Method and system of cyclic prefix overhead reduction for enabling cancellation of inter-symbol and inter-carrier interferences in OFDM wireless communication networks
09780915 · 2017-10-03
Assignee
Inventors
Cpc classification
H04L5/0007
ELECTRICITY
H04W72/0453
ELECTRICITY
H04L1/0048
ELECTRICITY
H04L5/0048
ELECTRICITY
International classification
H04W4/00
ELECTRICITY
H04L1/00
ELECTRICITY
Abstract
A system and method are provided for reducing the overhead caused by the presence of the cyclic prefix while enabling inter-carrier interference (ICI) and inter-symbol interference (ISI) cancellation in an Orthogonal Frequency Division Multiplexing (OFDM) network that includes an OFDM transmitter and an OFDM receiver.
Claims
1. A method for reducing cyclic prefix overhead while enabling cancellation of inter-symbol and inter-carrier interferences in Orthogonal Frequency-Division Multiplexing (OFDM) wireless networks, wherein information in a set of time-domain complex samples is to be sent by an OFDM transmitter to an OFDM receiver through a wireless channel within a Time Transmission Interval (TTI) the TTI comprising a number N.sub.sym of OFDM symbols, the method comprising: generating, by the OFDM transmitter, a time-domain signal which comprises: a first part of the TTI for carrying time-domain complex samples (r.sub.a.sup.TTI[n]) of a first OFDM symbol (S.sub.0), where r and a are reference letters that denote part of the received signal TTI (r.sup.TTI[n]), n is a time index taking values n=0, . . . , (N.sub.sym−1).Math.N.sub.OFDM−1, and N.sub.OFDM is a natural number equal to the number of subcarriers, the first OFDM symbol (S.sub.0) being obtained in the time domain through an inverse Fourier Transform of the complex samples to be carried by a number of subcarriers in the frequency domain, the inverse Fourier Transform having a length N.sub.OFDM, the subcarriers comprising both data subcarriers and pilot subcarriers for channel estimation; a cyclic prefix (CP) carried in the first part of the TTI and appended to the beginning of the first OFDM symbol (S.sub.0), containing a replica of the last samples of the first OFDM symbol (S.sub.0), which has a length given by the largest expected delay spread of the wireless channel; Forward Error Correction encoded information bits to be transmitted, which are pseudo-random interleaved prior to a mapping of the encoded information bits to time-frequency resources; a second part of the TTI for carrying (N.sub.sym−1).Math.N.sub.OFDM time-domain complex samples (r.sub.b.sup.TTI[n]), where b is a reference letter that denote another part of the received signal TTI (r.sup.TTI[n]), which samples result from the mapping to time-frequency resources of a set of (N.sub.sym−1).Math.N.sub.OFDM complex subcarriers in the frequency domain corresponding to the information to be sent in the second part of the TTI, without appending any cyclic prefix, the set of (N.sub.sym−1).Math.N.sub.OFDM complex subcarriers comprising a concatenation of subcarriers corresponding to the remaining OFDM symbols (S.sub.1, . . . S.sub.Nsym−1) of the TTI, the concatenated subcarriers comprising both data subcarriers and pilot subcarriers for channel estimation, and the remaining OFDM symbols (S.sub.1, . . . S.sub.Nsym−1) being obtained in the time domain by means of an enlarged inverse Fourier Transform with length equal to the number (N.sub.sym−1).Math.N.sub.OFDM of the concatenated subcarriers; and concatenating the time-domain complex samples (r.sub.a.sup.TTI[n]) of the first part of the TTI and the time-domain complex samples (r.sub.b.sup.TTI[n]) of the second part of the TTI, to be sent by the OFDM transmitter to the OFDM receiver which performs cancellation of inter-symbol and inter-carrier interferences using the time-domain complex samples (r.sub.a.sup.TTI[n], r.sub.b.sup.TTI[n]) of the first part and the second part of the TTI.
2. The method according to claim 1, wherein pilot subcarriers in the second part of the TTI are inserted and arranged in the frequency domain to cover a whole bandwidth (BW) with a frequency separation between pilot subcarriers equal to (N.sub.sym−1) times the frequency separation between pilot subcarriers of the subcarriers in the first part of the TTI.
3. The method according to claim 2, wherein the encoded information bits to be transmitted are pseudo-random interleaved by writing input information bits to elements of a rectangular matrix by rows, and reading the output information bits by columns after reordering the columns of the matrix according to a pseudo-random pattern.
4. The method according to claim 3, further comprising reservation of guard bands in the frequency domain before and after the subcarriers corresponding to the information to be transmitted in the second part of the TTI, the guard bands comprising a number of null subcarriers equal to (N.sub.sym−1) times a number of guard subcarriers reserved in the first part of the TTI.
5. The method according to claim 4, further comprising recovering information contained in a current TTI by the OFDM receiver performing the following steps: detecting the first OFDM symbol (S.sub.0) by separating time-domain complex samples (r.sub.a.sup.TTI[n]) of the first part of the current TTI, from the appended cyclic prefix (CP) and from the remaining time-domain complex samples (r.sub.b.sup.TTI[n]) of the second part of the current TTI; estimating a carrier frequency offset, CFO, using the detected first OFDM symbol (S.sub.0) and the appended cyclic prefix (CP); compensating the CFO in both the first part and the second part of the TTI; estimating the channel frequency response (H[f]) in the detected first OFDM symbol (S.sub.0); recovering information in the detected first OFDM symbol (S.sub.0) through channel equalization and symbol decoding; reconstructing a time-domain transmitted signal s.sub.a.sup.TTI[n] corresponding to the detected first OFDM symbol (S.sub.0) by applying an inverse Fourier transform of the recovered information with length N.sub.OFDM; obtaining the channel impulse response, CIR, by performing an inverse Fourier Transform of the channel frequency response (H[f]) estimated in the first OFDM symbol, and identifying a number of CIR taps, the CIR being written as:
6. The method according to claim 5, wherein identifying the number of CIR taps N.sub.taps in the current TTI and the number of CIR taps N′.sub.taps of the subsequent TTI by the OFDM receiver comprises a comparison of the absolute CIR amplitude with a threshold to discard radio channel components being below the threshold.
7. The method according to claim 6, wherein the OFDM wireless network is a Long Term Evolution wireless network.
8. The method according to claim 2, further comprising reservation of guard bands in the frequency domain before and after the subcarriers corresponding to the information to be transmitted in the second part of the TTI, the guard bands comprising a number of null subcarriers equal to (N.sub.sym−1) times a number of guard subcarriers reserved in the first part of the TTI.
9. The method according to claim 1, wherein the encoded information bits to be transmitted are pseudo-random interleaved by writing input information bits to elements of a rectangular matrix by rows, and reading the output information bits by columns after reordering the columns of the matrix according to a pseudo-random pattern.
10. The method according to claim 1, further comprising reservation of guard bands in the frequency domain before and after the subcarriers corresponding to the information to be transmitted in the second part of the TTI, the guard bands comprising a number of null subcarriers equal to (N.sub.sym−1) times a number of guard subcarriers reserved in the first part of the TTI.
11. The method according to claim 1, further comprising recovering information contained in a current TTI by the OFDM receiver performing the following steps: detecting the first OFDM symbol (S.sub.0) by separating time-domain complex samples (r.sub.a.sup.TTI[n]) of the first part of the current TTI, from the appended cyclic prefix (CP) and from the remaining time-domain complex samples (r.sub.b.sup.TTI[n]) of the second part of the current TTI; estimating a carrier frequency offset, CFO, using the detected first OFDM symbol (S.sub.0) and the appended cyclic prefix (CP); compensating the CFO in both the first part and the second part of the TTI; estimating the channel frequency response (H[f]) in the detected first OFDM symbol (S.sub.0); recovering information in the detected first OFDM symbol (S.sub.0) through channel equalization and symbol decoding; reconstructing a time-domain transmitted signal s.sub.a.sup.TTI[n] corresponding to the detected first OFDM symbol (S.sub.0) by applying an inverse Fourier transform of the recovered information with length N.sub.OFDM; obtaining the channel impulse response, CIR, by performing an inverse Fourier Transform of the channel frequency response (H[f]) estimated in the first OFDM symbol, and identifying a number of CIR taps, the CIR being written as:
12. The method according to claim 11, wherein identifying the number of CIR taps N.sub.taps in the current TTI and the number of CIR taps N′.sub.taps of the subsequent TTI by the OFDM receiver comprises a comparison of the absolute CIR amplitude with a threshold to discard radio channel components being below the threshold.
13. The method according to claim 1, wherein the OFDM wireless network is a Long Term Evolution wireless network.
14. An Orthogonal Frequency-Division Multiplexing (OFDM) transmitter for reducing cyclic prefix overhead while enabling inter-symbol and inter-carrier interferences cancellation at an OFDM receiver to which the OFDM transmitter sends information within a Time Transmission Interval (TTI) in a set of time-domain complex samples through a wireless channel of an OFDM wireless network, the TTI comprising a number N.sub.sym of OFDM symbols, the OFDM transmitter comprising: a generator of a time-domain signal for generating the time-domain signal comprising a first part of the TTI for carrying time-domain complex samples (r.sub.a.sup.TTI[n]) of a first OFDM symbol (S.sub.0) and a second part of the TTI for carrying (N.sub.sym−1).Math.N.sub.OFDM time-domain complex samples (r.sub.b.sup.TTI[n]), where r, a and b are reference letters that denote parts of the received signal TTI (r.sup.TTI [n]), n is a time index taking values n=0, . . . , (N.sub.sym−1).Math.N.sub.OFDM−1, and N.sub.OFDM is a natural number equal to the number of subcarriers; an inverse Fourier Transform performer applied to the complex samples to be carried by a number of subcarriers in the frequency domain for obtaining the first OFDM symbol (S.sub.0) in the time domain, the inverse Fourier Transform having a length N.sub.OFDM, the subcarriers comprising both data subcarriers and pilot subcarriers for channel estimation; a cyclic prefix (CP) adder for appending the cyclic prefix (CP) with a length given by the largest expected delay spread of the wireless channel to the beginning of the first OFDM symbol (S.sub.0), to be carried in the first part of the TTI containing a replica of the last samples of said first OFDM symbol (S.sub.0); a Forward Error Correction encoder for encoding information bits to be transmitted; a pseudo-random interleaver for interleaving the encoded information prior to a mapping of the encoded information bits to time-frequency resources; means for mapping the second part of the TTI to time-frequency resources to obtain a set of (N.sub.sym−1).Math.N.sub.OFDM complex subcarriers in the frequency domain, without appending any cyclic prefix, the set of (N.sub.sym−1).Math.N.sub.OFDM complex subcarriers comprising a concatenation of subcarriers corresponding to the remaining OFDM symbols (S.sub.1, . . . S.sub.Nsym−1) of the TTI, the concatenated subcarriers comprising both data subcarriers and pilot subcarriers for channel estimation; an enlarged inverse Fourier Transform with length equal to the number (N.sub.sym−1).Math.N.sub.OFDM of the concatenated subcarriers for obtaining the remaining OFDM symbols (S.sub.1, . . . S.sub.Nsym−1) in the time domain; and a concatenator for concatenating the time-domain complex samples (r.sub.a.sup.TTI[n]) of the first part of the TTI and the time-domain complex samples (r.sub.b.sup.TTI[n]) of the second part of the TTI, to be sent by the OFDM transmitter to the OFDM receiver which performs cancellation of inter-symbol and inter-carrier interferences using said time-domain complex samples (r.sub.a.sup.TTI[n], r.sub.b.sup.TTI[n]).
15. The OFDM transmitter according to claim 14, further comprising a pilot subcarriers insertion means for inserting pilot subcarriers in the second part of the TTI which are arranged in the frequency domain to cover a whole bandwidth (BW) with a frequency separation between pilot subcarriers equal to (N.sub.sym−1) times the frequency separation between pilot subcarriers of the subcarriers in the first part of the TTI.
16. An Orthogonal Frequency-Division Multiplexing (OFDM) receiver for cancelling inter-symbol and inter-carrier interferences in OFDM networks, which receives time-domain complex samples (r.sub.a.sup.TTI[n]) in a first part of a current Time Transmission Interval (TTI) and remaining time-domain complex samples (r.sub.b.sup.TTI[n]), where r, a and b are reference letters that denote parts of a received signal TTI (r.sup.TTI[n]), n is a time index taking values n=0, . . . , (N.sub.sym−1).Math.N.sub.OFDM−1, and N.sub.OFDM is a natural number equal to the number of subcarriers, the remaining time-domain complex samples (r.sub.b.sup.TTI[n]) in a second part of the current TTI, the OFDM receiver comprising: a symbol detector for detecting a first OFDM symbol (S.sub.0) in the first part of the current TTI by separating time-domain complex samples (r.sub.a.sup.TTI[n]) of the first part of the current TTI, from a cyclic prefix (CP) appended to the beginning of the time-domain complex samples (r.sub.a.sup.TTI[n]) and from the remaining time-domain complex samples (r.sub.b.sup.TTI[n]) of the second part of the current TTI; a carrier frequency offset estimator for estimating the carrier frequency offset, CFO, by using the detected first OFDM symbol (S.sub.0) and the appended cyclic prefix (CP); a carrier frequency offset corrector for compensating the CFO in both the first part and the second part of the TTI; a channel frequency response estimator for estimating the channel frequency response (H[f]) in the detected first OFDM symbol (S.sub.0); a channel equalizer and symbol decoder for recovering information in the detected first OFDM symbol (S.sub.0); an inverse Fourier transform with length N.sub.OFDM for reconstructing a time-domain transmitted signal s.sub.a.sup.TTI[n] corresponding to the detected first OFDM symbol (S.sub.0); a channel impulse response estimator for estimating the channel impulse response, CIR, by performing an inverse Fourier Transform of the channel frequency response (H[f]) estimated in the first OFDM symbol, and identifying a number of CIR taps, the CIR being written as
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) For the purpose of aiding the understanding of the characteristics of the invention, according to a preferred practical embodiment thereof and in order to complement this description, the following figures are attached as an integral part thereof, having an illustrative and non-limiting character:
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DESCRIPTION OF THE PREFERRED EMBODIMENTS
(13) The matters defined in this detailed description are provided to assist in a comprehensive understanding of the invention. Accordingly, those of ordinary skill in the art will recognize that variation changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the invention. Also, description of well-known functions and elements are omitted for clarity and conciseness.
(14) Of course, the embodiments of the invention can be implemented in a variety of architectural platforms, operating and server systems, devices, systems, or applications. Any particular architectural layout or implementation presented herein is provided for purposes of illustration and comprehension only and is not intended to limit aspects of the invention.
(15) It is within this context, that various embodiments of the invention are now presented with reference to the
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(18) The cyclic prefix CP introduces a loss in efficiency that can be quantified by the expression:
(19)
where η is the loss in efficiency, N.sub.CP is the length of the cyclic prefix CP and N.sub.OFDM is the length of the useful part UP.sub.1 of the first symbol S.sub.0, i.e., the OFDM symbol length excluding the CP length, (both N.sub.CP and N.sub.OFDM given as a number of samples). This loss in efficiency directly translates into a loss in throughput compared to the Shannon bound.
(20) The second and subsequent symbols in the remaining part 202 of the TTI have no appended CP, therefore reducing the loss in efficiency to:
(21)
where η′ is the efficiency loss after application of the proposed invention and N.sub.sym is the number of OFDM symbols in the TTI.
(22) The way for transforming the OFDM subcarriers 30, 30′ in frequency-domain (f) into time-domain (t) samples, in order to obtain the proposed frame structure 300 is depicted in
(23)
(24) The first symbol S.sub.0 contains a regular CP with a length N.sub.CP given by the maximum delay spread supported by the OFDM system, thus avoiding ISI and ICI. The remaining part 302 of the TTI however lacks from any CP in order to increase efficiency, and transmission and reception procedures must be changed for this remaining part 302 in order to overcome the resulting ISI and ICI.
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(26) It is to note that this way of translating information from the frequency domain f to the time domain t is completely different than in prior art techniques. Concatenation of the subcarrier amplitudes in the second part 402 of the TTI leads to a time-domain signal which is completely different than the one obtained using standard techniques, where a cascade of inverse FFTs provides the symbols in a serial way (after inclusion of the CP). In fact, the original number of subcarriers per each OFDM symbol in prior art techniques is now replaced by a proportionally higher number of subcarriers for the remaining part of the TTI. The occupied bandwidth BW is not changed, as it comprises the same information over the same time interval, but the samples are obtained from a single IFFT of the concatenation of all the subcarriers after the first OFDM symbol, thus increasing the frequency resolution by a factor (N.sub.sym−1) compared to prior art. The main advantage of this arrangement is a more efficient way to deal with ISI and ICI, while not impacting the maximum supported CFO that is determined by the first OFDM symbol. In addition, the ISI and ICI cancellation algorithm only depends on proper channel estimation in the first OFDM symbol, thus improving reliability thanks to the preserved CP.
(27) In order to perform channel estimation over the second part of the TTI for successful decoding, pilot subcarriers must be arranged so as to cover the system bandwidth with a frequency separation given by the minimum channel coherence bandwidth to be supported (see
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(29) A fundamental difference of the proposed frame structure with respect to prior art lies in the CFO compensation capabilities. It could be argued that the proposed structure is essentially similar to having a single, longer OFDM symbol with the duration of a TTI and a cyclic prefix appended to it, thereby allowing detection of the samples with a single FFT/IFFT. However, with only one OFDM symbol in the TTI, the maximum allowed CFO would be decreased in the same way as the width of the subcarriers would do because of the longer OFDM symbol. In the proposed frame structure, the maximum supported CFO is however unchanged, as determined by the first OFDM symbol, while the second part of the TTI can effectively collect the samples from the remaining original OFDM symbols for easier ISI/ICI removal without impacting the maximum CFO. The proposed structure also has advantages in terms of an easier decoding process of the control signals in the first OFDM symbol, which is a key aspect in order to reduce battery consumption at the user device, provide robust control signaling and allow discontinuous reception (DRX). The proposed arrangement of subcarriers in the frequency domain of the second part of the TTI, as shown in
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(31) Let us denote with r.sup.TTI[n] the signal received in a given TTI received by the OFDM receiver 702, and the two parts of the received TTI are denoted as r.sub.a.sup.TTI[n] and r.sub.b.sup.TTI[n] respectively, where r.sub.a.sup.TTI[n] refers to the first OFDM symbol (excluding CP) and r.sub.b.sup.TTI[n] refers to the remaining original (N.sub.sym−1) OFDM symbols. For ease of notation, the time indices run from zero in both parts, thus:
r.sub.a.sup.TTI[n]=r.sup.TTI[n+N.sub.CP], n=0, . . . ,N.sub.OFDM−1,
r.sub.b.sup.TTI[n]=r.sup.TTI[n+N.sub.CP+N.sub.OFDM], n=0, . . . , (N.sub.sym−1).Math.N.sub.OFDM−1.
r.sub.a.sup.TTI[n] comprises the useful part of the first OFDM symbol after the CP, and
r.sub.b.sup.TTI[n] comprises the remaining samples of the TTI (beginning with index zero).
(32) From the first part r.sub.a.sup.TTI[n], it is possible to detect the transmitted information through standard OFDM detection techniques, including estimation of the channel frequency response H[f], shown in
(33) The remaining part r.sub.b.sup.TTI[n] of samples in the TTI suffers from ISI and ICI due to the absence of cyclic prefix. At the OFDM receiver 702, an objective is to effectively remove ISI and ICI according to the procedure explained below.
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(35) After identification of the most significant or strongest taps, the CIR in the first OFDM symbol can be written in the form:
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where N.sub.taps is the number of significant taps, a.sub.j is the complex amplitude of the j-th tap, τ.sub.j is the delay associated to the j-th tap, and δ(•) represents the discrete delta function.
(37) The ISI component towards the second (remaining) part r.sub.b.sup.TTI[n] of the TTI can then be written in the form:
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where n is the time index, τ.sub.max is the maximum value of the channel delays, and {tilde over (s)}.sub.a.sup.TTI[n] is equal to s.sub.a.sup.TTI[n] for 0≦n<N.sub.OFDM and zero outside:
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(40) The ISI component can be subtracted from r.sub.b.sup.TTI[n], thus yielding the signal r.sub.b,ISI.sup.TTI[n] with ideally no ISI from the first OFDM symbol:
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where the index n in this equation can take the values n=0, . . . , (N.sub.sym−1).Math.N.sub.OFDM−1. r.sub.b,ISI.sup.TTI[n] will thus be a “cleaned” version of the second part r.sub.b.sup.TTI[n] of the TTI after ISI removal.
(42) Prior to performing frequency-domain equalization, it is also necessary to restore the cyclicity of the OFDM signal, i.e. to cancel ICI. Cyclicity is lost because, as a consequence of the multipath components, the delayed replicas of the signal do not appear as cyclic shifts (as would happen with a proper CP). The OFDM samples which are “lost” to the right of the TTI are then introduced to the left as in a circular shift register, after being affected by the complex amplitudes and delays of the multipath components.
(43) The samples to be reconstructed are in principle unknown, but they can be found in the form of ISI towards the first OFDM symbol of the next TTI. This ISI component can in turn be obtained by subtracting the delayed replicas of the reconstructed cyclic prefix from the beginning of the first symbol in the next TTI. Denoting with r.sub.a.sup.TTI+1[n] the received signal of the first symbol in the next TTI, and s.sub.a.sup.TTI+1[n] the corresponding reconstructed samples in the time-domain after equalization, demodulation and inverse FFT, we have:
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where ISI.sup.TTI+1[n] represents the ISI component from the current TTI that extends towards the first symbol of the next TTI; N′.sub.taps, a′.sub.j and τ′.sub.j refer to the channel tap components estimated in the first OFDM symbol of the next TTI; and:
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(46) The equation exploits the fact that the CP is present at the end of the reconstructed first OFDM symbol, which can therefore be subtracted from the received signal in order to obtain the ISI term. This component is exactly the same term that is added to the beginning of the second part r.sub.b.sup.TTI[n] of the current TTI in order to remove ICI. Denoting with r.sub.b,ISI,ICI.sup.TTI[n] the received second part of the TTI after removing the ISI and ICI components, we can write:
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(48) for n=0, . . . , (N.sub.sym−1).Math.N.sub.OFDM−1.
(49) The resulting signal in the second part r.sub.b.sup.TTI[n] of the TTI ideally has no ISI and ICI from the absence of the CP. The only requirement is that the receiver additionally decodes the first OFDM symbol of the TTI next to the one to be detected. However, this is not a major problem as receivers usually have to decode that first symbol except in DRX mode, in order to obtain important control information such as scheduling and paging.
(50) In contrast to prior art techniques, the algorithm does not operate over each of the OFDM symbols for ICI cancellation, but rather cancels ICI over the whole remaining part of the TTI after the first symbol thus leading to significantly lower complexity. In addition it does not rely on complex iterative methods that can suffer from chained estimation errors. The first OFDM symbol can be estimated with very low error probability given that it is usually QPSK-modulated for robust detection, which improves reliability of the ISI and ICI cancellation algorithm.
(51) Channel estimation in the second part r.sub.b.sup.TTI[n] of the current TTI can then be performed with the aid of the pilot subcarriers PS, arranged as in
(52) An added advantage of the proposed invention is that the ISI and ICI cancellation algorithm only relies on accurate channel estimation in the first OFDM symbol of both the current and the next TTIs, which can be performed almost ideally with the aid of the CP.
(53) After ISI and ICI cancellation, the second part r.sub.b.sup.TTI[n] of the TTI can be detected by means of an FFT of length (N.sub.sym−1).Math.N.sub.OFDM, followed by standard channel equalization and demodulation according to prior art techniques. It is assumed that the channel frequency response remains valid over the whole second part r.sub.b.sup.TTI[n] of the TTI (as there is only one set of pilot subcarriers PS for channel estimation), that is, the channel coherence time is greater than the duration of the second part r.sub.b.sup.TTI[n] of the TTI.
(54) The main fundamental difference of this procedure with respect to prior art techniques is that it can be applied over the whole second part r.sub.b.sup.TTI[n] of the TTI after the first OFDM symbol, instead of having to cancel ISI and ICI successively for each of the symbols. The ICI cancellation procedure particularly benefits from this, as it comprises a relatively complex iterative algorithm. Arranging the information after the first symbol with a longer FFT allows for easier ISI and ICI cancellation, while at the same time retaining the desirable properties of CFO robustness and channel estimation thanks to the presence of the first OFDM symbol. At the same time, the proposed ISI and ICI cancellation procedure relies on reconstruction of the first OFDM symbol of both the current and the next TTI, which by definition are ISI- and ICI-free.
(55) The maximum supported CFO is not changed with respect to prior art solutions as the first symbol allows for estimation of the CFO up to half the subcarrier width. This can be exploited for CFO compensation in the whole TTI in spite of the higher FFT length required for the second part of the TTI, which gives rise to narrower subcarriers.
(56) Applicability of this algorithm relies on the invariance of the channel impulse response along the second part r.sub.b.sup.TTI[n] of the TTI. The channel coherence time T.sub.c should be higher than the duration of the second part r.sub.b.sup.TTI[n] of the TTI according to the formula:
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where f.sub.d is the Doppler frequency, c is the speed of light, v is the speed of the user and f.sub.c is the carrier frequency. Comparison of T.sub.c with the duration of the second part of the TTI would yield a maximum practical limit for user speed. If the second part r.sub.b.sup.TTI[n] is small enough (in order to keep the end-to-end latency of the system at a low value), then this assumption is also valid for a significant range of user speeds.
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(61) The proposed embodiments can be implemented as a collection of software elements, hardware elements, firmware elements, or any suitable combination of them.
(62) Note that in this text, the term “comprises” and its derivations (such as “comprising”, etc.) should not be understood in an excluding sense, that is, these terms should not be interpreted as excluding the possibility that what is described and defined may include further elements, steps, etc.
(63) Changes and modifications to the specifically described embodiments may be carried out without departing from the principles of the present invention, which is intended to be limited only by the scope of the appended claims as interpreted according to the principles of patent law including the doctrine of equivalents.