GB2425024A - Generation of a training sequence in the time domain - Google Patents

Abstract

A signal is adapted for channel estimation of channels associated with a transmission by the inclusion of training sequence data in the signal. The generation of the signal includes the steps of: selecting a training-sequence length, and deriving the training-sequence data in the time domain by numerical optimisation of any one of the channel estimate mean squared error, and the peak to average power ratio of the training sequence. The numerical estimation may be performed by a gradient descent method such as an interior point method, a primal dual method, or a barrier method. Use of the system is particularly envisaged for channel estimation in communication systems using frequency domain equalisation, such as orthogonal frequency division multiplexing (OFDM) and single-carrier frequency domain equalised (SC-FDE) systems.

Description

TRANSMISSION SIGNALS, METHODS AND APPARATUS This invention relates to

apparatus, methods, processor control code and signals for channel estimation in communication systems utilising frequency domain equalisation, such as orthogonal frequency division multiplexing (OFDM) and single-carrier frequency domain equalised (SC-FDE) systems.

The current generation of high data rate wireless local area network (WLAN) standards, such as Hiperlanl2 and IEEE8O2. 11 a and g, provide data rates of up to 54 Mbit/s.

However, the ever increasing demand for even higher data rate services, such as Internet, video and multi-media, have created a need for improved bandwidth efficiency from next generation wireless LANs. The current IEEE8O2.lla standard employs the bandwidth efficient scheme of Orthogonal Frequency Division Multiplex (OFDM) and adaptive modulation and demodulation. The systems were designed as single-input single-output (SISO) systems, essentially employing a single transmit and receive antenna at each end of the link. However within ETSI BRAN some provision for multiple antennas or sectorised antennas has been investigated for improved diversity gain and thus link robustness.

Hiperlanl2 is a European standard for a 54Mbps wireless network with security features, operating in the 5GHz band. IEEE 802.11 and, in particular, IEEE 802.11 a, is a US standard defining a different networking architecture, but also using the 5GHz band and providing data rates of up to 54Mbps. The Hiperlan (High Performance Radio Local Area Network) type 2 standard is defined by a Data Link Control (DLC) Layer comprising basic data transport functions and a Radio Link Control (RLC) sublayer, a Packet based Convergence Layer comprising a common part definition and an Ethernet Service Specific Convergence Sublayer, a physical layer definition and a network management definition.

A typical wireless LAN (Local Area Network) based on the Hiperlanl2 system.

comprises a plurality of mobile terminals (MT) each in radio communication with an access point (AP) or base station of the network. The access points are also in communication with a central controller (CC) which in turn may have a link to other networks, for example a fixed Ethernet-type local area network. In some instances, for example in a Hiperlanl2 network where there is no local access point, one of the mobile terminals may take the role of an access point/central controller to allow a direct MT to MT link. However in this specification references to "mobile terminal" and "access point" should not be taken to imply any limitation to the Hiperlan/2 system or to any particular form of access point (or base station) or mobile terminal.

Orthogonal frequency division multiplexing is a well-known technique for transmitting high bit rate digital data signals. Rather than modulate a single carrier with the high speed data, the data is divided into a number of lower data rate channels each of which is transmitted on a separate subcarrier. In this way the effect of multipath fading is mitigated. In an OFDM signal the separate subcarriers are spaced so that they overlap, as shown for subcarriers 12 in spectrum 10 of Figure 1 a. The subcarrier frequencies are chosen so that the subcarriers are mutually orthogonal, so that the separate signals modulated onto the subcarriers can be recovered at the receiver. One OFDM symbol is defined by a set of symbols, one modulated onto each subcarrier (and therefore corresponds to a plurality of data bits). The subcarriers are orthogonal if they are spaced apart in frequency by an interval of I IT, where T is the OFDM symbol period.

An OFDM symbol can be obtained by performing an inverse Fourier transform, preferably an Inverse Fast Fourier Transform (IFFT), on a set of input symbols. The input symbols can be recovered by performing a Fourier transform, preferably a fast Fourier transform (FFT), on the OFDM symbol. The FFT effectively multiplies the OFDM symbol by each subcarrier and integrates over the symbol period T. it can be seen that for a given subcarrier only one subcarrier from the OFDM symbol is extracted by this procedure, as the overlap with the other subcarriers of the OFDM symbol will average to zero over the integration period T. Often the subcarriers are modulated by QAM (Quadrature Amplitude Modulation) symbols, but other forms of modulation such as Phase Shift Keying (PSK) or Pulse Amplitude Modulation (PAM) can also be used. To reduce the effects of multipath OFDM symbols are normally extended by a guard period at the start of each symbol.

Provided that the relative delay of two multipath components is smaller than this guard time interval there is no inter-symbol interference (IS I) , at least to a first approximation.

Figure lb shows a simplified architecture for an OFDM system 180 and SCFDE system 190. In the OFDM system, data 181 is provided in the frequency domain to an inverse Fourier transform 182, which generates a time sequence. This time sequence has a guard interval 183 added to it. The resulting signal is transmitted over a broadband channel 184, which results in the addition of noise 185. Upon reception, the guard interval is removed 186 and the signal converted back to the frequency domain by an FFT 187. Equalisation is performed in the frequency domain 188, and the data symbols 189 recovered.

The SC-FDE system 190 can be thought of as a version of the OFDM system 180 where the IFFT stage has been moved from the transmitter to the receiver. This difference allows symbol definition in the time domain rather than the frequency domain, while the remainder of the system is essentially the same. Data 191, in the form of a time sequence, has a guard interval 192 added to it. The resulting signal is transmitted over a broadband channel 193, which results in the addition of noise 194. Upon reception, the guard interval is removed 195 and the signal converted into the frequency domain by an FFT 196. Equalisation is performed in the frequency domain 197, before an IFFT 198 converts the signal back to a symbol sequence 199 in the time domain.

Consequently, both systems require an estimate of the channel conditions for each sub- channel of the frequency domain equaliser.

Providing more detail for the OFDM case, Figure 1 c shows an example of a conventional SISO (single-input, single-output) OFDM system including a transmitter (here in a mobile terminal, MT) receiver 150 (here in an access point, AP) . In the transmitter 100 a source 102 provides data to a baseband mapping unit 104, which optionally provides forward error correction coding and interleaving, and which outputs modulated symbols such as QAM symbols. The modulated symbols are provided to a multiplexer 108 which combines them with pilot symbols from a pilot symbol generator 106, which provides reference amplitudes and phases for frequency synchronisation and coherent detection in the receiver and known (pilot) data for channel estimation. The combination of blocks 110 converts the serial data stream from multiplexer 108 to a plurality of parallel, reduced data rate streams, performs an IFFT on these data streams to provide an OFDM symbol, and then converts the multiple subcarriers of this OFDM symbol to a single serial data stream. This serial (digital) data stream is then converted to an analogue time-domain signal by digital-to-analogue converter 112, up-converted by up-converter 114, and after filtering and amplification (not shown) output from an antenna 116, which may comprise an omni-directional antenna, a sectorised antenna or an array antenna with beamforming.

In more detail, a series of modulation data symbols such as QAM symbols, is arranged as a vector, optionally padded with zeros to introduce oversampling. This (column) vector is then multiplied by an inverse discrete Fourier transform (IDFT) matrix to provide an output (column) vector comprising a set of values which when passed to a digital-toanalogue converter, one at a time, will define a waveform which effectively comprises a set of orthogonal carriers modulated by the modulation symbols, this being termed an OFDM symbol. In practice (although not shown explicitly in Figure lc) a cyclic extension such as a cyclic prefix is added in the time domain, for example by copying some of the final samples of the IDFT output to the start of the OFDM symbol.

This cyclic prefix extends the OFDM symbol (the symbol may be extended at either end) to provide a guard time which effectively eliminates intersymbol interference for multipaths delays of less than this guard time. (When decoding the FFT integration time does not begin until after the cyclic prefix guard time). Windowing may also be applied (in the time domain) to reduce the power of out-of-band subcarriers.

The signal from antenna 116 of transmitter 100 is received by an antenna 152 of receiver 150 via a "channel" 118. Typically the signal arrives at antenna 152 as a plurality of multipath components, with a plurality of different amplitudes and phases, which have propagated via a plurality of different channels or paths. These multipath components combine at the receiver and interfere with one another to provide an overall channel characteristic typically having a number of deep nulls, rather like a comb, which generally change with time (particularly where the transmitter or receiver is moving). This is discussed in more detail later.

A particular problem arises where transmit diversity is employed, that is where more than one transmit antenna is used, for example in a MIMO (Multiple-Input Multiple- Output) OFDM communication system, where the "input" (to a matrix channel) is provided by a plurality of transmit antennas and the "output" (from a matrix channel) is provided by a plurality of receive antennas. In such a communication system, the signals from different transmit antennas may interfere with one another causing decoding difficulties.

The antenna 152 of receiver 150 is coupled to a down-converter 154 and to an analogue-to-digital converter 156. Blocks 158 then perform a serial-toparallel conversion, FFT, and parallel-to-serial re-conversion, providing an output to demultiplexer 160, which separates the pilot symbol signal 162 from the data symbols.

The data symbols are then demodulated and de-mapped by base-band demapping unit 164 to provide a detected data output 166. Broadly speaking the receiver 150 is a mirror image of the transmitter 100. The transmitter and receiver may be combined to form an OFDM transceiver.

OFDM techniques may be employed in a variety of applications and are used, for example, for military communication systems and high definition TV as well as Hiperlanl2 and ADSL. SC-FDE is similarly usable.

The receiver of Figure 1 c is somewhat simplified as, in practice, there is a need to synchronise the FFT window to each OFDM symbol in turn, to avoid introducing non- orthogonality and hence ISI/ICI (Inter-Symbol Interference/Inter-Carrier Interference).

This may be done by auto-correlating an OFDM symbol with the cyclic extension of the symbol in the guard period but it is generally preferable, particularly for packet data transmission, to use known OFDM symbols which the receiver can accurately identify and locate, for example using a matched filter.

Figures 2a and 2b show, respectively, a receiver front end 200 and receiver signal processing blocks 250 of a conventional Hiperlanl2 mobile terminal (MT) OFDM receiver. The receiver 250 shows some details of the analogue-to-digital conversion circuitry 252, the synchronisation, channel estimation and control circuitry 252 and the de-packetising, deinterleaving and error correcting circuitry 256.

The front end 200 comprises a receive antenna 202 coupled to an input amplifier 204 and a mixer 206, which has a second input from an IF oscillator 208 to mix the RF signal to IF. The IF signal is then provided to an automatic Automatic Gain Control (AGC) amplifier 212 via a band pass filter 210, the AGC stage being controlled by a line 226 from control circuitry 254, to optimise later signal quantisation. The output of AGC 212 provides an input to two mixers 214, 216, which are also provided with quadrature signals from an oscillator 220 and splitter 218 to generate quadrature I and Q signals 222, 224. These I and Q signals are then over-sampled, filtered and decimated by analogue-to-digital circuitry 252. The over-sampling of the signal aids the digital filtering, after which the signal is rate reduced to the desired sample rate.

In Figure ic and 2b, FFT and IFFT operations may be implemented at least partially in software, as schematically illustrated by Flash RAM 262, for example using one or more digital signal processors (DSPs) and/or one or more ASICs or FPGAs. The exact point at which the signal is digitised in a software radio will generally depend upon a cost/complexity/power consumption trade-off, as well as upon the availability of suitable high speed analogue/digital converters and processor.

A known symbol, for example in preamble data or one or more pilot signals may be used for channel estimation, to compensate for the effects of a transmission channel.

Figure 2c shows a block diagram illustrating the basic concept of one type of channel estimation procedure 270. Embodiments of the invention to be described later preferably use a Least Squares (LS) technique but may use other conventional channel estimation techniques, for example Maximum Likelihood Sequence Estimation (MLSE) in which a most probable received sequence is chosen from a set of all possible received sequences, although the solution may be less optimal than with a Least Squares channel estimator. The procedure shown in Figure 2c aims to modify the coefficients of an adaptive digital filter, labelled as "channel estimate" 278 in Figure 2c, so that the behaviour of the filter matches, as closely as possible, the behaviour of a transmission channel 274 being modelled.

A known training signal 272 is applied both to the transmission channel 274 to be modelled and to the adaptive filter 278 providing the channel estimate. The received version of the training signal corresponds to the output 276 from channel 274 and reflects the impulse response of the channel 204. The output 280 from channel estimate adaptive filter 278 comprises the estimated response of the channel, and this is subtracted from the actual response in subtracter 282 to create an error signal 284 which is fed back to the adaptive channel estimate filter 278 to update the coefficients of the filter according to an adaption algorithm.

Any one of many suitable conventional algorithms may be employed, such as a Recursive Least Square (RLS) or Least Mean Square (LMS) algorithm or a variant thereof. Such algorithms will be well-known to the skilled person but, for completeness, an outline description of the LMS algorithm will also be given; reference may also be made to Lee and Messerschmitt, "Digital Communication", Kluwer Academic Publishers, 1994.

Consider an input u(n) where n labels the number or step of an input sample, buffered into an input vector u(n), a desired filter response d(n) , and a vector of estimated filter tap weights w(n). The output of the filter is given by y(n) = wH(n) u(n) where wH denotes the Hermitian conjugate of w. Then, according to the LMS algorithm, an improved weight estimation is given by w(n+l) = w(n) +u(n)[d*(n) - y*(n)] where * denotes a complex conjugate and p. is the adaption step size of the algorithm.

Convergence of the algorithm can be determined using the mean squared error, that is Id(n)-y(n) 12 which tends to a constant value or 0 as n tends to infinity. In Figure 2c the training signal 272 corresponds to u(n), the received signal 276 to d(n), and the output 280 of channel estimate adaptive filter 278 to y(n).

In the receiver 250 of Figure 2b a known preamble symbol, referred to as the "C symbol", is used to determine a channel estimate. The receiver synchronises to the received signal and switch 258 is operated to pass the received C symbol to channel estimator 260. This estimates the effect of the channel (amplitude change and phase shift of the symbols in the sub-carriers) on the known C symbol so that the effects of the channel can be compensated for, by multiplying by the reciprocal (or complex conjugate) of the channel response. Alternatively the one or more pilot signals (which also contain known symbols) can be used to determine a channel estimate. Again the phase rotation and amplitude change required to transform the received pilot into the expected symbol can be determined and applied to other received symbols. Where more than one pilot is available at more than one frequency improved channel compensation estimates can be obtained by interpolation/extrapolation to other frequencies using the different frequency pilot signals.

Figure 3 shows a plot 300 in the frequency and time domain illustrating the relative positions of preamble sequences 302, pilot signals 304, and data signals 306 for Hiperlan/2, which has 48 data sub-carriers and 4 pilots (and one unused, central carrier channel 308). As can be seen from Figure 3 the first four OFDM symbols comprise preamble data, and the pilot signals 304 continue to carry their preamble symbols.

However on the remaining (data-bearing) sub-carriers OFDM symbols 5 onwards carry data. In other OFDM schemes similar plots can be drawn, although the preamble and pilot positions may vary (for example, the pilots need not necessarily comprise continuous signals).

The skilled person will appreciate that in general in wireless LAN packet data communications systems packet lengths are short enough to assume a substantially constant channel over the duration of a packet. For this reason the preamble pilot data 302 can be used for training symbols to obtain channel estimates which may be assumed to be substantially constant until the next packet. The four continuous pilot sub-carriers may be used for frequency synchronisation. However in other types of communication system, such as digital audio or video broadcasting, other channel estimation techniques may be required. For example known pilot values for channel estimation may be inserted at intervals in both time (i.e. every few symbols) and frequency (i.e. on a subset of the subcarriers) and two-dimensional interpolation used to obtain channel estimates for the complete time and frequency space (i.e. for all the subcarriers and for successive symbols). Such interpolation techniques are well established in the art.

Until recently considerable effort was put into designing systems so as to mitigate for the perceived detrimental effects of multipath propagation, especially prevalent in indoor wireless LAN environments. However it has been recognised (see, for example, G.J. Foschini and M.J. Gans, "On limits of wireless communications in a fading environment when using multiple antennas" Wireless Personal Communications vol. 6, no.3, pp.311-335, 1998) that by utilising multiple antenna architectures at both the transmitter and receiver, so-called multiple-input multiple- output (MIMO) architectures, much increased channel capacities are possible. Attention has also turned to the use of space-time coding techniques (a generalisation of trellis coded modulation, with redundancy in the space domain) in OFDM-based systems. This is described in Y Li, N. Seshadri & S. Ariyavisitakul, "Channel Estimation for OFDM Systems with Transmitter Diversity in Mobile Wireless Channels", IEEE JSAC, Vol. 17, No. 3, 1999.

Li et al. are particularly concerned with the estimation of channel state or parameter information (CSI), typically acquired via training sequences such as the Hiperlanl2 and IEEE8O2.l la and g.

Figure 4 shows a space-time coded MIMO-OFDM communications system 400 similar to that discussed by Li et al. A block of input data 402 b[n,kJ at transmission time (or OFDM symbol or frame) n, k labelling elements of the block, is processed by a coding machine 404 which performs a space- time encoding operation. The input data may already been forward error corrected for example by a block encoder. The space-time (ST) encoder 404 provides a plurality of output signal blocks t[n,k] (Li et al consider a two transmit anteima case, i=1,2) for driving a plurality of IFFT (Inverse Fast Fourier Transform) blocks 406, which in turn drive corresponding rf stages 408 and transmit antennas 410. The IFFT blocks 406 are configured to add a cyclic prefix to the transmitted OFDM symbols, in the time domain. A plurality of pilot signals for channel estimation and frequency synchronisation and phase tracking is also inserted (not shown in Figure 4).

In the corresponding receiver a plurality of receive antennas 412 provide inputs to rf front ends 414, which in turn drive respective FFT (Fast Fourier Transform) blocks 416 each providing an input Rx[n,k], to a spacetime decoder 418. Channel information is determined from the outputs of FFT blocks 416 and from estimates of t[n,k] provided by ST encoder 421, by CSI (channel parameter estimator) block 420, and this information is provided to the decoder 418. Decoder 418 provides an output 422 comprising an estimate of the data sequence on input 402 of the transmitter.

The arrangement of Figure 4 effectively provides a set of parallel OFDM transmitters each transmitting a coded sequence of data derived from a codeword produced by the encoder 404. Broadly speaking the encoder 404 and IFFT blocks 406 of Figure 4 accept a string of length 1 of modulation symbols, as might be applied to a single OFDM transmitter, and produce a set of NT of OFDM symbols, where NT is the number of transmit antennas, each of the same length 1.

The skilled person will appreciate that although OFDM systems such as the transmitter and receiver of Figure 4 (and embodiments of the invention discussed later) are, for convenience, generally drawn in block diagram form in practice elements of these transmitters and receivers other than rf blocks 408 and 414 are likely to be implemented in software, for example on a digital signal processor, or may be specified in software by a design engineer using, for example, a hardware description language such as VHDL, the precise hardware implementation then being determined by the hardware

description language compiler.

C

As previously mentioned, channel estimation in OFDM is usually performed by transmitting known symbols. Since OFDM can be viewed as a set of parallel flat channels the received signal on each subcarrier is divided by the transmitted pilot symbol to obtain the channel. Broadly speaking, the actual value of the symbols (apart from its power) is irrelevant. The same applies for SC-FDE.

Channel parameter estimation in an OFDM system may conveniently be performed by transforming received data to the time domain, windowing the data as necessary, and then, in effect, correlating it with training data. For an SC-FDE system, the data is already in the time domain. In a MIMO OFDM or SC-FDE system with Mtransmitting antennas and a channel length of L there is a need to estimate LM parameters, but, there is also a need to avoid interference between training signals transmitted from different transmit antennas.

Techniques for channel estimation in multiple-antenna OFDM systems are described in Tai-Lai Tung, Kung Yao, R.E. Hudson, "Channel estimation and adaptive power allocation for performance and capacity improvement of multiple-antenna OFDM systems", SPA WC'Ol (Taoyuan, Taiwan), pp 82-85, Mar 2001.

Consider a training sequence of length K and a channel with an impulse response length or "span" L sample periods T where (T is the sampling interval of the system and l/T the entire channel bandwidth of the OFDM system). The channel span, in terms of time, is (L-I)T and the OFDM frame length T = (K + v) T where v is the number of cyclic prefix symbols. To avoid ISI normally v? L -1 although for the purpose of later described embodiments of the invention prior to channel estimation the length of a channel will not be known and L may therefore be assumed to be equal to the length of the cyclic prefix. In a receiver the channel is modelled as a FIR (Finite Impulse Response) filter with L taps and, again, a sampling interval T. The time domain channel impulse response from a transmit antenna, say p, to a receive antenna, say q, of a MIMO system at OFDM symbol, may be denoted h [n], or more simply h, where h = (ho hL/)', a vector of size L x 1. The corresponding frequency n response H (size K x 1) is given by H = F h where F is a K x L discrete Fourier transform (DFT) matrix of an L - point sequence producing a K - point DFT sequence.

The received signal at a receive antenna is the sum of signals from each transmit antenna, each multiplied by the channel response from the respective transmit antenna to the receive antenna. The vector H lies in an L - dimensional subspace and by projecting into it the noise in the estimate of H, can be reduced by a factor of KIL (since white noise has equal power in all dimensions).

Tung et al. (ibid) derive the condition for a training sequence in a MIMO OFDM system to be usable to determine a channel estimate (for each transmit-receive antenna channel) with a substantially minimum MSE (mean square error). It transpires that for a training sequence utilising all sub-carriers, the condition is an orthogonality condition; that is that training sequences transmitted from the transmit antennas are substantially mutually orthogonal, as defined by Equation (1) below. This also ensures that interference between training sequences transmitted from different transmit antennas is mitigated.

Equation 1 ccI, In Equation (1), L is an all zero matrix of size L x L, IL is the identity matrix of size L x L, c is an arbitrary scalar constant, and, m and n are both between 1 and M where M is the number of transmit antennas. The superscript denotes a Hermitian conjugation operation. The matrix is a diagonal matrix (that is a matrix of zeros except for the diagonal elements), the diagonal elements comprising a training sequence for antenna m, that is X(m) = diag {XhlI,..Xrnk,. . . Xmk} where Xmk is the Kth element of a training sequence of length K (although in Tung et al. k more specifically indexes OFDM subcarriers). It will be recognised that Equation (1) is a condition that the training sequences from antennas m and n are orthogonal unless m = n (a condition on training sequences prior to Fourier transformation since subcarriers are in any case mutually orthogonal in an OFDM system). Details of one least square channel estimation method for a matrix channel of a MIMO system (i.e. for multiple transmit antennas) are given in Tung et al. (see, for example, equation (7)) and hereby incorporated by reference.

Since there are LMparameters to estimate to determine a complete set of channel estimates for the matrix channel between each transmit and each receive antenna the training sequences must (each) be of length LM, that is K? LM. However the sequences which Tung et al. derive (equation (15)) require K? 2M1L to achieve a minimum MSE for the channel estimates. Thus the required sequence length (or number of subcarriers where each subcarrier carries a training sequence element) grows exponentially with the number of transmitting antennas. This was seen as a potentially severe drawback to MIMO OFDM systems with more than two transmit antennas, as in for example systems with four or eight transmit antennas.

Consequently, several training sequence design methodologies have been proposed: Larsson, E., and Li, J., in preamble design for multipleantenna OFDM-based WLANs with null subcarriers', IEEE Signal Processing Letters, Vol. 8, No. 11, Nov. 2001, propose deriving a linear sequence length relationship with respect to antenna number for training symbols on all sub-carriers by transmitting from each antenna simultaneously, but on mutually exclusive sets of frequency tones (see Figure 7b).

GB 2393618 (Toshiba), incorporated herein by reference, proposes an alternative methodology that addresses the PAPR problem whilst stillmaintaining a linear sequence relationship with antenna number. By using sequences constructed in this manner for least-squares (LS) channel estimation, the mean-square error (MSE) of the channel estimate is minimized. Significantly, in 618 the OFDM training signal is derived from substantially orthogonal training sequences of length K for each transmit antenna, wherein the training sequences are constructed to provide linear dependence upon the number of said transmit antennas.

However, all the above solutions share one feature - namely that they design the training sequence in the frequency domain. Each solution operates by modification of parameters of the OFDM sub-channels. 2)

In OFDM, the available channel bandwidth W is subdivided into N= W/4f subchannels, each having a bandwidth zlf Bandwidth zlf is sufficiently narrow that sub-channel frequency response characteristics are assumed to be close to ideal.

A sub-carrier x(t) is associated with each sub-channel, wherein typically x(t) = sin 2rf,21 for n=O, 1, ... N-i, and whereJ is the centre frequency of the sub- channel.

Orthogonality is achieved by selecting a symbol rate 1/Ton each of the sub-carriers to be equal to the separation zf of adjacent sub-channels. The sub-channels are then orthogonal as the centre frequency of each subchannel coincides with the zero points of adjacent sub-channel side lobes in frequency space.

It will be appreciated that, because i/T=zlf, for an OFDM system with N sub-channels the symbol rate on each sub-carrier is N times slower than on a single carrier system employing the full bandwidth W. This renders OFDM advantageous for high data-rate applications that are affected by multi-path time dispersion, or channel spread, such as mobile telecommunications. Channel spread is caused by the reflection of signals in the propagation environment causing multiple copies of the signal to arrive at the receiver at different times and amplitudes. For digital signals, this overlap of received bit values reduces their certainty, so increasing the bit error rate in communication. By splitting the data over N sub-channels, the symbol intervals become N times longer than for a single channel with the same data rate, as noted above. When N is sufficiently large, the symbol interval T becomes larger than the duration of channel spread, which causes significant reduction in inter- symbol interference.

The OFDM system obtains a signal from the N sub-carriers by performing an inverse discrete Fourier transform (preferably an inverse fast Fourier transform, IFFT) to generate a sequence XN. The sequence is then generally padded with a cyclic guard interval, converted to an analogue wave from, up-converted for RF frequencies and amplified for transmission, as known in the art.

An important consequence of this, however, is that the solutions described above therefore generate a training sequence whose length is equal to the number of sub- channels N. If N is large, the resulting training sequence places a considerable overhead on communications.

This problem is not restricted merely to OFDM, but also applies to other transmission systems that employ frequency-domain equalisation (FDE), such as single-carrier FDE (SC-FDE). As noted previously, SC-FDE can be thought of as an OFDM system rearranged to allow the definition of symbols in the time domain. However, the equalisation process uses the same sub-channels as those found in OFDM, and requires similar knowledge of the channel conditions via training sequences.

The problem in either case is further compounded in systems utilising multiple antennas, such as MIMO. Here, the channel conditions between each transmit and receive antenna must be estimated. The simplest means to provide training sequences in such systems involves transmitting a training sequence from one antenna at a time. This prevents the training signals from interfering with one another (see Figure 7a), but further increases the overhead as it is now both a factor of sequence length N and the number of transmit antennas M. With modern communications standards such as digital audio broadcasting (DAB) stipulating the provision of as many as N = 512 or 1024 sub-channels, this overhead and the resulting reduction of throughput and increase in delay are undesirable.

Consequently, it would be advantageous to develop a method and means by which to generate comparatively short training sequences for frequency domain equalising systems such as OFDM and SC-FDE.

Accordingly, aspects of the present invention seek to mitigate, alleviate or eliminate the above-mentioned problem.

In a first aspect of the present invention, a method of generating an training signal for transmission from an OFDM or SC-FDE transmitter using one or more of 7) transmit antennas, the training signal being operable for use in channel estimation for channels associated with said transmission by the inclusion of training sequence data in the signal from each said antenna, comprises the steps selecting a training sequence length Q, and deriving said training sequence data in the time domain by numerical optimisation of any one of the channel estimate mean squared error, and the peak to average power ratio of the training sequence.

In one configuration of the above aspect, an interior point gradient descent method is used for the numerical optimisation.

In another configuration of the above aspect, the numerical optimisation process is constrained to satisfy conditions such as mean squared channel estimation error, or the peak to average power ratio.

In another aspect of the present invention, a transmitter has one or more transmit antennas, said transmitter being configured to transmit, from each said transmit antenna, training sequence data based upon a training sequence, said training sequences upon which said training sequence data for said antennas is based being derived by numerical optimisation of a channel estimate mean squared error, or a peak to average power ratio.

In another aspect of the present invention, an OFDM transmitter is configured to transmit an OFDM signal from a plurality of transmit antennas, the OFDM transmitter comprising a data memory operable to store training sequence data for each of said plurality of antennas; an instruction memory operable to store processor implementable instructions; and a processor coupled to said data memory and to said instruction memory, operable to read and process said training sequence data in accordance with said instructions, said instructions comprising instructions for controlling the processor to read said training sequence data for each antenna; inverse Fourier transform said training sequence data for each antenna; provide a cyclic extension for said Fourier transformed data to generate output data for each antenna; and provide said output data to at least one digital-to-analogue converter for transmission; and wherein said training sequence data for said antennas is derived by numerical optimisation.

In another aspect of the present invention, an SC-FDE transmitter is configured to transmit an SC-FDE signal from a plurality of transmit antennas, the SC-FDE transmitter comprising a data memory operable to store training sequence data for each of said plurality of antennas; an instruction memory operable to store processor implementable instructions; and a processor coupled to said data memory and to said instruction memory, operable to read and process said training sequence data in accordance with said instructions, said instructions comprising instructions for controlling the processor to read said training sequence data for each antenna; provide a cyclic extension for said data to generate output data for each antenna; and provide said output data to at least one digital-to-analogue converter for transmission; and wherein said training sequence data for a said antenna is derived by numerical optimisation.

In another aspect of the present invention an signal is produced for a transmitter having a plurality of transmit antennas with training sequence data for determining a channel estimate for each of said transmit antennas, the signal being produced by inserting training sequence data for each said transmit antenna into said signal, said training sequence data being derived by numerical optimisation of a channel estimate mean squared error or a peak to average power ratio.

In a further aspect of the present invention, a data carrier carries training sequence data for each of the one or more antennas, either separately or concatenated.

In a configuration of the above aspect, the data carrier further carries processor implementable instructions for using the sequence data.

The skilled person will recognize that each training sequence is capable of providing at least one channel estimate, and possibly more than one channel estimate where more than one multipath component is associated with a channel.

The training sequence data is based upon the training sequences but may, for example, be derived from scrambled versions of the sequences. The training sequence data may be included in a signal as one or more symbols by adding a cyclic extension such as a cyclic prefix to the training sequence data. Thus the training sequence data may be effectively incorporated within symbols transmitted from each of the transmit antennas.

The invention further provides a transmitter configured to transmit the above-described signal, a data carrier (such as mentioned below) carrying the above-described training sequence data, and a receiver configured to receive the above-described signal.

The above-described training sequence data, and/or processor control code to implement the above-described transmitters and methods may be provided on a data carrier such as a disk, CD- or DVD-ROM, programmed memory such as read-only memory (Firmware), or on a data carrier such as optical or electrical signal carrier. For many applications, embodiments of the above-described transmitters, and transmitters configured to function according to the above-described methods will be implemented on a DSP (Digital Signal Processor), ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array). Thus code (and data) to implement embodiments of the invention may comprise conventional program code, or microcode or, for example, code for setting up or controlling an ASIC or FPGA. Similarly the code may comprise code for a hardware description language such as Verilog (Trade Mark) or VHDL (Very high speed integrated circuit Hardware Description Language).

As the skilled person will appreciate, such code and/or data may be distributed between a plurality of coupled components in communication with one another.

These and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures in which: Figure 1 a shows sub-carriers of an OFDM signal spectrum, with frequency on the x- axis, and an arbitrary scale on the y-axis; Figure lb shows two block diagrams illustrating the architectural relationship between OFDM and SC- FDE systems; Figure ic shows a conventional OFDM transmitter and receiver; Figures 2a to 2c show, respectively, an OFDM receiver front end, an OFDM receiver signal processor, and a conceptual illustration of a channel estimation procedure; Figure 3 shows a time and frequency domain plot of a Hiperlanl2 OFDM signal showing preamble and pilot signal positions; Figure 4 shows a known space-time coded MIMO OFDM communications system; Figure 5 shows two example Kronecker delta sequences, with sequence elements listed on the x-axis and magnitude on the y-axis.

Figure 6 is a flow diagram of a method of generating training sequences in accordance with an embodiment of the present invention.

Figures 7a and b show schematic diagrams of training signals for multiple antennas, staggered respectively in time and frequency, as known in the art.

Figure 8 shows a MIMO OFDM communications system embodying aspects of the present invention; Figure 9 shows a block diagram of a MIMO OFDM transmitter according to an embodiment of the present invention; Figure 10 shows a graph of a training sequence of length N and a short training sequence obtained in accordance with an embodiment of the present invention, with sequence length on the x-axis and sequence values on the y-axis.

Figure 11 shows a graph illustrating the frequency domain transform (Fourier transform) of the short training sequence of Figure 10 with an optimal training sequence, with frequency channels on the x-axis and target magnitude on the y-axis.

A method and apparatus for the generation and transmission of training signals is disclosed. In the following description, a number of specific details are presented in K. order to provide a thorough understanding of embodiments of the present invention. It will be apparent, however, to a person skilled in the art that these specific details need not be employed to practice the present invention.

The inventors of the present invention have appreciated that, in contrast to the present solutions for devising training sequences, a training sequence may be derived in the time domain rather than the frequency domain. In so doing, the relationship between the training sequence length and number of sub-channels N is removed, advantageously enabling the design of shorter sequences.

The ability to generate a short training sequence in the time domain that provides channel information for all N sub-channels can be demonstrated in principle, by use of a Kronecker delta sequence.

As is known in the art, time and frequency can be considered conjugate variables.

Precision in time requires uncertainty (distribution) in frequency, and vice versa. For example, an exact singular position in frequency must exist for all time, or else there will also be frequency components associated with the envelope defining the start and end of the signal. Conversely an exact, singular position in time (e.g. an infinitely short pulse or delta function) requires, through Fourier synthesis, the summation of values from all frequencies of the spectrum.

Referring now to Figure 5 a time sequence of length Q, (where Q<N), that comprises zero values at all but one position will therefore have a frequency response that encompasses all the sub-channels of the OFDM or SC-FDE system. Figure 5 shows two examples of such a Kronecker delta sequence.

In practice, the duration of the Kronecker delta pulse will be constrained by the relation between pulse duration and sub-channel width in the communication system. However, the duration is assumed sufficiently short to encompass the frequency range of base- band W. The Kronecker delta function has one drawback, however. Transmission systems such as those described herein are sensitive to large peak to average power ratios (PAPR) in their signals. Large PAPR significantly affects non-linear components of the transmit chain such, as the power amplifier. The result is a need to either back-off the amplifier, which is highly inefficient, or suffer from signal distortion, which compromises the training signal (as well as data signals) so reducing performance. The Kronecker delta function, consisting of a sequence of all zeros except for one peak, has a very large peak to average power ratio, making it undesirable.

One approach to solving this problem would be to render all zeros a selected non-zero value, being lower than the peak value, in order to reduce the PAPR. However, the mean squared error of the channel estimate at the receiver would degrade as a result, due to the large DC component introduced and the windowing effects caused by having non-zero values across a finite sequence.

Consequently, an alternative method and means to derive, in the time domain, a training sequence of less than length N and with better PAPR properties than the Kronecker delta is required.

The training sequence to be derived ideally embodies two properties; it is near optimal in the MSE sense (i.e. encompassing as uniform a frequency response as possible) and that it is near-optimal in the PAPR sense (having as uniform an amplitude as possible).

In practice, MSE optimality does not consider PAPR optimality, and vice versa.

Consequently a trade-off predicated on preference for MSE or PAPR performance may be found.

Minimising MSE In an embodiment of the present invention, to determine a near-optimal (in the MSE sense) short training sequence of length Q for systems employing least-squares channel estimation, one may minimise the MSE metric f(x)= f,"x2 (2) where f'1xI denotes the absolute value f fHy the Qxl vector f denotes the nth column of the normalised partial (Q x N where Q-zIV) inverse DFT matrix, and x is the short sequence in time that is to be optimised. The IDFT matrix provides the means to evaluate the mean squared error of the channel estimate over the N sub-channels due to the current values of x.

To minimise the MSE metric of equation (2), a gradient descent method is used. For reasons that will be discussed later, in a preferred embodiment of the present invention the gradient descent method is an interior point method, such as the primal dual method or the barrier method.

Without loss of generalisation to the scope of gradient descent optimisation, application of the barrier method will now be disclosed in detail.

To apply the barrier method, the first derivative (gradient) and the second derivative (Hessian) off(x) must be computed.

The gradient \7f(x) is given by Vf(x)= -2f,'x4ff,'x, (3) and the Hessian \72f(x) is given by . (4) Equations (2), (3) and (4) are then employed by the barrier method, as described below, to derive a near-optimal (in the MSE sense) training sequence of length Q. Whilst the above metric is suitable for deriving a near-optimal training sequence in the MSE sense, it would also be desirable to constrain the derivation to avoid converging on solution with a high PAPR. n

Advantageously, interior point methods such as the primal dual method and the barrier method allow for the imposition of constraints on the optimisation process.

Consequently a constrained minimisation off(x) may be termed minimize f(x) = f (x) + E i(f, (x)) where I: 9 - is the indicator function for nonpositive real numbers, f0 (x) is the objective function given by equation 2, and /,(x) are p inequality constraints (i.e. f(x)<O).

The indicator function can, in practice, be approximated by the function i(u)= _!log(_ u), where t is the logarithmic barrier accuracy parameter and (by convention) l(u) = for u > 0.

The functions/(x) can define, but are not limited to: constraints on total transmit power, transmitted energy per subcarrier, peak to average power ratio (PAPR) of the transmitted time domain signal, and the dynamic range of the signal (for example with reference to the desired operating range of the power amplifier).

Thus, for example, a constraint on the total power to be transmitted can be expressed as follows: 11x02 = p f (x)= xJ2 - p where P is the maximum power constraint.

Similarly, a constraint on the PAPR of the transmitted signal can be expressed as follows: for all i where, a1 is the ith length-Q unit vector (i.e. the ith column of the QxQ identity matrix), and Sis the maximum peak power constraint. Note that this constraint also requires a constraint to be placed on the total transmit power (as shown above). fl

Thus, a near optimal (in the MSE sense) short training sequence of length Q can be derived subject to an acceptable PAPR constraint.

Minimising PAPR In an embodiment of the present invention, to determine a near-optimal (in the PAPR sense) short training sequence of length Q for systems employing least-squares channel estimation, one may minimise the PAPR metric f(X,Eç)=E (5) where E is the upper bound on the peak power of the transmitted signal, such that = E. for all i. This inequality constraint must be applied when minimising the PAPR metric.

As with the MSE case, in an embodiment of the present invention the PAPR metric, together with its gradient and Hessian, are applied to the barrier method.

As a corollary to the MSE case, whilst the above metric is suitable for deriving a near- optimal training sequence in the PAPR sense, it would also be desirable to constrain the derivation to avoid converging on solution with a high MSE.

As with the MSE case, functionsf(x) can be used to define complementary constraints on the optimisation. In addition to the constraints disclosed previously, a constraint on the MSE of the channel estimate can be expressed as fx2 = 0 = f(x)= fx2 -,where 0 is the maximum MSE constraint.

Thus, a near optimal (in the PAPR sense) short training sequence of length Q can be derived subject to an acceptable MSE constraint.

Applying the MSE or PAPR metrics to the barrier method Referring now to Figure 6, the barrier method is outlined qualitatively in steps si to s7, and detailed using pseudo-code in Table I below.

In step si, the MSE or PAPR metric is expressed as in equation 2 or 5 respectively. In step s2, any constraints of the problem are chosen, as discussed above. In step s3, parameters t, u and inner and outer tolerances of the algorithm e, , s,, are initialised.

Typical values might be, for example t = 0.5, u 2, e = 0.00 1, and e, = 0. 001.

In step s4, an initial sequence vector x that satisfies the constraints is chosen. In step s5, Newton's method is run until the iimer tolerance e, is met. Once the inner tolerance e, is met, the outer tolerance i is evaluated; if the outer tolerance is also met, then in step s6 the new near-optimal vector x is taken as the output of the process. However, if outer tolerance e is not met, then in step s7 the logarithmic barrier accuracy parameter t is increased by a factor jx, and the Newtonian process re-started using the last vector x.

Accuracy parameter t provides a trade-off between convergence performance and the number of iterations required for convergence. As t increases it provides a better approximation to the indicator function, but at the cost of slower convergence.

It will be clear to a person skilled in the art however that, particularly in the case of pre- computed sequences where the number of iterations may not be an important consideration, the barrier method may be initialised with a relatively high value of t and eliminate step s7.

The barrier method is a convex optimisation algorithm (i.e. it generally only works with convex problems). However, the problem stated here is in general not convex.

Consequently, the algorithm may find several solutions that differ, each one corresponding to a local minimum of the optimisation problem and converge to the closest. One way of ameliorating this problem is to apply the barrier method as stated above for several different starting points. If a large number of starting vectors are used, the likelihood that the barrier method will converge to a low local minimum, or indeed the global minimum, is high.

However, in consequence it will be clear to a person skilled in the art that the above process, and more generally any gradient descent process, can generate training sequences of varying optimality. Thus, whilst not preferred, it is envisaged within the scope of the invention that a lessoptimal training sequence so generated may be selected for use.

given strictly feasible x. t > 0, p > 1, s, > 0, s > 0 repeat I. Newton's method (x. sj > 0) a. Ax= -V2f(x)tVf(x) = -Vf (x)H Ax b. quit if A2/2 < sj return x:= x c. line search (determine 8) d. x x + /Ax 2. x x 3. quit if p/t < so 4. t:= jit Table 1: Psuedo code for barrier method optimisation of the cost functions of equations 2 and 5.

Using the short training sequences in multi-antenna systems As noted previously, the simplest method by which to perform channel estimation in a system with M transmit antennas is illustrated in Figure 7a, wherein sequential transmission on each antenna prevents cross-interference. In prior-art systems, the resulting overhead was proportionate to NxM. However, using the method of generating short training sequences described herein, this overhead can be substantially reduced.

In an embodiment of the present invention, if a previous channel estimate is available, then the training sequence can be designed to have a length Q = N/M.

If a previous channel estimate is not available, then the training sequence can be designed to be of length Q = (N/M)-L, where L is the known or assumed memory order of the channel impulse response (i.e. channel spread). L zeros are then padded onto the training sequence.

The sequence may then be transmitted from each antenna in a timemultiplexed fashion, as shown in Figure 7a.

A receiver receives the sequences at each receive antenna. If previous channel estimates are available, then for each receive antenna these can be used with knowledge of the training sequence to remove the interference caused by the channel from each received sequence. Note that if the sequence was padded with L zeros, then there will not be interference in the training sequence and so this step is unnecessary.

The length-N channel frequency response for each channel can then be estimated.

Advantageously, by defining length Q as N/M (or N/M-L), the exponential or linear relationships with antenna number seen in the prior art is eliminated entirely, at least for moderate numbers of antenna.

As noted previously, the present invention is applicable to OFDM, SC-FDE and other systems employing FDE. However without loss of generalisation, for the purposes of clarity a communications system will now be described with respect to OFDM systems.

Referring now to Figure 8, this shows an OFDM communications system 500 suitable for use with the above described training sequences. Thus a user data stream 502 is input to a conventional MIMO transmitter processor 504 which provides a plurality of outputs to JFFT blocks 510 each driving a respective one of a set of transmit antennas 512 to transmit a set of OFDM symbols. A MIMO training sequence is provided by block 506, either being constructed as described above or being stored, for example in a look-up table. The MIMO training sequence is optionally provided to a scrambling block 508, and the scrambled training sequence is then inserted in the data stream to be transmitted as OFDM symbols by MIMO processor 504. In practice training sequence and scrambling blocks 506, 508 may comprise temporary or permanent data storage such as Flash RAM or EPROM. Although two separate blocks are shown for clarity, in practice a scrambled training sequence is likely to be precalculated and stored in a local storage medium.

Continuing to refer to Figure 8, each of a plurality of receive antennas 514 receives signals from each of the transmit antennas 512, the received signals being passed to FFT blocks 516 and thence to a conventional MIMO OFDM receiver processor 518, which provides an output data stream 522. Processor 518 also receives a set of MIMO channel estimation values from MIMO channel estimation block 520. Any conventional least square (LS) algorithm may be employed for MIMO channel estimation.

Figure 9 shows an example of an OFDM transmitter 700 configured to use training sequences according to embodiments of the present invention. Broadly speaking the majority of the signal processing is performed in the digital domain, conversion to analogue signals only taking place for the final RF stages.

In Figure 9, two transmit antennas 702a,b are driven by respective RF stages 704a,b, typically comprising an up-converter, power amplifier and, optionally, windowing filters. The RF stages are driven by I and Q outputs of respective digital-to-analogue converters 706a,b that receive inputs from a digital signal processor (DSP) 708. Digital data for transmission is provided on an input 710 to DSP 708.

DSP 708 will generally include one or more processors 708a and workingmemory 708b, and has a data, address and control bus 712 to couple the DSP to permanent program and data memory 714, such as Flash RAM or ROM. Memory 714 stores processor control code for controlling DSP 708 to provide OFDM functions, in particular IFFT code 71 4a, cyclic prefix addition code 71 4b, training sequence insertion code 7l4c, and block error (such as ReedSolomon) correction and ST encoding code 714d. Memory 714 also stores training sequence data, here with sequence insertion code 714c, for inclusion in OFDM symbols transmitted from antennas 702a,b for channel estimation by a complementary OFDM receiver. As illustrated, some or all of the data and/or code stored in memory 714 may be provided on a removable storage medium 716 or on some similar data carrier. Although only two transmit antennas are shown in Figure 9 the skilled person will recognise that in practice more transmit antennas, such as 4, 6 or 8 antennas, may be employed.

It will be clear to a person skilled in the art that similar communications systems, transmitters and receivers to those described above, suitably rearranged for SC-FDE communication as known in the art, may incorporate the invention described herein.

The above-described technology is useful for OFDM and SC-FDE communications systems using either SISO or MIMO antenna arrangements. The technology is applicable to both terminals and base stations or access points and is not limited to any of the existing standards employing OFDM of SC-FDE communication.

No doubt many other effective alternatives will occur to the skilled person. It will be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art lying within the scope of the claims appended hereto.

Figure 10 shows a graph illustrating an example short training sequence (solid line) in accordance with an embodiment of the present invention, compared to a length N- sequence (dotted line) as known in the art for a 64 sub-channel frequency domain equaliser. Sequence length is shown on the x-axis, whilst sequence values are shown on the y-axis. The sequence is clearly shorter than N. Referring now to Figure 11, the resulting Fourier transform of the short training sequence of Figure 10 is shown (solid line) compared with the optimal solution the would be generated by a Kronecker delta sequence (dotted line). 64 frequency channels are shown on the x-axis, with a target magnitude range shown on the y-axis. It can be seen that, advantageously, the deviation from the optimal value is minimal, so providing a near-optimal solution in terms of mean squared error.

Thus embodiments of the present invention are seen to provide a nearoptimal short training sequence for frequency domain equalisation.

It will be understood that the method of generating training sequences, the training sequences themselves and the OFDM and SC-FDM systems operable to use them as described above provide at least one or more of the following advantages: i. provision of near-optimal (in the MSE sense) training sequences of a specified length Q; ii. provision of near-optimal (in the PAPR sense) training sequences of a specified length Q; iii. The ability to specify length Q, for example to mitigate transmission on multiple antennas, and; iv. the ability to constrain the optimisation process to meet various requirements for training signal characteristics including, inter alia, peak to average power ratio and channel estimation means squared error.

v. The ability to compensate for a linear relationship between total training sequence duration and antenna number.

Claims (29)

1. CLAIMS: 1. A method of generating a signal for transmission, the signal

   including training sequence data for aiding channel estimation upon reception of said signal at a receiver, the method comprising the steps of selecting a training sequence length, and; deriving training sequence data in the time domain by numerical optimisation of any one of: the channel estimate mean squared error, and; the peak to average power ratio of the training sequence.
2. 2. A method of generating a signal according to claim 1, wherein the numerical optimisation is performed by gradient descent.
3. 3. A method of generating a signal according to claim 2, wherein the gradient descent method is an interior point method.
4. 4. A method of generating a signal according to claim 2 or claim 3, wherein the gradient descent method is any one of i. a primal dual method, and; ii. a barrier method.
5. 5. A method of generating a signal according to any one of claims 2 to 4, wherein one or more constraints are imposed upon the numerical optimisation.
6. 6. A method of generating a signal according to claim 5, wherein said one or more constraints include at least one of: i. total transmit power; ii. energy transmitted per sub-carrier, and; iii. dynamic range.
7. 7. A method of generating a signal according to any one of claims 5 and 6, wherein in the case where said training sequence data is derived in the time domain by numerical optimisation of the channel estimate mean squared error, a constraint on the peak to average power ratio of the training sequence is imposed on the numerical optimisation.
8. 8. A method of generating a signal according to any one of claims 5 and 6, wherein in the case where said training sequence data is derived in the time domain by numerical optimisation of the peak to average power ratio of the training sequence, a constraint on the channel estimate mean squared error is imposed on the numerical optimisation.
9. 9. A method of generating a signal according to any one of claims 1 to 7 wherein the cost function is substantially of the form f(x)= =0 where IfnHxI denotes the absolute value of fHx the Qx 1 vector f denotes the th column of the normalised partial (Q x N where Q<N) inverse DFT matrix, and x is the short sequence that is to be optimised.
10. 10. A method of generating a signal according to any one of claims 1 to 6 and 8 wherein the cost function is substantially of the form f(x,EJ= Eç where E5 is the upper bound on the peak power of the transmitted signal, such that a'x2 = E for all i, a, is the ith length-Q unit vector, and x is the short sequence that is to be optimised.
11. 11. A method of transmitting a signal comprising generating a signal in accordance with any preceding claim and transmitting said signal into a suitable communications channel.
12. 12. A signal generated according to the method of any one of claims 1 to 10.
13. 13. A signal according to claim 12 wherein training sequences are scrambled.
14. 14. An OFDM transmitter configured to transmit an OFDM signal of any one of claims 12 and 13.
15. 15. An SC-FDE transmitter configured to transmit an SC-FDE signal of any one of claims 12 and 13.
16. 16. An OFDM transmitter configured to transmit an OFDM signal from one or more transmit antennas, the OFDM transmitter comprising: a data memory storing training sequence data generated according to the method of any one of claims ito 10, for each of said one or more antennas; an instruction memory storing processor implementable instructions; and a processor coupled to said data memory and to said instruction memory to read and process said training sequence data in accordance with said instructions, said instructions comprising instructions for controlling the processor to: read said training sequence data for each antenna; provide a cyclic extension for said training sequence data to generate output data for each antenna; and provide said output data to at least one digital-to-analogue converter for transmission.
17. 17. An SC-FDE transmitter configured to transmit an SC-FDE signal from one or more transmit antennas, the SC-FDE transmitter comprising: a data memory storing training sequence data generated according to the method of any one of claims 1 to 10, for each of said one or more antennas; an instruction memory storing processor implementable instructions; and a processor coupled to said data memory and to said instruction memory to read and process said training sequence data in accordance with said instructions, said instructions comprising instructions for controlling the processor to: read said training sequence data for each antenna; provide a cyclic extension for said training sequence data to generate output data for each antenna; and provide said output data to at least one digital-to-analogue converter for transmission.
18. 18. A transmitter according to any one of claims 16 and 17 wherein said training sequence data is pre-computed and stored in a storage means.
19. 19. A transmitter according to any one of claims 16 to 18 wherein the numerical optimisation of the channel estimate is by gradient descent.
20. 20. A transmitter according to claim 19 wherein the gradient descent method is any one of i. a primal dual method, and; ii. a barrier method.
21. 21. A receiver operable to receive a signal comprising training sequence data in accordance with any one of claims 1 to 10, and further operable to use said training sequence data to assist in channel estimation.
22. 22. A data transmission system comprising the transmitter of any one of claims 16 to 20 and the receiver of claim 21.
23. 23. A data carrier carrying said training sequence data for each transmit antenna of any one of claims 16 to 22.
24. 24. A data carrier as claimed in claim 23 further comprising said processor implementable instructions.
25. 25. Processor control code and training sequence data to, when running, implement the transmitter of any one of claims 16 to 22.
26. 26. A method of generating an OFDM signal substantially as hereinbefore described with reference to the accompanying drawings.
27. 27. An OFDM transmitter substantially as hereinbefore described with reference to the accompanying drawings.
28. 28. A method of generating an SC-FDE signal substantially as hereinbefore described with reference to the accompanying drawings.
29. 29. An SC-FDE transmitter substantially as hereinbefore described with reference to the accompanying drawings.

    29. An SC-FDE transmitter substantially as hereinbefore described with reference to the accompanying drawings.

    Amendments to the claims CLAIMS: 1. A method of generating a signal for transmission, the signal including training sequence data for aiding channel estimation upon reception of said signal at a receiver, the method comprising the steps of selecting a training sequence length, and; deriving training sequence data in the time domain by numerical optimisation of any one of: the channel estimate mean squared error, and; the peak to average power ratio of the training sequence.

    2. A method of generating a signal according to claim 1, wherein the numerical optimisation is performed by gradient descent.

    3. A method of generating a signal according to claim 2, wherein the gradient descent method is an interior point method.

    4. A method of generating a signal according to claim 2 or claim 3, wherein the gradient descent method is any one of i. a primal dual method, and; ii. a barrier method.

    5. A method of generating a signal according to any one of claims 2 to 4, wherein one or more constraints are imposed upon the numerical optimisation.

    6. A method of generating a signal according to claim 5, wherein said one or more constraints include at least one of: i. total transmit power; ii. energy transmitted per sub-carrier, and; iii. dynamic range.

    7. A method of generating a signal according to any one of claims 5 and 6, wherein in the case where said training sequence data is derived in the time domain by numerical optimisation of the channel estimate mean squared error, a constraint on the peak to average power ratio of the training sequence is imposed on the numerical optimisation.

    8. A method of generating a signal according to any one of claims 5 and 6, wherein in the case where said training sequence data is derived in the time domain by numerical optimisation of the peak to average power ratio of the training sequence, a constraint on the channel estimate mean squared error is imposed on the numerical optimisation.

    9. A method of generating a signal according to any one of claims 1 to 7 wherein the cost function is substantially of the form f(x)= fx2 where IfnHXI denotes the absolute value of fHx the Qx I vector f denotes the n' column of the normalised partial (Q x N where Q<N) inverse DFT matrix, and x is the short sequence that is to be optimised.

    10. A method of generating a signal according to any one of claims Ito 6 and 8 wherein the cost function is substantially of the form f(x,E5)= Eç where E is the upper bound on the peak power of the transmitted signal, such that aTx2 = E for all 1, a1 is the ith length-Q unit vector, and x is the short sequence that is to be optimised.

    11. A method of transmitting a signal comprising generating a signal in accordance with any preceding claim and transmitting said signal into a suitable communications channel.

    12. A signal generated according to the method of any one of claims ito 10.

    13. A signal according to claim 12 wherein training sequences are scrambled.

    14. An OFDM transmitter configured to transmit an OFDM signal of any one of claims 12 and 13.

    15. An SC-FDE transmitter configured to transmit an SC-FDE signal of any one of claims 12 and 13.

    16. An OFDM transmitter configured to transmit an OFDM signal from one or more transmit antennas, the OFDM transmitter comprising: a data memory storing training sequence data generated according to the method of any one of claims I to 10, for each of said one or more antennas; an instruction memory storing processor implementable instructions; and a processor coupled to said data memory and to said instruction memory to read and process said training sequence data in accordance with said instructions, said instructions comprising instructions for controlling the processor to: read said training sequence data for each antenna; provide a cyclic extension for said training sequence data to generate output data for each antenna; and provide said output data to at least one digital-to-analogue converter for transmission.

    17. An SC-FDE transmitter configured to transmit an SC-FDE signal from one or more transmit antennas, the SC-FDE transmitter comprising: a data memory storing training sequence data generated according to the method of any one of claims ito 10, for each of said one or more antennas; an instruction memory storing processor implementable instructions; and a processor coupled to said data memory and to said instruction memory to read and process said training sequence data in accordance with said instructions, said instructions comprising instructions for controlling the processor to: read said training sequence data for each antenna; provide a cyclic extension for said training sequence data to generate output data for each antenna; and provide said output data to at least one digital-to-analogue converter for transmission.

    18. A transmitter according to any one of claims 16 and 17 wherein said training sequence data is pre-computed and stored in a storage means.

    19. A transmitter according to any one of claims 16 to 18 wherein the numerical optimisation of the channel estimate is by gradient descent.

    20. A transmitter according to claim 19 wherein the gradient descent method is any one of i. a primal dual method, and; ii. a barrier method.

    21. A receiver operable to receive a signal comprising training sequence data in * : accordance with any one of claims 1 to 10, and further operable to use said training *: : : :* sequence data to assist in channel estimation. ****

    22. A data communication system comprising the transmitter of any one of claims **S 16 to 20 and the receiver of claim 21. *** * * S...

    * :* 23. A data carrier carrying said training sequence data for each transmit antenna of any one of claims 16 to 20, and claim 22.

    24. A data carrier as claimed in claim 23 further comprising said processor implementable instructions.

    25. Processor control code and training sequence data to, when running, implement the transmitter of any one of claims 16 to 20, and claim 22.

    26. A method of generating an OFDM signal substantially as hereinbefore described with reference to the accompanying drawings.

    27. An OFDM transmitter substantially as hereinbefore described with reference to the accompanying drawings. qo

    28. A method of generating an SC-FDE signal substantially as hereinbefore described with reference to the accompanying drawings.