths num="31"><df><img file="KR20080098485A_D0121.tif" /></df></maths>

where E<sb>It's</sb>includes AWGN. In addition, the MLE of the CIR of H may include:

<maths num="32"><df><img file="KR20080098485A_D0122.tif" /></df></maths>

The LMMSE of CIR H may include:

<maths num="33"><df><img file="KR20080098485A_D0123.tif" /></df></maths>

When decorrelated periodic complementary sequence sets are used, Equation 32 can be simplified to:

<maths num="34"><df><img file="KR20080098485A_D0124.tif" /></df></maths>

Equation 33 can be simplified to:

<maths num="35"><df><img file="KR20080098485A_D0125.tif" /></df></maths>

5 and 6 show graphs illustrating the MSE of channel estimation of other alternative schemes. 5 is a graph showing the MSE of a complementary sequence set and/or an orthogonal periodic complementary sequence set. In this graph, L=15, which means that there are 16 taps in each sub-channel,<img file="KR20080098485A_D0126.tif" />=2, <img file="KR20080098485A_D0127.tif" />=2, and N=16. The normalized theoretical minimum CRLB is<img file="KR20080098485A_D0128.tif" /> and MSE of simulated channel estimation <img file="KR20080098485A_D0129.tif" /> may be denoted as versus other SNR levels, where <img file="KR20080098485A_D0130.tif" />may refer to the Frobenius norm. The graph of Figure 3 shows that in this example, a minimum CRLB can be achieved.

Referring now to Figure 6, in this graph, L=15, <img file="KR20080098485A_D0131.tif" />=4, <img file="KR20080098485A_D0132.tif" />=4 and N=32. The normalized theoretical minimum CRLB is,

<maths num="36"><df><img file="KR20080098485A_D0133.tif" /></df></maths>

and normalized MSE of MLE and LMMSE <img file="KR20080098485A_D0134.tif" /> versus other SNR levels, where <img file="KR20080098485A_D0135.tif" />is the arithmetic mean. The graph of Figure 3 shows that in this example, a minimum CRLB can be achieved.

In the foregoing, various aspects of the claimed subject matter have been described. For purposes of explanation, systems and configurations have been described in order to provide a thorough understanding of the claimed subject matter. However, it will be apparent to those skilled in the art having the benefit of the disclosure herein that the claimed subject matter may be practiced without the specific details. In other instances, well-known features have been omitted and/or simplified so as not to obscure claimed subject matter. Although specific configurations have been illustrated and/or described herein, numerous modifications, substitutions, changes and/or equivalents will occur to those skilled in the art. Accordingly, it is to be understood that the appended claims are intended to cover all such modifications and/or variations that fall within the actual concept of the claimed subject matter.