GB2423898A - Optimising OFDM training data sequences using a cost function - Google Patents

Abstract

This invention relates to apparatus, methods, processor control code and signals for channel estimation in OFDM (Orthogonal Frequency Division Multiplexed) communication systems with a plurality of transmitter antennas, such as MIMO (Multiple-input Multiple-output) OFDM systems. A method of generating an OFDM signal for transmission from an OFDM transmitter using a plurality of transmit antennas is provided, the OFDM signal being adapted for channel estimation for channels associated with said transmit antennas by the inclusion of training sequence data in the signal from each said antenna wherein one or more sub-carriers are null, the method comprising the step of deriving said training sequence data by numerical optimisation of a channel estimate. The optimisation involves deriving a cost functions to establish the minimum mean squared error (MSE) metric. The optimisation is performed using a gradient descent process, preferably an interior point method such as the primal dual or barrier methods.

Description

1 2423898 TRANSMISSION SIGNALS, METHODS AND APPARATUS This invention

relates to apparatus, methods, processor control code and signals for channel estimation in OFDM (Orthogonal Frequency Division Multiplexed) communication systems. More particularly it relates to channel estimation in systems with a plurality of transmitter antennas, such as MIMO (Multiple-input Multiple-output) OFDM systems.

The current generation of high data rate wireless local area network (WLAN) standards, such as Hiperlanl2 and IEEE8O2. 1 la and g, provide data rates of up to 54 Mbitls.

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.lla, 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 Hiperlan/2 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 Hiperlanl2 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 that 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 l/T, 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 (ISI), at least to a first approximation.

Figure lb shows an example of a conventional SISO (single-input, singleoutput) OFDM system including a transmitter 100 (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 omnidirectional 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 lb) 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 minor 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.

The receiver of Figure lb 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 HIPERLAN 2 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 lb 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) andlor 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) w"(n) u(n) where wH denotes the Flermitian conjugate of w. Then, according to the LMS algorithm, an improved weight estimation is given by w(n+1) = w(n) +jLu(n)[d*(n) - y*(n)I where * denotes a complex conjugate and.t is the adaption step size of the algorithm.

Convergence of the algorithm can be determined using the mean squared error, that is d(n)-y(n) 2 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 OFDM 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 OFDM 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 OFDM 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.3 11-335, 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 Fliperlanl2 and IEEE8O2.1 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,k] 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 t1[n,k] (Li et al consider a two transmit antenna 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 t1[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 N1 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.

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.

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. In a MIMO OFDM system with M transmitting 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.

The simplest form of training sequence for use in such systems involves transmitting a training sequence from one antenna at a time, which prevents the training signals from interfering with one another (see Figure 7a). However, this approach requires a large amount of overhead, which obviously grows linearly with the number of transmit antennas M. 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", SPAWC'Ol (Taoyuan, Taiwan), pp 82-85, Mar 2001.

Consider a training sequence of length K (in Tung et al., equal to the number of subcarriers) and a channel with an impulse response length or "span" L sample periods I'S where (T5 is the sampling interval of the system and lIT5 the entire channel bandwidth of the OFDM system). The channel span, in terms of time, is (L-I)T5 and the OFDM frame length T5 = (K + v) T5 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 T5.

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 hLj)T, a vector of size L x 1. The corresponding frequency 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. (lb/cl) 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.

FHX(m)HX(n)F = O Equation 1 LcI L In Equation (1), L is an all zero matrix of size L x L, L 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 H denotes a Hermitian conjugation operation. The matrix X(m) 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 {Xml,.. Xmk,. . .Xm} where Xmk is the Kth element of a training sequence of length K (although in Tung et a!. 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 LM parameters 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? 2ML 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.

In response to this problem, several training sequence design methodologies have been proposed: Larsson, E., and Li, J., in preamble design for multiple-antenna 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).

However, whilst this achieves the desired linear relationship, the training sequences are non-optimal in to the presence of null subcarriers (see figure 8), and the training signals suffer from a high peak to average power ratio (PAPR) that can induce signal distortion.

GB 2393618 (Toshiba), incorporated herein by reference, proposes an alternative methodology that addresses the PAPR problem whilst still maintaining 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 such that a minimum required sequence length K needed to determine a channel estimate for at least one channel associated with each transmit antenna is still linearly dependent upon the number of said transmit antennas.

However, the analytical solution proposed in GB 2393618 assumes that all sub-carriers are utilised. By contrast, it cannot generate optimal training sequences in the presence of null sub-carriers, due to theintractability of clearly defining the requirements that sequences must have in order to be optimal when null sub-carriers are employed; lower bounds on MSE for systems with null sub-carriers have not yet been derived in the literature.

Consequently it is desirable to develop a method and means by which to generate near- optimal training sequences for OFDM MIMO systems with null sub-carriers that have a similarly near-linear relationship between sequence length and antenna number whilst still mitigating high peak to average power ratios.

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 OFDM signal for transmission from an OFDM transmitter using a plurality of transmit antennas, the OFDM signal being adapted for channel estimation for channels associated with said transmit antennas by the inclusion of training sequence data in the signal from each said antenna wherein one or more sub-carriers are null, comprises the step of deriving said training sequence data by numerical optimisation of a channel estimate.

In one configuration of the above aspect, an interior point gradient descent method is used to optimise a channel estimate cost function.

In another configuration of the above aspect, the numerical optimisation process is constrained to satisfy conditions such as total transmitted power and the peak to average power ratio.

In another aspect of the present invention, an OFDM transmitter has a plurality of transmit antennas, said OFDM 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.

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 storing training sequence data for each of said plurality of 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; 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-toanalogue converter for transmission; and wherein said training sequence data for a said antenna is derived by numerical optimisation of a channel estimate.

In another aspect of the present invention an OFDM signal is produced for an OFDM 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 OFDM signal, said training sequence data being derived by numerical optimisation of a channel estimate.

In a further aspect of the present invention, a data carrier carries training sequence data for each antenna, 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 the OFDM signal as one or more OFDM symbols by performing an inverse Fourier transform (IFFT) on a training sequence and then adding a cyclic extension such as a cyclic prefix. Thus the training sequence data may be effectively incorporated in OFDM symbols transmitted from each of the transmit antennas.

Since the training sequences should have lengths which grow linearly with the number of transmit antennas, the training sequence overhead in MIMO OFDM communication systems may be significantly reduced, in effect allowing shorter training sequences or, equivalently, larger numbers of transmit antennas, for MIMO OFDM systems with null sub-carriers.

The training sequences upon which the training sequence data incorporated in the OFDM signal is based may have values distributed in time andlor frequency space.

That is, k may index subcarriers of the OFDM signal andlor OFDM symbols. Thus K may run over all the subcarriers of the OFDM signal so that an OFDM training symbol incorporates data for a complete sequence of values, for example each value in a training sequence being carried by one of the subcarriers of the training OFDM symbol.

Alternatively training sequence values may be placed, for example, on alternate subcarriers or in some other pattern, or training sequence values may be spaced out in time over two or more OFDM training symbols. In a simplified case, however, K may be equated with the total number of subcarriers and data from one training sequence value placed on each subcarrier. Training sequence values, or scrambled training sequence values, or data derived from such sequences or scrambled sequences may be stored in a look-up table to avoid the need for the values or data to be calculated in real time.

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

The above-described training sequence data andlor processor control code to implement the above-described OFDM 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: Figures 1 a and lb show, respectively, subearriers of an OFDM signal spectrum, and 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 Hiperlan 2 OFDM signal showing preamble and pilot signal positions; Figure 4 shows a known space-time coded MIMO OFDM communications system; Figure 5 shows a MIMO OFDM communications system embodying aspects of the present invention; Figure 6 shows a block diagram of a MIMO OFDM transmitter according to 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 schematic diagram of an OFDM symbol in the frequency domain, comprising utilised and null sub-carriers.

Figure 9 is a flow diagram of a method of generating training sequences in accordance with an embodiment of the present invention.

Figure 10 shows a graph of normalised mean square error per sub-carrier against channel length L, comparing the performance of embodiments of the present invention with prior art techniques, including a lower bound for training sequence wherein all sub-carriers are used.

Figures 11 a,b show graphs of bit error rate against signal to noise ratio for various training sequences generated in accordance with embodiments of the present invention, in comparison with reference results.

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 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 the absence of an analytical solution to the problem of training sequence generation in the presence of one or more null sub-carriers, a numerical optimisation process can be constructed to provide a near-optimal alternative.

However, deriving a tractable and computationally efficient cost function for such an optimisation is a non-trivial matter: The goal, for a system employing least squares channel estimation, is to minimise the mean squared error metric f(XI,...,XM)=Tr((IM WXAHA)(IM W)t1) (2) where M is an identity matrix of size M, W is a K x L partial discrete Fourier transform (DFT) matrix picking out the K active subcarriers and the L time domain channel taps, 0 denotes the Kronecker product and A = [x1w. .. XMWI (see Larson, E., and Li, J., ibid).

To derive a tractable and computationally efficient cost function based on equation 2, in an embodiment of the present invention one may note that in the matrix A, Xm is a K x K diagonal matrix with the training symbols for antenna m on the diagonal. The expression for MSE in equation 2 depends on A H A, which is an M x M block matrix where each submatrix has size L x L. Each submatrix has the form WHXXmW which can be expressed as G00... GOLI WHXXmW=(IL Xm)H. (i1 x1.) GL_l,o GL_I,L_1 where G r.s = 0 WK_I,rW;I.c is a diagonal matrix and Xm is a length-K column vector containing the training symbols for antenna m.

Column vectors Xm can then be concatenated to form a single vector x = .. , x 7 Q00 QO,M- AHA=(IML x)I... (IML x) QM_J.O QM_I,M_1 where (emeZ) Goo... (eme) GoL_l Qm,m...

(emeZ) GL_l,o... ) GL__l and em is the mth length-M unit vector (i.e. the mth column of IM).

Thus the resulting cost function is f(x) = Tr((IM WX(IML x)H Q(I x)) ' (IM W)F) (3) where Q is an M2KL x M2KL sparse matrix that does not depend on x, but only contains elements of W. By expressing the cost function as the function of a vector x, optimisation is possible by a gradient descent processes.

For reasons that will be discussed later, in a preferred embodiment of the present invention the optimisation process 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) of f(x) must be computed.

Defining Z = (IM w)11 (IM w) and B = (IML x)" Q(IML x), then the jth element of the gradient Vf(x) can be written as =Tr(_B1ZBi(IML uJ)HQ(IML x)) (4) where u is the jth length-MK unit vector (i.e. thejth column of IMK).

The (kf)th element of the Hessian V2f(x) is given by =Tr{(B(IML Uk) Q(IML x)BZB' +B'ZB'(IML Uk) Q(IML x)B)x (5) (IMJ x) Q(IML uJ) -BZB(IML uk) Q(IML u,)} Equations (3), (4) and (5) are then employed by the barrier method to derive a vector of M near-optimal length K training sequences.

Referring to figure 9, the barrier method is outlined qualitatively in steps si to s7, and detailed using pseudo-code in Table 1 below.

In step si, the MSE metric is expressed as in equation 3. In step s2, any constraints of the problem are chosen, as discussed below. In step s3, parameters t, u and inner and outer tolerances of the algorithm s, , e are initialised. Typical values might for example be t=0.5, 1u=2, e =0.1, and e, = 0.1).

In step s4, a starting vector x that satisfies the constraints is chosen. In step s5, Newton's method is run until inner tolerance e, is met. Once inner tolerance e, is met, outer tolerance s 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 is not met, then in step s7 the logarithmic barrier accuracy parameter t is increased by a factor p, 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 an indicator function (see below), 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, the barrier method may be initialised with a relatively high value of t and eliminate step s7.

Note that 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, > 0. 6? > 0 repeat 1. Newton's method (x. e > 0) a. Ax = -V2f(x)' Vf(x) = _Vf(x)Ix b. quit if 2/2 < s.

return x x c. line search (determine 13) d. x:=x+3Ax 2. x x 3. quit if p/t < o 4. t at Table 1: Psuedo code for barrier method optimisation for the cost function of equation 3.

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) = f0 (x) + (x)) where I: R - R is the indicator function for non- positive real numbers, f0 (x) is the objective function given by equation 3, and f, (x) are p inequality constraints (i.e. f,(x)<0).

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) I(u) for u > 0.

The functions f (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: llxI2 = p = fi (x) = - where P is the maximum power constraint.

Similarly, a constraint on the PAPR of the transmitted signal can be expressed as follows: aT(IM F')x2 =8 f(x)=a(IM F'')x2-5 for all i where F is the K x N partial DFT matrix picking out the active sub-carriers, N is the total number of subcarriers, a, is the ith length-MN unit vector, and 5 is the maximum peak power constraint. Note that this constraint also requires a constraint to be placed on the total transmit power (as shown above).

As noted previously, the channel impulse response length L must be assumed, at least initially. This is of significance because the MSE of the LS channel estimate is closely related to this parameter, as shown in figure 10.

Figure 10 shows the relationship between the channel impulse response length on the x- axis, and the mean squared error on the y-axis. One can see that, compared with a lower bound represented by the MSE for a training set utilising all sub-carriers, the error increases notable beyond a certain channel length, but advantageously does so more slowly than for the non- optimised null sub-carrier training sequence disclosed by Larsson and Li, ibid. For Larsson and Li's method of transmitting training symbols on mutually exclusive sets of sub-carriers, the assumption of L is of little relevance as the design of the training sequences is the same for all values of L. However, for the method of designing training sequences disclosed herein, L is significant because the application of the barrier method may result in different length-K training sequences for different values of L. A solution to this problem is to pre-compute various training sequences for different values of L. These sequences can be stored by the transmitter and receiver for use during communication. By pre-computing in this manner, an OFDM data transmission system comprising a transmitter and receiver can select training sequences for an appropriate value of L at any appropriate time.

Typically, however, since the length of a channel will not generally be known prior to its estimation L may initially be taken to be equal to or greater than the cyclic prefix length, as the cyclic prefix is normally selected to be longer than the channel.

Where one training sequence value Xk is allocated to each active subcarrier, an OFDM training symbol for transmission by an antenna of an OFDM transmitter may be constructed by performing an inverse Fourier transform of the K samples or values of the training sequence and then adding a cyclic prefix (conversion to an analogue waveform by a digitalto-analogue converter is understood). The skilled person will recognise that the training sequences may be oversampled, for example by altering the inverse Fourier transform matrix from a K x K matrix to a K x 2K matrix to provide an output data sequence of length of 2K.

A common problem in OFDM signals is that the inverse Fourier trainsform generates large peaks in the time domain when in-phase subcarriers interefere constructively. This results in a large dynamic range in the signal and a large peak to average power ratio.

Both these signal characteristics can induce distortions in the transmitted signal due to nonlinearities in the power amplifier. A number of mechanisms attempting to reduce PAPR are known in the art, for example scrambling the training signal (see GB 2393618 Toshiba, ibid).

Advantageously however, as noted above embodiments of the present invention enable the imposition of constraints including the PAPR and dynamic range of the signal.

Consequently there is no need for additional mitigation strategies.

Referring now to Figure 5, 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 IFFT 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 required 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 5, 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.

Preferably, the receiver will only apply MIMO channel estimation to the K active sub- channels comprising training symbols. Embodiments of the invention using the above- described training sequences do not otherwise require any modification to a conventional MIMO OFDM receiver (although, as usual, the receiver needs to know the training sequence(s) used). Thus a standard adaptive filter based channel estimation technique may be employed to estimate one or more channels (depending upon the number of receive antennas) for each transmit antenna.

Li et al. (ibid) describe one example of a least square channel estimation technique (employing windowing in the time domain). For further details of the algorithm reference may be made to the Li et al. paper, ibid (hereby incorporated by reference).

Figure 6 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 6 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 working memory 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 714c, 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 andlor 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 6 the skilled person will recognise that in practice more transmit antennas, such as 4, 6 or 8 antennas may be employed.

Figures 11 a and 11 b show graphs illustrating comparisons of the performance of the above-described training sequences with known training sequences for least-squares algorithms.

In figure 1 la, the bit error rate is shown on the y-axis and the SNR on the x-axis for two designs of training sequences, compared with the third case when the channel is known.

The training signal consists of 3 repeated OFDM symbols and 104 out of 128 active subcarriers, with L = 16. One can see that the numerically optimised training sequence significantly outperforms the known alternate subcarrier design.

Similarly in figure 1 ib, the bit error rate is shown on the y-axis and the SNR on the x- axis for two different types of training sequence, the first designed for 4 antennas and then repeated over 2 OFDM symbols with L=12, and the second designed for 2 antennas and time multiplexed (i.e. staggered in time) with L20. Again, the numerically optimised training sequences consistently outperform the known alternate subcarrier design.

The above-described technology is useful for OFDM communications systems with multiple transmit antennas such as MIMO systems. 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 communication. With conventional techniques for use with least square channel estimation (which is simple and provides good performance) the required training sequence length is K = 2M1 L and grows exponentially with the number of antennas whereas with the above described techniques the required sequence length is K = ML and is linearly proportional to the number of transmit antennas.

Moreover, the above described techniques are applicable to OFDM MIMO systems wherein a proportion of sub-carriers are unused, or null, for training signals. The above described techniques can also constrain peakto-average power ratio of close to unity by constraining the numerical optimisation process, which enables the use of OFDM transmitter power amplifiers with a reduced specification.

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 spirit and scope of the claims appended hereto.

It will be understood that the method of generating training sequences, the training sequences themselves and the OFDM transmitter operable to transmit 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 in the presence of one or more null sub-carriers; ii. provision of a tractable cost-function for numerical optimisation of the training sequences; iii. the ability to constrain the optimisation process to meet various requirements for training signal characteristics including, inter alia, peak to average power ratio; iv. the ability to store a plurality of L-dependent training sequences for later selection, and; v. Improved bit error performance as a function of signal to noise ratio, as compared with known methods of training sequence generation.

Claims (23)

1. CLAIMS: 1. A method of generating an OFDM signal for transmission from an

   OFDM transmitter using a plurality of transmit antennas, the OFDM signal being adapted for channel estimation for channels associated with said transmit antennas by the inclusion of training sequence data in the signal from each said antenna wherein one or more sub- carriers are null, the method comprising the step of deriving said training sequence data by numerical optimisation of a channel estimate.
2. 2. A method of generating an OFDM signal according to claim 1, wherein the numerical optimisation of the channel estimate is by gradient descent.
3. 3. A method of generating an OFDM signal according to claim 2, wherein the gradient descent method is an interior point method.
4. 4. A method of generating an OFDM 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 an OFDM 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 an OFDM signal according to claim 5, wherein any or all of the following constraints i. total transmit power; ii. energy transmitted per sub-carrier; iii. peak to average power ratio, and; iv. dynamic range are imposed on the numerical optimisation.
7. 7. A method of generating an OFDM signal according to any one of the preceding claims, wherein the numerical optimisation assumes a channel impulse response of length L.
8. 8. A method of generating an OFDM signal according to any one of the preceding claims, wherein the cost function f(x) is a function of a single vector x of concatenated training symbols Xm for each transmit antenna.
9. 9. A method of generating an OFDM signal according to any one of the preceding claims wherein the cost function f(x) is dependent upon an M2KL x M2KL sparse matrix comprising Fourier transforms of K active subcarriers and L time domain channel taps for Mtransmit antennas.
10. 10. A method of generating an OFDM signal according to any one of the preceding claims wherein the cost function f(x) is substantially of the form f(x)= Tr((IM 0 WX(IML 0 x)H Q(IML x)) (IM 0 W)'') where I is an identity matrix, W is a Fourier transform matrix of K active subcarriers and L time domain channel taps, Q is a sparse matrix comprising elements of W, H denotes a Hermitian conjugation and 0 denotes the Kronecker product.
11. 11. An OFDM signal generated according to the method of any one of the preceding claims.
12. 12. An OFDM signal according to claim 11 wherein training sequences are scrambled.
13. 13. An OFDM transmitter configured to transmit the OFDM signal of any one of claims 11 and 12.
14. 14. An OFDM transmitter in configured to transmit an OFDM signal from a plurality of transmit antennas, the OFDM transmitter comprising: a data memory storing training sequence data for each of said plurality of 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; 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 a said antenna comprises data derived by numerical optimisation of a channel estimate.
15. 15. An OFDM transmitter according to claim 14 wherein said OFDM signal is pre- computed and stored in a storage means.
16. 16. An OFDM transmitter according to claim 14 or claim 15 wherein the numerical optimisation of the channel estimate is by gradient descent.
17. 17. An OFDM transmitter according to claim 16 wherein the gradient descent method is any one of i. a primal dual method, and; ii. a barrier method.
18. 18. An OFDM data transmission system comprising the transmitter of any one of claims 14 to 17 and an OFDM receiver configured to receive the OFDM signal.
19. 19. A data carrier carrying said training sequence data for each transmit antenna of any one of claims l4to 18.
20. 20. A data carrier as claimed in claim 19 further comprising said processor implementable instructions.
21. 21. Processor control code and training sequence data to, when running, implement the OFDM transmitter of any one of claims 14 to 18.
22. 22. A method of generating an OFDM signal substantially as hereinbefore described with reference to the accompanying drawings.
23. 23. An OFDM transmitter substantially as hereinbefore described with reference to the accompanying drawings.