WO2004073276A1  Twodimensional channel estimation for multicarrier multiple input outpout communication systems  Google Patents
Twodimensional channel estimation for multicarrier multiple input outpout communication systems Download PDFInfo
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 WO2004073276A1 WO2004073276A1 PCT/EP2003/001495 EP0301495W WO2004073276A1 WO 2004073276 A1 WO2004073276 A1 WO 2004073276A1 EP 0301495 W EP0301495 W EP 0301495W WO 2004073276 A1 WO2004073276 A1 WO 2004073276A1
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 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L25/00—Baseband systems
 H04L25/02—Details ; Arrangements for supplying electrical power along data transmission lines
 H04L25/0202—Channel estimation
 H04L25/0204—Channel estimation of multiple channels

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L1/00—Arrangements for detecting or preventing errors in the information received
 H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
 H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L25/00—Baseband systems
 H04L25/02—Details ; Arrangements for supplying electrical power along data transmission lines
 H04L25/0202—Channel estimation
 H04L25/022—Channel estimation of frequency response

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L25/00—Baseband systems
 H04L25/02—Details ; Arrangements for supplying electrical power along data transmission lines
 H04L25/0202—Channel estimation
 H04L25/0224—Channel estimation using sounding signals

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L25/00—Baseband systems
 H04L25/02—Details ; Arrangements for supplying electrical power along data transmission lines
 H04L25/0202—Channel estimation
 H04L25/024—Channel estimation channel estimation algorithms

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L27/00—Modulatedcarrier systems
 H04L27/26—Systems using multifrequency codes
 H04L27/2601—Multicarrier modulation systems
 H04L27/2647—Arrangements specific to the receiver
Abstract
Description
TWODIMENSIONAL CHANNEL ESTIMATION FOR MULTICARRIER MULTIPLE INPUT OUTPUT COMMUNICATION SYSTEMS
Field of Invention
The present invention relates to channel estimation for multiple input multiple output communication systems, and in particular to a method and related channel estimator for multiple input multiple output communication systems using multi carrier modulation schemes.
Background Art
The use of coherent transmission techniques in wireless communication systems requires the tracking of mobile radio channels, known as channel estimation. Since the signals transmitted from multiple transmit antennas are observed as mutual interference, channel estimation for multiple input multiple output MIMO communication systems is different from the single transmit antenna scenario. For multiple input multiple output MIMO communication systems using multicarrier modulation schemes the received signal after multicarrier demodulation is typically correlated in two dimensions, i.e. in time and frequency. In the following, orthogonal frequency division multiplexing OFDM will be referred to as one typical example for mutlicarrier moduilation schemes. The reason for this is that orthogonal frequency division multiplexing OFDM and variants thereof are the most popular multicarrier modulation schemes.
Communication systems employing multiple transmit and receive antennas, known as multiple input multiple output MIMO communication systems, can be used with orthogonal frequency division multiplexing OFDM to improve the communication capacity and quality of mobile radio systems. For orthogonal frequency division multiplexing OFDM communication systems with multiple transmit antennas, such as spacetime codes as decibed in A. Naguib, N.Seshadri, and A. Calderbank: "Space Time Coding and Signal Processmg for High Data Rate Wireless Communications", IEEE Signal Processing Magazine, pp. 7692, May 2000 or spacial multiplexing, different signals are transmitted form different transmit antennas simultaneously. Consequently, the received signal is the superposition of these signals, which implies challenges for channel estimation. Channel parameters are required for diversity combining, if spacetime codes are used or alternatively for separation of superimposed signals if spatial multiplexing is used.
Approaches to such channel estimation are described in Y. Li, N. Seshadri, and S. Aήyavisitakul: "Channel Estimation for OFDM Systems with Transmitte Diversity in Mobile Wireless Channels", IEEE Journal of Selected Areas on Communications, Vol 17., pp. 461470, March 1999 and Y. Li: "Simplified Channel estimation for OFDM Systems with Multiple Transmit Antennas", IEEE Transactions on Wireless Communications, Vol 1., pp. 6775, January 2002, in particular a channel estimation scheme for orthogonal frequency division multiplexing OFDM with multiple transmit antennas based on the difcrete fourier transform DFT.
Further, the estimators based on the least squares LS and minimum mean squared error MMSE criterion for OFDMMIMO systems have been systematically derived in Y. Gong and K. Leta/ef: "Low .Ran Channel Estimation for SpaceTime Coded Wideband OFDM Systems", Proc. IEEE Vehicular Technology Conference (VTC'2001Fall), Atlantic City, USA, pp. 722776, 2001. Related solutions deal with one dimensional approaches where a known pilot OFDM symbol is followed by L data bearing OFDM symbols. This scheme is applicable for a quasistatic environment where the channel does not change significantly during L OFDM symbols, i.e. indoor systems such as wireless local area networks WLAN.
To accomodate some mobility, the receiver may switch to decision directed channel estimation during the reception of the L data bearing OFDM symbols, as suggested in Y Li, N. Seshadri, and S. Aviyavisitakul: "Channel Estimation for OFDM Systems with Transmitte Diversity in Mobile Wireless Channels", IEEE Journal of Selected Areas on Communications, Vol 17., pp. 461470, March 1999 and Y. Li: "Simplified Channel estimation for OFDM Systems with Multiple Transmit Antennas'", IEEE Transactions on Wireless Communications, Vol I., pp. 6775, January 2002. However, decision directed channel estimation which uses prior decisions of data symbols as pilot symbols, is significantly more complex than channel estimation schemes relying on pilots only.
Further, for OFDMbased systems with one transmit antenna, two dimensional channel estimation utilizing a scattered pilot grid can be employed, which satisfy the sampling theorem in time and frequency. For pilotsymbol aided channel estimation PACE known pilot symbols are multiplexed into the data stream. Interpolation is used to obtain the channel estimate for the information carrying symbols. PACE for single carrier systems was introduced in J.K. Cavers: "An analysis of Pilot Symbol assited Modulation for Rayleigh Fading Channels", IEEE Transactions on Vehicular Technology, Vol. VT40, pp. 686693, November 1991. In R. Nils son, O. Edfors, M. Sandell, and P. Boerjesson: "An Analysis of TwoDimensional PilotSymbol Assisted Modulation for OFDM", Proc. IEEE Intern. Conf. on Personal Wireless Communications (ICPWCV7), Mumbai (Bombay), India, pp. 7174, 1997 and P. Hoeher, S. Kaiser, and P. Robertson: "TwoDimensional Pilot SymbolAided Channel Estimation by Wiener Filtering", Proc. IEEE Intern. Conf. on Acoustics, Speech, and Signal Processing.(ICASSP'97), Munich, Germany, pp. 18451848, 1997 twodimensional 2D filtering algorithms have been proposed for pilotsymbol aided channel estimation PACE. However, such a 2D estimator structure is generally too complex for practical implementation.
To reduce the complexity, separating the use of time and frequency correlation has been proposed in P. Hoeher, S. Kaiser, and P. Robertson: "PilotSymbolAided Channel Estimation in Time and Frequency", in Proc. Communication Theory MiniConference (CTMC) in conjunction with IEEE Global Telecommunications Conference (GLOBECOM'97), Phoenix, USA, pp. 9096, 1997. This combined scheme, termed double onedimensional (2 x ID) pilotsymbol aided channel estimation PACE, uses separate Wiener filters, one in frequency direction and one in time direction.
Another approach to reduce the computational complexity is based on a transformation which concentrates the channel power to a few transform coefficients. Estimators based on the discrete Fourier transform DFT have the advantage that a computationally efficient transform in form of the FFT does exist, and that DFT based interpolation is simple. In Y. Li: "PilotSymbolAided Channel Estimation for OFDM in Wireless Systems", IEEE Transactions on Vehicular Technology, Vol. 49, pp. 12071215, July 2000, the approach based on discrete Fourier transform DFTbased pilotsymbol aided channel estimation PACE was extended to two dimensional pilotsymbol aided channel estimation PACE by using the two dimensional FFT for the single antenna case.
However, a major problem for extending the approach to two dimensional channel estimation utilizing a scattered pilot grid to multiple input mulitple output MIMO communication systems is that the limitation of the number of transmit antennas which can be separated by a certain number of pilots. The minimum number of pilot symbols Np which are required to estimate iV_{T} channel impulse responses (CIR) each of which having Q taps has been shown in Y. Gong and K. Letaief: "Low Rank Channel Estimation for SpaceTime Coded Wideband OFDM Systems", Proc. IEEE Vehicular Technology Conference (VTC "2001 Fall), Atlantic City, USA, pp. 722776, 2001 to be
N£ ≥ N_{T} Q (1)
However, this means that the number of pilots required for channel estimation grows with the number of transmit antennas N_{?}.
Summary of Invention
In view of the above, the object of the present invention is to extend the concept ot two dimensional channel estimation to MLMO systems.
According to the present invention this object is achieved through a method of two dimensional channel estimation for multiple input multiple output transmission systems using multicarrier modulated transmission signals impinging from a plurality of transmit antennas and carrying a two dimensional data sequence with embedded pilot symbols. In a first step the plurality of transmit antennas is divided into disjoint transmission antenna subsets. In a second step impinging pilot sequences are seperated in relation to transmission antenna subsets by performing a first stage channel estimation to yield tentative estimates of a channel response in a first dimension of transmission. In a third step impinging pilot sequences are seperated in relation to antennas in transmission antenna subsets by performing a second stage channel estimation for each antenna in each transmission antenna subset to yield an estimation of the channel response.
An important advantage of the present invention is increased fiexibilty in channel estimation. The reason for this is that by dividing the separation task of the superimposed transmission signals in time and frequency direction, a more efficient usage of the pilot symbols is possible. Hence, either the number of required pilot symbols may be reduced or the performance can be improved.
In view of the above, another important advantage of the present invention is the increase in the number of transmit antennas which can be estimated with a certain number of pilot symbols through application of a two stage channel estimaiton approach.
Yet another important advantage of the present invention is that the two stage channel estimation approach allows for tracking of channel variations even at high Doppler frequencies. This is a prerequisite to support high velocities of mobile users and therefore to enable truely mobile multiple input multiple output MLMO communication systems.
According to a preferred embodiment of the present invention the first stage channel estimation is performed using pilot sequences arranged as a two dimensional grid of pilot symbols, wherein pilot symbols used for first stage channel estimation depend on the first dimension of transmission only and pilot symbols used for second stage channel estimation depend on a second dimension of transmission only. Preferably, pilot sequences are expressed in a product form for achieving seperability of pilot sequences in the first dimension of transmission and the second dimension of transmission.
An advantage of this preferred embodiment of the present invention is that utilization of a scattered pilot grid allows for efficient use of pilot symbols. Further, by matching the pilot spacing in time and frequency to the worst case channel characteristics higher mobile velocities can be supported with respect to conventional one dimensional schemes.
According to another preferred embodiment of the present invention, for a pilot spacing having a value of one the first stage channel estimation and/or the second stage channel estimation is achieved in a noninterpolating manner through yield of tentative estimates in relation to pilot symbol grid positions in the dimension of estimation. Alternatively, for a pilot spacing having a value larger than one the first stage channel estimation and/or the second stage channel estimation is achieved in an interpolating manner through yield of tentative estimates for all data sequence grid positions in the dimension of estimation.
An important advantage of this preferred embodiment is flexible support of different two dimensional pilot grids. In other words, the present invention may be flexibly applied using any type of pilot spacing, both, in frequncy and time direction the application of suitable interpolation techniques.
Further preferred embodiments of the present invention relate selection of first dimension of transmission for the first channel estimation stage and the second channel estimation stage  i.e., in frequence direction or in time direction  and further to the selection of channel estimation domain  i.e., frequency domain channel estimation or time domain channel estimation. Here, according to the present invention any combination of dimension of transmission and channel estimation domain is supported.
The free selectability of dimension of transmission and channel estimation domain is further reason for flexibility of the channel estimation approach according to the present invention. It enables optimal consideration of multicarrier related transmission parameters, selected pilot grid structure, and also application of com putationanally most suitable channel estimation techniques.
According to another preferred embodiment of the present invention the channel estimation approach is applied to a celluar communication system with a frequency reuse factor of one such that base stations and related anntenna arrays form the plurality of transmit antennas and such that transmission antenna subsets and related transmission antennas are defined in relation to this plurality of transmit antennas.
An important advantage of this preferred embodiment of the present invention is the application of the two stage channel estimation techiques as outlined above to distributed antennas. In particular, it allows to handle a situation where a mobile user roams at a cell border. While data bearing symbols can be protected against interference using a channel code or spreading, this is not possible for pilot symbols. According to the present invention through appropriate definition of subset in relation to cells in the celluar communication system.
According to yet another preferred embodiment ofthe present invention there is provided a computer program product directly loadable into the internal memory of a channel estimator for estimating multiple input multiple output transmission channels in two dimensions comprising software code portions for performing the steps of the method of two dimensional channel estimation according to the present invention when the product is run on a processor of the channel estimator.
Therefore, the present invention is also provided to achieve an implementation of the inventive method steps on computer or processor systems. In conclusion, such implementation leads to the provision of computer program products for use with a computer system or more specifically a processor comprised, e.g., in a channel estimator for estimating multiple input multiple output transmission channels in two dimensions.
The programs defining the function of the present invention can be delivered to a computer/processor in many forms, including, but not limited to information permanently stored on nonwriteable storage media, e.g., read only memory devices such as ROM or CD ROM discs readable by processors or computer I/O attachments; information stored on writable storage media, i.e. floppy discs and hard drives; or information convey to a computer/processor through communication media such as local area network and/or telephone networks and/or Internet or other interface devices. It should be understood, that such media when carrying processor readable instructions implementing the inventive concept represent alternate embodiments of the present invention.
Description of Drawing
In the following the best mode and preferred embodiments of the present invention will be explained with reference to the drawing in which:
Fig. 1 shows a schematic diagram of an OFDM based multiple input multiple output MIMO communication system for explanation of the system model under lying the present invention;
Fig. 2 shows a schematic diagram illustrating OFDM modulation and demodulation, respectively;
Fig. 3 shows a scattered pilot grid suitable for two dimensional channel estimation according to the present invention;
Fig. 4 shows a schematic diagram of a channel estimator for estimating multiple input multiple output transmission channels of mutlicarrier communication systems according to the present invention;
Fig. 5 shows a flowchart of operation of the channel estimator shown in Fig. 5;
Fig. 6 shows a schematic diagram illustrating the principle of 2xlD channel estimation underlying the present invention;
Fig. 7 shows a schematic diagram of a channel estimator for estimating multiple input multiple output transmission channels of mutlicarrier communication systems according to the present invention, wherein channel estimation is performed in frequency direction first;
Fig. 8 shows a further scattered pilot grid suitable for two dimensional channel estimation according to the present invention;
Fig. 9 shows a further scattered pilot grid corresponding to an digital video broadcast DVBT application and suitable for two dimensional channel estimation according to the present invention;
Fig. 10 shows a schematic diagram of a channel estimator for estimating multiple input multiple output transmission channels of mutlicarrier communication systems according to the present invention, wherein channel estimation is per formed in time direction first;
Fig. 11 shows a schematic diagram of an estimator stage adapted to achieve channel estimation in the time domain according to the present invention;
Fig. 12 shows a schematic diagram of a further estimator stage adapted to achieve channel estimation in the time domain according to the present invention; and
Fig. 13 shows an application of the two stage channel estimation approach according to the present invention to a cellular communication system with a frequency reuse factor of one.
Description of Best Mode and Preferred Embodiments
In the following, the best mode and preferred embodiments of the present invention will be explained with reference to the drawing. Initially, some basic considerations underlying differential multiplelength transmit diversity and related diversity reception will be explained for a better understanding of the present invention.
Basic Considerations
The present invention addresses pilotsymbol aided channel estimation PACE schemes for multicarrier multiple input multiple output MIMO communication systems which are based on the insertion of a pilot grid. Typically for a multi carrier multiple input multiple output MIMO communication system, pilotsymbol aided channel estimation PACE  also referred to as PACE in the following  is applied across subcarriers in frequency direction and over several multicarrier transmission symbols  e.g., OFDM symbols  in two dimensions, resulting in two dimensional 2D PACE.
The present invention as explained in the following is not restricted to a par ticual type of multicarrier multiple input multiple output MLMO communication system, and may be applied, e.g., to orthogonal frequency divsion multiplexing OFDM, discrete multitone transmission DMT, filtered multitone transmission FMT, or biorthogonal frequency division multiplexing BFDM.
Another multicarrier multiple input multiple output MLMO communication system is multicarrier code divsion mutliple access MCCDMA where spreading in frequency and/or time direction is introduced in addition to the multicarrier modulation. Yet another multicarrier multiple input multiple output MIMO communication system is a multicarrier code divsion mutliple access MCCDMA system with a variable spreading factor, namely variable spreading factor orthogonal frequency and code division multiple access VSFOFCDM.
From the above, it should be understood that pilot symbol aided channel estimation PACE may be applied to all multicarrier multiple input multiple output MLMO communication systems operating with transmission signals being correlated in two dimensions. Therefore, all these multicarrier multiple input multiple output MLMO communication systems may employ the different embodiments of the present invention as explained in the following.
System Model
Fig. 1 shows a schematic diagram of an OFDM based multiple input multiple ^{•} output MLMO communication system  also referred to as OFDM system in the following  for explanation of the system model underlying the present invention. Further, Fig. 2 shows a schematic diagram illustrating OFDM modulation and demodulation in correspondence to the OFDM based multiple input multiple output MIMO communication system shown in Fig. 1.
As shown in Fig. 1, for the considered OFDMbased MIMO system, one OFDM modulator is employed on each transmit antenna, while OFDM demodulation is performed independently for each receive antenna. The signal stream is divided into N_{c} parallel substreams, typically for any multicarrier modulation scheme. The i^{th} substream, also referred to as subcarrier in the following, of the £^{th} symbol block, named OFDM symbol in the following, is denoted by X_{iti}. An inverse DFT with Nppr points is performed on each block, and subsequently the guard interval having Noi samples is inserted to obtain x_{i<n}. After D/A conversion, the signal x(t) is transmitted over a mobile radio channel with response h(t, r).
As shown in Fig. 1, the received signal at receive antenna v consists of superimposed signals from Nγ transmit antennas. Assuming perfect synchronization, the received signal of the equivalent baseband system impinging at receive antenna v at sampling instants t — [n + lN_{Sym}}T_{Sp}i is in the form
NT /.OO
V = y^{iu)}([n + W_{sym}]T_{spl}) = ∑ h^ t, r)  x^{w}(t  τ) dr + n(t)
»=^{l ~}°° t=[n+£N_{sym}]T_{sp} where χ^{w}(t) denotes transmitted signal of transmit antenna μ after OFDM modulation, n(t) represents additive white Gaussion noise, and N_{sym} = N_{FPT} + NQ_{I} accounts for the number of samples per OFDM symbol.
As shown in Fig. 2, at the receiver the guard interval is removed and the information is recovered by performing an DFT on the received block of signal samples, to obtain the output ofthe OFDM demodulation Y^. The received signal at receive antenna υ after OFDM demodulation given by
£ = ∑, X^{w}ι,i Hϊi^{¥)} + Nι,i (2) μ=l where and H ^{v)} denotes the transmitted information symbol and the channel transfer function (CTF) of transmit antenna μ, at subcarrier i ofthe ^{th} OFDM symbol, respectively. The term N^ accounts for additive white Gaussian noise AWGN with zero mean and variance N_{0}. It is assumed that the transmitted signal consists of L OFDM symbols, each having N_{c} subcarriers. Channel Characteristics
While in the following, a way to model channel characteristics will be explained, it is important to note that the present invention is not restricted in any way through such a model. To the contrary the present invention is applicable to actually existing mobile radio channels. For the application of the present invention it is only of relevance that mobile radio channels are band limited. Preferably, they should also be be limited in time, which practically is the case in view of maximum delay of mobile radio channel. Further, preferably different transmit antennas and receive antennas should be uncorrelated.
The present invention considers a time variant frequency selective fading channel. The number of nonzero taps is typically smaller or equal to the maximum delay of the channel, Q_{0} < Q. The channel impulse response CIR between transmit antenna μ and receive antenna v is defined by
Qo
9=1
where h}^ ^{υ)} (t) and r^ ^{υ)} are the complex amplitude and delay of the q^{th} channel tap.
According to the present invention it is assumed that the Q_{0} channel taps and all antennas are mutually uncorrelated. The channel taps h}^{»}' ^{υ)}(t) are zeromean complex independent identically distributed (i.i.d.) Gaussian random variables. Due to the motion of the vehicle h^^{, v)}(t) will be timevariant caused by the Doppler effect. The g^{th} channel tap h£' ^{v)} (t) is a wide sense stationary WSS Gaussian process, being bandlimited by the maximum Doppler frequency v_{max}.
Further, it is commonly assumed that the channel impulse response CIR is approximately constant during one OFDM symbol, so the time dependency of the CIR within one OFDM symbol can be dropped, i.e. h%'^{v)}(t) «
for t 6 [£T, (t+ l)T\. Although this is strictly true only for timeinvariant channels, this assumption seems to be most often justified in practice, and a good system design should ensure that the OFDM symbol duration is sufficiently short.Further, the channel transfer function CTF of equation (2), is the the Fourier transform of the CIR h ^{β}'^{u)}(t, r). Sampling the result at time t — l%_{ym} and frequency / = i/T, the CTF at subcarrier i of OFDM symbol I becomes
Qo Hl = H^ £T_{sym}, i/T) = Kf ^{e~J2πT}" ^{i/T (4)}
where T_{sym} = N_{F}F_{Γ} + N_{GI})T_{sp}ι and T = N_{FFT}T_{Sp}i represents the OFDM symbol duration with and without the guard interval, respectively. The matrix form of equation (4) is given by
where T^{l}"'"^{)} represents the transformation matrix which transforms h^'"^{5} into the frequency domain, defined by
{ ^} . = exp ( 2τr ~^) ; 0 < i < N_{c}  1 , 1 < q < Q_{0} (6) of dimension N_{c} x Qo
Further, if the guard interval is longer than the maximum delay of the channel, i.e. N_{GI} > Q, where Q > Q_{0} denotes the total number of channel taps, the orthogonality at the receiver after OFDM demodulation is maintained, and the received signal of equation (2) is obtained.
Assuming the fading at the receiver antennas is mutually uncorrelated, the channel estimation according to the present invention will be performed independently for each antenna. Therefore, in the description to follow the marker for the receive antenna v is omitted.
Further, according to the present invention a channel is defined to be sample spaced if the tap delays τ_{q} are multiples of the sample instant T_{sp} , i.e.
τ_{q} = T_{spl}β_{g} ; l ≤ q ≤ Qo , β_{g} e {0, l,   ' , Q} (^{7}) where β_{q} is an arbitrary integer, equal to or larger than zero. In this case Hf^ in equation (4) becomes the DFT of the ClRh^{(}[^
In view of the above, Hf ^{υ)} can be expressed in matrix notation
where F represents the DFTmatrix of dimension N_{G}ι x N_{c}, defined by
{F}_{n>}. = e^{~j2π ni/NpFr} ; 0 < i < N_{c}  1 , 0 < n < N_{GI} ~ 1 (9)
While for a real channel the tap delays τ_{q} will not be multiples of the sample duration T_{sp}ι, however, for many applications the sample spaced channel model does approximate a real channel sufficiently well.
Principle of Pilot Symbol Aided Channel Estimation for OFDMbased MIMO
Systems
Fig. 3 shows a scattered pilot grid suitable for two dimensional channel estimation according to the present invention.
As shown in Fig. 3, pilot aided channel estimation PACE is based on periodically inserting known symbols, termed pilot symbols in the data sequence. If the spacing of the pilot symbols is sufficiently close to satisfy the sampling theorem, channel estimation and interpolation for the entire data sequence is possible.
For two dimensional pilot aided channel estimation in the sense of the present invention it must be taken into account that for OFDM the fading fluctuations are in two dimensions, in time and frequency. In order to satisfy the twodimensional sampling theorem, the pilot symbols are therefore scattered throuout the time frequency grid, which yields a twodimensional pilot grid. Another reason for selecting scattered pilot grids is to maximize spectral efficiency. Description of Pilot Grids in Two Dimensions
To formally describe a regular grid in the 2D plane according to the present invention the total number of pilots transmitted in one frame is defined to Np = Λ£ • Ng, with N£ = N_{c}/D[ and Ng = L/D_{t} being the number of pilots in frequency and time direction respectively. Here, the following notation is used: given a matrix describing a 2D structure X, the subsets which describe the dimension corresponding to the frequency and time directions are denoted by X' and X", respectively.
Denoting the pilot symbol of subcarrier i and OFDM symbol I by p = [i, £}^{τ}, any regular 2D grid for use in the framework of the present invention is be described by
{ρ : p = Gp + g_{0)} V p € l^^{x}^ } (10)
where p = [z, £}^{τ} denotes the index of the i^{th} and I^{th} pilot in frequency and time direction, respectively, and g_{0} defines a pilot grid offset.
For multiple input multiple output MIMO communication systems  also referred to as MLMO system in the follwoing  every transmission signal at transmit antenna may to use its own pilot grid. This enables the receiver to separate the superimposed transmission signals from different transmission antennas.
To describe pilot symbolassisted channel estimation in the sense of the present
rate i = \i/Df in frequency direction, and at a D_{t} times lower rate £ = [£/D_{t}\ in time direction, respectively. As a general convention, variables describing pilot symbols will be marked with a ^{"} in the following description.
Further, without restricting scope of protection, it may be assumed that the pilots X^{(μ)}n are chosen from a PSK constellation, so \X . \ = 1.
For the particular example shown in Fig. 3 the structure of the pilot grid is defined by G which is
D_{f} 0
G = 0 A
where and A denotes the socalled pilot spacing in frequency and time, respectively. For the pilot grid shown in Fig. 3 the particular values are = 5 and A = 5.
It should be noted that before transmission, the pilots
may be multiplied by an outer pilot sequence {X^.} which is identical for all transmit antennas to yield the transmitted pilot sequencex$ ^{x}t,i_ = x_{0f} ι,ι, x £p,ι
Further, the outer pilot sequence { J _{0} ,} is chosen to have a low peak to power average ratio in the time domain and/or to have good correlation properties for synchronization.
As shown in Fig. 2, at the receiver the cyclic prefix is removed and an FFT is performed to yield the received signal after OFDM demodulation. Assuming perfect synchronization, the received signal Y^ of equation (2) is obtained. For channel estimation the received signal at the pilot positions are demultiplexed from the data stream, and after removing the outer pilot sequence, by dividing through Xo„ the received pilot is obtained according to
N_{τ}
where Gp is defined in (10). Basic Consideration for 2x1 DPilot Assisted Channel Estimation for Multiple Input Multiple Ouput Communication Systems
Fig. 4 shows a schematic diagram of a channel estimator for estimating multiple input multiple output transmission channels of mutlicarrier communication systems according to the present invention.
As shown in Fig. 4, the channel estimatior 10 comprises a first estimator stage 12 and a second estimator stage 14. Further, the channel estimator comprises a transmission antenna subset memory 16.
Fig. 5 shows a flowchart of operation of the channel estimator shown in Fig. 4.
As shown in Fig. 5, operation of the channel estimator according to the presen invention relies on a method where in a firsat step S10 the plurality of transmit antennas into disjoint transmission antenna subsets. Then, in a step S 12 impinging pilot sequences in relation to transmission antenna subsets are seperated by performing a first stage channel estimation to yield tentative estimates of a channel response in a first dimension of transmission. Then, in a step S14 impinging pilot sequences in relation to antennas in transmission antenna subsets by performing a second stage channel estimation for each antenna in each transmission antenna subset to yield an estimation of the channel response.
Fig. 6 shows a schematic diagram illustrating the principle of channel estima tiong according to the present invention.
As shown in Fig. 6 and outlined above, in the step S12 channel estimation is performed in one dimension, yielding tentative estimates for all subcarriers of these OFDM symbols. These tentative estimates are then used in step S14 as new pilots, in order to estimate the channel for the entire frame.
As shown in Fig. 6, the second stage does not only interpolate between OFDM symbols having pilots, but it does also improve the accuracy of the tentative esti mates.
Further, according to the present invention Either channel estimation in frequency direction or time direction may be performed first. Reference to the case where channel estimation in frequency direction is performed first will be made by 2 x IDPACE type I in the following. Further, reference to the case where channel estimation in time direction is performed first will be mde by 2 x IDPACE type II in the following.
To formally describe the problem, the received pilot of OFDM symbol £D_{t} is considered at the (z\D/)^{th} subcarrier
ϊ = {1, 2,    , N_{C}/D_{f}}
where X^{(μ)}ι_{Dt iD} and H^{i}X^{v)} denotes the transmitted pilot symbol and the channel transfer function (CTF) of transmit antenna μ, at subcarrier i = iDf of the t = ΪD_{t} ^{th} OFDM symbol, respectively.
Further, it is assumed that the CTF varies in the £ and in the i variable, i.e. in time and in frequency. The term Ni_{Dtji}jo_{f} accounts for additive white Gaussian noise AWGN. L represents the number of OFDM symbols per frame, N_{c} is the number of subcarriers per OFDM symbol, D_{/} and denote the pilot spacing in frequency and time, and N_{τ} is the number of transmit antennas.
The overall object underlying the present invention is to estimate H for all {£, i, μ} within the frame.
To achieve this object, generally for MIMO channel estimation, in addition to channel estimation and interpolation it is also necessary to separate the impinging signals from N transmit antennas. Dividing the signals corresponding to the N_{τ} transmit antennas into iV_{T1} subsets, yields iV_{T1} groups each of which having Nχ_{2} signals, such that N_{τ} = Nτ_{\}N_{T} . In other words, for a MIMO system having N_{τ} transmit antennas, according to the present invention signals corresponding to N_{T2} transmit antennas into one set, to form JV_{T1} subsets.
In other words, the basic concept underlying the present invention is to divide the separation task into two stages, in the way that in step S12 channel estimation is performed in one dimension, at OFDM symbols £ — £D_{t}, yielding tentative estimates for all subcarriers of these OFDM symbols. The second step S14 uses these tentative estimates as new pilots, in order to estimate the channel for the entire frame.
As shown in Fig. 6, the second stage estimation does not only interpolate between OFDM symbols having pilots, but it does also improve the accuracy of the tentative estimates. Therefore, the different embodiments of the present invention as explained in detail in the following have significantly reduced complexity while there is little degradation in performance.
According to Fig. 6 channel estimation in frequency direction is performed first, to reverse the order such that channel estimation in time direction is performed first is straightforward. In the following reference will be made to the case where channel estimation in frequency direction is performed first by 2 x IDPACE type I. to the contrary, reference to the case where channel estimation in time direction is performed first will be made to as 2 x IDPACE type II.
Considering channel estimation in time direction, it is proposed to use the pilots _{t}.zj ^{• • •} _{>}
€ Q, in order to estimate HfJ. Further, for smoothing type filtering it is proposed to use past as well as future pilots to estimate H l, this means 1 < £ < D_{t}N_{p}. Therefore, for smoothing an estimate cannot be obtained until all pilots have been received, which requires buffering of A£ = D_{t}Np — £ OFDM symbols.As will be shown in more detail in the follwoing, the alternative is to use prediction type filtering where £ > D_{t}Np' . In this case only past pilots are used for channel estimation in time direction.
Obviously, prediction type filtering does not require any buffering, however, the performance with respect to smoothing degrades. For channel estimation in frequency direction, on the other hand, all pilots of one OFDM symbol are being received together, so no buffering is required. However, the accuracy of the channel estimates typically degrades near the band edges.
2 x IDPACE type I
Fig. 7 shows a schematic diagram of a channel estimator for estimating multiple input multiple output transmission channels of mutlicarrier communication systems according to the present invention, wherein channel estimation is performed in frequency direction first.
According to the present invention it is prposed to extend 2 x IDPACE to OFDMbased MLMO channel estimation. For MIMO channel estimation it is necessary to separate the impinging signals from N_{τ} transmit antennas. Let the MIMO system having N_{?} transmit antennas be denoted by set the A. Further, according to the present invention the set of N_{τ} transmit antennas is devided into Nχι subsets A_{μι} C A, with i = {!, ■ • ■ , N _{i}}. Each subset contains N_{T2} transmit antennas, such that iV_{T} = iV_{T}ιN_{T2}
In other words, for a MIMO system having N transmit antennas, according to the present invention it is proposed to group the signals corresponding to N transmit antennas into one set, to form Nτι subsets of A. Without restricting scope of protection, one may assume that all sets have the same number of transmit antennas, and the subsets A_{μι} are disjoint, i.e. each transmit antenna can only be in one set.
The concept underlying tne present invention is to divide the separation task into two stages, in the way that we first separate a subset of the N ι < N_{T} signals together with channel estimation in the first estimation stage. The resulting signal Z A^{1} will be a superposition of N _{2} = N_{τ}/N_{T}ι signals.
In the second estimation stage the remaining N _{2} superimposed signals are seperated for each of the Nχ_{\} signals of the first estimation stage, together with channel estimation in the second dimension, to yield the estimate of the frequency response H ..
Fig. 7 illustrates the basic idea for type I of the proposed scheme.
It should be noted, that the buffer shown in Fig. 7 is used in order to apply smoothing type filtering in time direction. However and as outlined above, the present invention is applicable to, both, smoothing and prediction type filtering, so the buffer shown in Fig. 7 is optional and depends on the particular channel estimation algorithm being used.
Fig. 8 and 9 show pilot sequence designs which may be used to support the two stage approach for OFDMbased MLMO channel estimation accordance to the present invention. Here, the pilot grid shown in Fig. 9 corresponds to the DVBT pilot grid according to ETSI EN 300 744, V 1.4.1 (200101). Further standards  however, not to be considered as restricting scope of protection  would be IEEE 802.1 la or ETSI TS 101 475 HIPERLAN/2.
In a more genral sense, in order to extend the pilot sequence design for an OFDMbased system with multiple transmit antennas, according to a preferred embodiment of the present invention the pilot sequence of transmit antenna μ is defined by {Xf!}.
It is proposed to choose a pilot sequences that can be expressed in the product form
Xg = Xj • ^{>} , μ = μ_{2} + N_{T2}  (_{μι}  l) , μ_{x} = {1, • ^{•} • , N_{Tl}} μ2 = {!, ^{• • •} , N_{T2}}
1 < » < N , 1 < £ < Ng
(12) where X[^{μι)} and X are the pilot symbols for the first and second stage, respectively.
It should be noted that the pilot symbol of the first stage X[^{μ}° only depends on the subcarrier index i, while the pilot symbol of the second stage X_{2}.^{2)} only depends on OFDM symbol I.
This notation implies that {X^ } is identical for all OFDM symbols, indepen tent of £. Correspondingly, the sequence {X_{2}^} which accounts for the pilots of one subcarrier, is also independent of the subcarrier index i.
Preferably, the pilot sequences {X^^{1} } and {X_{2}.^{2)}} are chosen from orthogonal designs, e.g., Walsh sequences or phase shifted sequences.
Substituting the proposed 2D pilot sequence of (12) into the received pilots in (11), the following is obtained
where H Li is the frequency response of transmit antenna μ.
Further, the received pilot sequence of subset A_{μι} is given by
Z^{l}^{μ} = + ^{N} _{T2}  ^{(}Mi  1^{))}
In view of the above, the task of the first estimation stage is to estimate ^°; that is to separate the Nyi groups, and then to estimate and interpolate the channel in frequency direction.
It should be noted that the pilot sequence X_{2}t^{2)} is constant with respect to the subcarrier index i. This means that Z  is a superposition of N _{2} waveforms H multiplied with a constant phase term X_{2} ^{μ}A
Further, the outputs of the first estimation stage are subsequently used as inputs for the second estimation stage shown 7.
As shown in Fig. 7, in the second estimation stage the channel is estimated in time direction to separate the remaining N_{?2} signals per subset to yield the estimate of the frequency response H l
Using this framework, according to the present invention it is ϋroposed to apply available one dimensional schemes for OFDMbased MLMO systems to perform channel estimation.
2 x IDPACE type II
Fig. 10 shows a schematic diagram of a channel estimator for estimating multiple input multiple output transmission channels of multicarrier communication systems according to the present invention, wherein channel estimation is performed in time direction first.
As shown in Fig. 10, the major difference of 2 x IDPACE type II over 2 x ID PACE type I is that that the separation JVπ subsets in the first estimation stage is performed in conjunction with channel estimation in time direction. This yields for the pilot symbols of 2 x IDPACE type II:
Xg = X[f ^{■} _{2} , μ = μ_{2} + N_{T2} ^{■} ( _{l}  1) , μ_{x} = {1, ^{• • •} , N_{τι}} μ_{2} = {!, ^{■ ■ ■} , N_{T2}}
1 < i ≤ N_{P} , l ≤ i^{'} ≤ Ng
(15) From the above, it may be seen that the pilot sequences are very similar to 2 x IDPACE type I in equation (12), the only difference is that the subcarrier index i and the OFDM symbol index I are exchanged. Substituting the proposed 2D pilot sequence of equation (15) into the received pilots in equation (11), the received pilot sequence can be represented according to
zi^{μι}
where again the subcarrier index i and the OFDM symbol index £ are exchanged with respect to (13).
This allows the separation of the Nj subsets in time direction. The received pilot sequence of subset A_{μx} is defined by
Z^{iμi)} = \ ^{^} Ϋ^' T ^{2} + ^{N}T2 ' ^{(} l  ^{1))} (17)
In view of he above and as shown in Fig. 10, the task of the first estiamtion stage is to estimate Z^ that is to separate the N ι groups, and then to estimate and interpolate the channel in time direction, i.e. over the £ variable.
As shown in Fig. 10, if smoothing type filtering is used, A£D_{t} OFDM symbols need to be buffered in order to estimate Z^{iμ}°. For the second estimation stage it is proposed estimate the channel in frequency direction to separate the remaining N _{2} signals per subset.
Comparison between 2 x IDPACE type I and type II It can be shown that the performance of both schemes type I and type II is identical for most implementations. However, the computational complexity, in terms of number of multiplications required for channel estimation may differ. The actual computational complexity very much depends on the system parameters, the pilot grid structure and the channel estimation algorithm which is used. Furthermore, the DSP or hardware architecture may favor one scheme.
More importantly however, does the selection of a certain pilot grid rule out the implementation of a particular scheme. For the pilot grid shown in Fig. 8 and Fig. 9 both schemes type I and type II can be applied. However, this is not generally the case. In order to motivate this problem consider the following grid
4 1
G 0 3 shown in Fig. 8. For such a grid structure it is more appropriate to employ 2 x ID PACE type I, since the pilots in frequency direction are placed along a line. On the other hand, successive pilots in time direction are shifted one subcarrier apart, which makes it difficult to employ 2 x IDPACE type II.
Accordingly, choosing the grid shown in Fig. 9, which is described by
to employ 2 x IDPACE type II is more appropriate. The grid according to Fig. 9 has been chosen for the DVBT standard, so for DVBT channel estimation according to a preferred embodiment of the present invention in time direction should be performed first if 2 x IDPACE is to be used.
Applications of 2 x IDPACE type I
To describe pilot symbolassisted channel estimation according to the present invention it is proposed to define a subset of the received signal sequence containing
rate % = \ i/Df\ in frequency direction, and at a D_{t} times lower rate £ = [£/D_{t}\ in time direction, respectively.In the following two channel estimation techniques are described for 2 x ID PACE type I, the first is to estimate the channel in the frequency domain by Wiener filter interpolation. The second approach is to transfer the received signal into the time domain.
Frequency Domain Channel Estimation
First Stage Wiener Filtering
For 2 x IDPACE type I, the first step is to estimate the channel in the frequency direction. In vector notation, the received pilot sequence of OFDM symbol £ becomes
ΫJ =
(18) μι=ιwhere Z'_{e} ^{l} represents the received pilot sequence of subset A_{μι} whose entries are defined in equation (14).
Further, the transmitted pilot sequence, the received pilot sequence of subset A_{μι}, and the additive noise term, of OFDM symbol £ transmitted from antenna μ are given by
X ^{1}' = diag ^ ,    , ^ ) € C^{NpχN}r
NJ = Nt,ι,    , N_{itNp}> ^{τ} g c^^{xl} Further, according to the present invention channel estimation in the frequency domain is preferably performed with an FIR interpolation filter, which can be expressed for the first stage in frequency direction
= W^{, ,l)}[i] Ϋ£ (19)
It should be noted that in general, the filter W ^{(μι,}[i] depends on the location of the desired symbol, i.e. the subcarrier index i. This means that not only for every transmit antenna but also for every subcarrier a different filter is required.
The optimum approach to estimate Z ° is to use a Wiener interpolation filter for W'^{Cμι)}[i]. A Wiener filter minimizes the means squard error MSE between the pilots sequence and the desired response. It is also known as the minimum MSE or equivalently MMSE estimator.
Further, in order to generate a Wiener filter knowledge about the channel statistics are required, which are described by the covariance matrix. The covariance matrix of the pilots in frequency direction is defined by R^._{γ} = E Y_{j}' Y^ ]. The entry of the ^{th} row and n^{th} column of the covariance matrix is given by
{^{R}Ϋγ}m,„ = ^{E} Y t—,in Y ^{x} l,im E
Y i_{Dfm} {*, *} € ≤!(20)Further, define the cross correlation vector between the frequency response of the desired sample Z ^ and the pilots Ϋ'. The m^{th} entry of the cross correlation vector B/Jitø] = E[Z[f Ϋ' "} can be expressed as
{R^[i]}_{m} = E 2 ^{μ} y*. tsfl—m = E l,i m)D_{s} ^{~}i = [i/D \ (21)
The quantities according to equation (20) and equation (21) are necessary to evaluate the Wiener interpolation filter. The optimum solution in the MMSE sense may be determined using the WienerHopf according to
Second Stage Wiener Filtering
In view ofthe above, performing equation (19) for the N_{T\} subsets and for each sucarrier is processed further in the second stage. Here, filtering and interpolation in time direction yields the frequency response estimate which is achieved in the form
N', = ∑>f tø ^{M}) ' > μ = 1*2 + N_{T2} ^{■} ( ι  1)  {i, ^{• • •} , N_{T}] i=ι
(23)
where w ^{μ} [£, AE] represents the FIR interpolation filter of the second stage of. OFDM symbol £ with filter delay A£ = D_{t}A£.
A positive A£ imposes a time delay of AE symbols at the receiver output. Then the estimation filter is a smoothing type filter. On the other hand, setting A£ = 0 specifies a linear prediction receiver without an induced time delay due to channel estimation, at the expense of a somewhat poorer estimate of the CIR.
It should be noted that the best performance is generally achieved if A£ = Np/2, i.e. the symbol to be estimated is in the middle of the pilot sequence which is used for estimation of that symbol. Therefore, for A£ = N_{p}/2 there are Np/2 future and past pilot symbols involved.
Further, in matrix notation equation (23) becomes
H  = "^{w}[t, A£] z ° μ = μ_{2} + N_{T2} . (_{μι}  l) = {!, ^{■ ■} • , N_{T}} (24) where w"^{(μ)}[^ A£] = [w ^{μ)}[£, Al], ■ ■ • , w^' ,^{iμ)}[£, A£]] is the channel estimation filter of stage two, and ZJ^{/ tμι} = [Z[^{μ}f, ■ ■ , Z ) ^ denotes the block Ng' outputs of stage one of subcarrier i.
In analogy to the first estimation stage, the optimum approach to estimate H is to use a Wiener interpolation filter for w"^{iμ)}[£, A£]. The covariance matrix ofthe first stage outputs in time direction is defined by R 'ig* = E[ z ^{μ}° z ^{μ}° ]. The entry of the ^{th} row and n^{th} column of the covariance matrix is given by
[ LR'≤ ZSZ'} J m.n = E l—m,i £—n,i (25)
Further, define the cross correlation vector between the frequency response of the desired sample Hf and the outputs of the first stage s Z"» ^{(}M^{)} . The m ,t^{m}h entry of
(Mi) ^{ff}, the cross correlation vector l\! ^{μ}~^{)} [£, A£] = E[Hfl _{tti} Z" ] can be expressed as
{ ! [l, At\}_{m} = E Hf *^{•}!l' Z —^{l} m^{)} .i . £ = [£/D_{t}] + A£ (26)
The quantities in equation (20) and equation (21) are necessary to evaluate the Wiener inteφolation filter. The optimum solution in the MMSE sense is derived using the WienerHopf equation according to
w"^{[μ)}[£, A£] = ΕL"Α A£] ■ R z^{μ}Az (27)
Time Domain Channel Estimation
Fig. 11 shows a schematic diagram of an estimator stage adapted to achieve channel estimation in the time domain according to the present invention.
As shwon in Fig. 11, an alternative approach to determine the frequency response He_{t}i according to the present invention is to estimate the channel impulse response (CIR), ti_{iιTl} ^{{μ)} in the time domain first. In terms of the CIR vector of OFDM symbol £ impinging from the μ^{th} transmit antenna,
the received pilot sequence of subset A_{βl} becomesZf ^{x)} = ∑ ^{<} F hf ' μ = μ_{2} + N_{T2} ■ (μ_{x}  1) (28) μ_{2}=l
where F denotes an N_{p}point DFT matrix defined by
0 < i < Ng l , 0 < n < Q  l (29)
It is assumed that the CIR is time limited to Q < N_{a}j samples. Strictly speaking this is only true for a sample spaced channel model explained above. For a nonsample spaced channel model where the DFT of H^ is not time limited, so oversampling is required in order to avoid aliasing. In this case, Q accounts for the number of significant taps.
Transforming Z'_{e} ^{*} into the time domain by an N_{P}point IDFT yields
N_{T2}
μ_{2}=ι
This implies that two stage channel estimation for OFDMbased MIMO systems can be employed in the time and frequency domains in the same way.
The received pilot sequency after OFDM demodulation is given by
Ϋ_{t}' = Xi Z'_{έ} + N_{έ}' = X\ F_{Nτι} z_{t}' + N_{e}' (31) where
(1) INTI)
Z , Z_{e}' _{G} (βNτιNp' X l
z', = / (!) i (W_{T} . ι.  i
F Wτι diag (F,    , F) 6 C^^{1}^^
In order to estimate z' ^{μι)} according to the present invention the received pilot sequency after OFDM demodulation is transformed into the time domain.
Further, for time domain channel estimation we choose to premultiply Ϋ by the transmitted pilot sequence X and then to transform the result into the time domain via an Nppoint IDFT, that is
H _ _ _{H} _
€ι — ( Xi FΛΓ_{T1} Y' = D Y: ς. (βNτιQxl
, H,
= O ^{■}v'^{"}Ω 'i' z' + O'^{"}N' (32)
where the definition D^ = X_{x} FJ_{VT1} has been introduced.
,^{(}μι)
In the following two basic estimator structures to determine z' according to the present invention will be described, namely the least squares LS estimator and the minimum mean squared error MMSE estimator.
Least Squares LS Estimator
Provided the the inverse of D'f D' does exists, the least squares (LS) estimator may be determined according to
Since the estimator depends on the transmitted signal, the pilot sequence should be properly chosen. The LS estimator exists if D^ is full rank, unfortunately this is not always the case. A necessary condition for the LS estimator to exist is
According to a preferred embodiment of the present invention, two times over sampling provides a good tradeoff between minimizing the system overhead due to pilots and optimizing the performance, i.e. Np « 2N_{T\} Q. It is assumed that Nor ≥ Q, ie. the guard interval is longer than the maximum delay of the channel.
Further, it should be noted that the LS estimator for more than one transmit antenna does only exist in the time domain.
Minimum Mean Squared Error MMSE Estimator
The MMSE estimator is given by an FIR filter which is for time domain channel estimation
(35)
The Wiener filter is determined by the WienerHopf equation
^[n] = R'^' • R^^{1} π = {1, • • • , N_{c}} (36)
In general, the Wiener filter w'^{iμ} [n], depends on the location of the desired symbol n. In order to generate the MMSE estimator knowledge of the correlation matrices R^ and R'^^{1 J}[ra] are required
Rξ_{ζ} = E{ _{t}?i^{H}} = Df R^D; eC^{3}^^^{1} (37)
= T
D'_{?}R _{S} Df D'_{?} + Nn D'fff D', andR' /(μ ilnl^jφ^} eC^{1} xQN_{Tl} (38)
Further, the covariance matrix of z' is denoted by R~ = {z^' g' } with dimension QN_{TX} x QN_{T\}. Furtermore, R'^'f ] is row n+ (μ_{x} 1)Q of R_{z5}. The covariance matrix in the time domain R is related to the covariance matrix in the frequency domain R^g by
Here, it is assumed that the fading of different transmit antennas is uncorrelated. It should be noted that while the LS estimator requires O'~ to be full rank, while the MMSE estimator requires invertability of R^ as seen from equation (36). For this to hold, however, ^{"}D^{1} need not to be full rank. Thus, the MMSE estimator can exist even if Np < N_{τx} Q.
For the case that D' is full rank, the inverse of Df D'~ does exist. Then the Wiener filter of equation (36) can be simplied to
w"" ] = R /'^{(}μι^{)}'r[n R4.+ (D' D'_{i})^{"} N_{0}j ^{■} (D'f Dj)
2 L^{μ}n^{ι)} = Rϊi : R_{z2}+(DfDj tμi) (40)
Further it should be noted that according to the present invention the separation of the N ι signals, which is performed by the LS estimator, can be separated from the filtering task.
As outlined above, the MMSE estimator is in general dependent on the choice of the pilot symbols. However, choosing orthogonal pilot sequences X^^{1}' the estimator becomes independent on the transmitted pilots. For orthogonal pilots where δ_{μjTn} denotes the Kronecker symbol, it can be shown
Therefore, the above LS estimator in equation (33) as well as the MMSE estimator in equation (40) can be grossly simplified, since the matrix inversion required in equation (33) and equation (40) become straightforward.
Further, it can be seen from equation (33) and equation (40) that the estimator has become independent of the chosen pilot sequence, which does significantly simplify the filter generation.
Fig. 11 shows a block diagram of channel estimation and interpolation in the time domain using orthogonal pilot sequences. First, the received pilot sequence is split into N_{rι} branches and each branch premultiplied by X_{x} ^{μι} . Then each branch of the received pilot sequence is transformed to the time domain. By means of  optional  filtering and/or windowing the channel is estimated in the time domain. Zero padding of the first stage estimate extends its lenght to N_{c} samples. The estimate of the CTF of an entire OFDM symbol (pilots and data), is obtained by an N_{c}point FFT of the CIR estimate
Z' = F,v_{T1} z' or Z'^{<μι,} = F z'^{(μι)} (41)
where Fyy_{T1} is a N_{Ti}N_{c} x NπN_{c} block diagonal matrix, consisting of Nπ blocks of N_{c} point DFT matrices F.
As shown in Fig. 11, the output of the first stage Z' ' can be fed to the second stage estimator in equation (23).
Alternatively, z'^{(μι)} may be fed into (23) to yield the CIR estimate h j which is then transformed into the frequency domain with N_{Tl} FFTs. Moreover, channel estimation of the second stage: in the Doppler domain is possible, that is Z' ^{1} or z ^{(μι)} are transformed into the Doppler domain using equivalent algorithms as in the time domain.
Fig. 12 shows a schematic diagram of an estimator stage adapted to achieve channel estimation in the time domain according to the present invention.
From Fig. 12 it can be seen that the channel estimation of the second stage may also be performed with DFTinteφolation cooresponding to the first estimation stage discribed above. However, it may be computationally more efficient to perform the second estimation stage in the time domain as well, i.e., before zero padding and the N_{c}point FFT.
As shown in Fig. 12, the filtering of the second stage itself remains unaffected as the correlation function in frequency and time  i.e. the first and second dimension of transmission  are mutually independent. Therefore, of Wiener filtering is chosen for the second stagem equations (23) and (27) referred to above may still be used, the only difference being that the input becomes _{n} instead of Z_{i} ^{(} , and the output is
where n is the sample index in the time domain. After the second stage filtering each of the overall N outputs  i.e., N_{r2} outputs per subset  are transformed back into the frequency domain.Application to a Cellular System with a Frequency Reuse Factor of One
Fig. 13 shows an application of the two stage channnel estimation approach according to the present invention to a cellular communication system with a frequency reuse factor of one.
As shown in Fig. 13, instead of having an antenna array with N_{T} antenna elements, the proposed scheme can be applied to distributed antennas as well. E.g., an application is to employ 2xlDPACE to a celluar system with a frequency reuse factor of one. In a scenario where the mobile user is at the cell border, the user will receive the desired signal from one base station and one or several interfering signals from other base stations.
Further, one may assume that each base station has N_{T2} antenna elements. While the data bearing symbols can be protected against interference using a channel code or by spreading, the pilot symbols cannot be protected in this way. Accurate channel estimation, however, is most important for the system to work efficiently. One solution is to boost the pilots; this however will increase the interference to users served by other base stations, and thus limits the system capcity.
According to the present invention, 2 x IDPACE can be applied to this scenario as follows: the base stations form N ι subsets, each subset having an antenna array with N_{T2} antenna elements, to form an resulting array of N_{τ} — NrιN_{T}2 elements. This would require intercell synchronization.
Abbreviations
AWGN Additive white Gaussian noise CIR Channel impulse response CTF Channel transfer function DFT Discrete Fourier transform FFT Fast Fourier transform GI Guard interval
IDFT Inverse discrete Fourier transform IFFT Inverse fast Fourier transform LS Least squares MIMO Multiple input multiple output, generally a system having several transmit and receive antennas
MMSE Minimum mean squared error
MSE Mean squared error
OFDM Orthogonal frequency division multiplexing
PACE Pilotsymbol aided channel estimation
List of Commonly Used System Parameters
NF_{FΓ} FFT length. N_{c} Number of subcarriers. N_{GI} Number of samples of the guard interval. L Number of OFDM symbols per frame. T OFDM symbol duration. T_{sp}ι Sample interval, given by T_{spi} = T/N_{F}FΎ
T_{sym} Total OFDM symbol duration including the guard interval T_{spl} — T+NGIT_{SP1}.
QQ Number of nonzero channel taps. Q Total number of channel taps. NR Number of receive antennas. NT Number of transmit antennas.
Nτι Number of subsets. Nτ_{2} Number of transmit antennas within one subset. Np Number of pilots in frequency direction. Ng Number of pilots in time direction.
Np Number of total pilots used for channel estimation (Np = NpNg). D_{f} Pilot spacing in frequency. A Pilot spacing in time.
List of Commonly Used Variables
g Transmitted OFDM symbol of the μ^{th} transmit antenna of OFDM symbol £ at subcarrier i. x^{lμ} (t) Transmitted signal of the μ^{th} transmit antenna after OFDM modulation.
Y f Received OFDM symbol of the z/^{th} receive antenna of OFDM symbol t at subcarrier i. y^{iμ)}(t) Received signal of the ^{th} receive antenna at time t before OFDM demodulation.
H ^{μ}(^{v)} Channel transfer function (CTF) of the ^{th} receive antenna arriving from the μ ^{h} transmit antenna of OFDM symbol £ at subcarrier i. h^{μ}' ^{u)}(t) Channel impulse response (CIR) of the ^{th} receive antenna arriving from the μ^{th} transmit antenna. hf_{n} * Sampled CIR of the ^{th} receive antenna arriving from the μ^{th} transmit antenna, at the n^{th} sample of OFDM symbol £.
Ne,i Sample of AWGN with zero mean and variance No of OFDM symbol £ at subcarrier i. n(t) Realization of a AWGΝ process at time t before OFDM demodulation.
Claims
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