WO2012035345A2 - Improvements in ofdm communication systems - Google Patents

Abstract

The present disclosure is related to a transmitter, a receiver, a method for transmitting information, and a method of receiving information in a system which simplifies receiver structure and improves the performance in an orthogonal frequency-division multiplexing (OFDM) system. The transmitter comprises a module for generating a passive phase conjugation probe signal for transmission. The receiver comprises a passive phase conjugation module. The method for transmitting information comprises generating a passive phase conjugation probe signal for transmission. The method for receiving information comprises extracting OFDM symbols from a received signal using a method which comprises performing passive phase conjugation on the received signal.

Description

IMPROVEMENTS IN OFDM COMMUNICATION SYSTEMS

In any broadband broadcast technology, multipath interference impairs high data rate transmission. OFDM is well suited for broadband applications due to its robustness against multipath interference by transforming a frequency selective channel into parallel flat fading channels.

The present invention is related to a transmitter, a receiver, a method for transmitting information, and a method of receiving information in a system which simplifies receiver structure and improves the performance in an OFDM system as well as providing other advantages that will be apparent to a person skilled in the art.

The OFDM technique has been adopted in several wireless standards, e.g., 802.1 1 a wireless local network (WLAN) system, and 3GPP Long Term Evolution (LTE), also known as Evolved-UMTS Terrestrial Radio Access.

Figure 1 is a block diagram of a typical OFDM system 100. At the transmitter 1 10, each group of two information bits {c„} is mapped into one of four

Quadrature Phase-Shift Key (QPSK) symbols s„ by modulator 1 1 1. A set of N symbols is serial to parallel converted and imposed onto orthogonal sub-carriers by the means of an inverse fast Fourier transform (IFFT) module 1 12. The output from IFFT module 1 12 is then passed to a cyclic prefix (CP) module 1 13, where it is converted into serial data and a cyclic prefix (CP) is inserted to form one OFDM symbol for transmission. Each symbol is assigned to a subcarrier frequency and then transmitted at module 1 14 over a noisy channel (H) 120 i.e. N symbols are assigned to N subcarrier frequencies (N subcarriers) and the nth symbol is transmitted on the nth subcarrier frequency (nth subcarrier). The length of the CP is assumed to be longer than the impulse response of the channel in order to combat intersymbol interference and inter-carrier interference. The use of a cyclic prefix longer than the channel delay spread will transform the linear convolution in the channel to a cyclic convolution.

After passing through channel 120, the symbols are received by receiver 130. The signals are initially picked up by an antenna 131. CP is then removed by a remove CP module 132. Denoting cyclic convolution by ®, we can write the nth received signal after CP removal as r_n = IFFT(¾) ® h„ + v„ where: h„ is the channel impulse response at the nth subfrequency padded with zeros to obtain a sequence of a length of N;

v„ is the additive white Gaussian noise (AWGN) with zero mean; and variance δ ², i.e. v„ ~ CK(0, δ_ν ²), where CK(0, δ_ν ²) represents the complex normal distribution with variance of δ_ν ².

Next a fast fourier transform (FFT) is performed on the signal by FFT module 133. After FFT operation, the received signal becomes y_n = FFT(r„) = FFT {IFFT(¾) ® h„ + v„\ which gives equation 1 :

y„ = FFT{IFFT(s„) ® h„} + η„ where: n = 1, 2, ..., N;

{y„} contains N received data samples;

{s„} contains N transmitted symbols;

η„ = FFT(v„) and represents uncorrelated Gaussian noise at the nth subcarrier. The FFT of two cyclically convolved signals is equivalent to the product of their individual FFTs, i.e., FFT( ® b) = FFT( ) · FFT(6), where · denotes element-by- element multiplication. Thus, equation 1 can be written as: y„ = s„» FFT(h„) + η„ which gives equation 2:

y„ = s„ · H„ + η„ where H„ is the frequency response of the channel at the nth subcarrier.

Next the signal is passed to an equalization module 134 to detect the transmitted symbol from the signal received at the receiver. In a conventional OFDM system, either a one-tap Zero-Forcing (ZF) equaliser or a one-tap Minimum Mean Square Error (MMSE) equaliser is applied to detect the transmitted symbol at the receiver (i.e. s„ = a„y„, where s„ is the detected symbol, and a_n is the equaliser coefficient). The equaliser coefficient can be derived as a„ = 1 1 H„ for a ZF equaliser or a„ = H„^* / ( | H„| ² + <5_v ²) for a MMSE equaliser, where H„ is an estimate of H„;

n = l, 2, ..., N;

H„^* is the complex conjugate of H„; and

δ_ν ² is the variance of the AWGN v„.

The equalized symbols are then passed to a demodulator 135 where they are demodulated from QPSK back to groups of two information bits {c„} . In OFDM systems a short training symbol (STS) and a long training symbol (LTS) are used as probes, normally these have a quadrature component, j, -1 and thus are complex. For example, the pilot sequences used in an IEEE 802.11a based OFDM system for synchronization and channel estimation purposes are:

STS = — x [001+j 000 -1-j 0001+j 000 -1-j 000 -1-j 0001+j 000000 - V 6

1-j 000 -1-j 0001+j 0001+j 0001+j 0001+j 00]; and

LTS = [1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1 1 1 1 1].

As is clear from the above description, in order to perform equalisation, we need to obtain an estimate of the channel frequency response H„ for each subcarrier by some channel estimation algorithm. Any real channel estimation (real CE) will imperfect, leading to errors in demodulating the received signal.

In addition, the above equations show that equaliser coefficient is obtained by inverting an estimation of the channel, and this must be done using complex division which is computationally burdensome to perform.

It is therefore desirable to provide a system which, while preserving the robustness of an OFDM system, reduces the computational burden and complexity of the channel estimation and signal equalization processes. Summary of the Invention

In a first aspect of the present disclosure a receiver is provided for retrieving OFDM symbols from a received signal, wherein the receiver comprises a passive phase conjugation (PPC) module. The PPC module comprises means for performing cross-correlation between received signals.

Preferably, the PPC module is adapted to cross-correlate a received data signal with a complex conjugate of a received probe signal.

Preferably the receiver comprises an antenna for receiving signals and a demodulator for decoding the retrieved OFDM symbols and the PPC module is connected to the signal path between the antenna and the demodulator.

The receiver can further comprise a plurality of antennas.

Preferably the receiver comprises a plurality of PPC modules, wherein each PPC module is connected to at least one antenna and the receiver comprises an adder to add the outputs from the PPC modules together.

Preferably the output from the adder is provided to the demodulator.

Preferably, output from the the demodulator is provided to a de-interleaver and the output of the de-interleaver is provided to a decoder.

Preferably the receiver comprises memory coupled to the PPC module, whereby in use the memory stores the received probe signal and provides the probe signal to the PPC module.

Preferably the receiver comprises a decision module for extracting a probe signal from a received signal and providing the received probe signal to memory.

Preferably the decision module extracts the probe signal from a data frame in the received signal. Preferably the receiver comprises- a fast Fourier transform (FFT) module.

Preferably the PPC module is located on the signal path between the FFT module and the demodulator.

Preferably the receiver comprises a cyclic prefix removal module for removing a cyclic prefix from a received signal.

In another aspect of the present disclosure a firmware module is provided for use with an OFDM receiver, wherein the firmware module comprises means for performing PPC.

The term firmware is used herein as an umbrella term to cover any circuit or memory structure which is able to execute a number of processing steps which are instructions executable by, and stored in, the circuitry of a firmware module, or circuitry which can execute processing steps through the layout of the circuitry alone (i.e. the processing steps are hardwired into the circuitry).

The firmware module is preferably a programmable logic array (PLA) structure, a read only memory (ROM), a programmable read only memory (PROM), flash memory, a discrete semiconductor diode matrix, or an integrated matrix of field effect transistors coupled to a ROM and/or a PLA matrix.

Preferably, the firmware module comprises means for performing cross- correlation between received signals.

Preferably, the firmware module is adapted to cross-correlate a received data signal with a complex conjugate of a received probe signal. Preferably the firmware module is adapted to perform a plurality of parallel PPC operations in use, each PPC operation being associated with at least one antenna of a plurality of antennas. Preferably the firmware module comprises an adder to add the results of the parallel PPC operations together.

The firmware module can also comprise firmware for demodulating OFDM symbols.

Preferably the firmware for demodulating OFDM symbols is coupled to the output of the adder.

Preferably, the firmware comprises a de-interleaver coupled to the output from the demodulator and a decoder coupled to the output from the de-interleaver.

The firmware module may comprise memory, whereby in use the memory stores the received probe signal for use in performing PPC. Preferably the firmware module comprises firmware for extracting a probe signal from a received signal and providing the received probe signal to memory.

Preferably the firmware for extracting a probe signal extracts the probe signal from a data frame in the received signal.

The firmware module may comprise firmware for performing a fast Fourier transform (FFT).

Preferably the FFT is performed prior to PPC. The firmware module may also comprise firmware for removing a cyclic prefix from a received signal.

In a further aspect of the present disclosure a method is provided for extracting OFDM symbols from a received signal, wherein the method comprises performing PPC on the received signal.

The step of performing PPC comprises performing cross-correlation between received signals.

Preferably, the cross-correlation is performed between a received data signal and a complex conjugate of the received probe signal.

Preferably the method includes demodulating the retrieved OFDM symbols after PPC has been performed.

Preferably the method performs a plurality of parallel PPC operations where each PPC operation is associated with the signal received by at least one antenna of a plurality of antennas.

Preferably the method includes the step of adding the results of the plurality of parallel PPC operations together.

Preferably the sum of the results of the plurality of parallel PPC operations is demodulated.

Preferably, the demodulated signal is de-interleaved and decoded.

Preferably the method includes storing the received probe signal and providing the probe signal in order to perform PPC. Preferably the method includes extracting the probe signal from a received signal.

Preferably the probe signal is extracted from a data frame in the received signal.

Preferably the method includes performing a fast Fourier transform (FFT) on a received signal.

Preferably PPC is performed after the FFT and before demodulation.

Preferably the method includes the step of removing a cyclic prefix from a received signal.

In another embodiment a transmitter is provided for transmitting an OFDM signal, wherein the transmitter comprises a module for generating a PPC probe signal for transmission.

Preferably the transmitter transmits the PPC probe is sent as part of a data frame comprising a plurality of OFDM symbols.

Preferably the data frame corresponds to an OFDM data frame with a PPC probe.

Preferably module for generating the PPC probe signal generates a probe signal which does not comprise a complex element.

Preferably the control module controls how frequently PPC probe signals are transmitted. Preferably the rate at which PPC probe signals are sent is dependent upon on the rate of change of the channel and increases when the rate of change of the channel increases. Preferably PPC probe signals are sent at intervals of around 4 ms or alternatively at intervals of around of around 10 ms.

In the IEEE 802.1 1a standard, one probe symbol is needed for every thousand OFDM symbols. As an IEEE 802.1 1 a OFDM symbol has a duration of 4 με, a probe with duration of 4 με followed by data transmission of duration 4 ms is used. Alternatively, in the Long Term Evolution (LTE) standard, each data frame is 10 ms in duration, the first 0.1 ms is allocated to probe.

In another aspect of present disclosure a method of transmitting an OFDM signal is provided, wherein the method comprises the step of generating a PPC probe signal for transmission.

Preferably, the method comprises determining the rate at which PPC probe signals are sent. Preferably PPC probe signals are sent at intervals of around 4 ms or alternatively at intervals of around of around 10 ms.

Preferably the rate at which PPC probe signals are sent is dependent upon on the rate of change of the channel and increases when the rate of change of the channel increases.

Preferably the PPC probe is sent as part of a data frame comprising a plurality of OFDM symbols. Preferably the data frame corresponds to an OFDM data frame with a PPC probe. Preferably the PPC probe does not comprise a complex element.

In a further aspect a transmission firmware module for an OFDM system is provided, wherein the transmission firmware module is adapted to generate a PPC probe signal for transmission.

Preferably the transmission firmware module is adapted to insert the PPC probe into a data frame for transmission, the data frame comprising a plurality of OFDM symbols.

Preferably the data frame corresponds to an OFDM data frame with a PPC probe.

Preferably the transmission firmware module generates a probe signal which does not comprise a complex element.

Preferably, the transmission firmware determines the rate at which PPC probe signals are sent. Preferably PPC probe signals are sent at intervals of around 4 ms or alternatively at intervals of around of around 10 ms.

Preferably the rate at which PPC probe signals are sent by the transmission firmware is dependent upon on the rate of change of the channel and increases when the rate of change of the channel increases.

Figures

Embodiments of the present disclosure will now be described by way of example only and with reference to and as shown in the accompanying drawings, in which: Figure 1 is a block diagram of a conventional OFDM system; Figure 2 is a block diagram of a conventional PPC system;

Figure 3A is a diagrammatic representation of a system in accordance with the present disclosure;

Figures 3B and 3C are block diagrams of the system of figure 3A, showing the functional modules for the transmitter and receiver respectively in more detail;

Figures 4 and 5 show the results of a comparison between average bit error rates (BERs) from simulation results and predicted BERs; Figure 6 shows predicted BERs for a number of array elements;

Figure 7 shows a comparison between a system in accordance with the present disclosure and conventional OFDM and PPC systems, where each system has a single antenna;

Figure 8 shows a comparison between a system in accordance with the present disclosure and conventional OFDM and PPC systems, where each system has two antennas; Figure 9 shows the array diversity gain for systems having one, two, three, or four receiver array elements;

Figure 10 shows the impact of different levels of mutual coupling (p) on different systems; Figure 1 1 shows in more detail the impact of different levels of mutual coupling (p) on a system in accordance with the present disclosure.

Detailed description

The present disclosure is directed towards an OFDM system modified with PPC which significantly outperforms the conventional PPC system in terms of both power and spectral efficiency, and which has additional benefits with respect to the classical OFDM scheme. For example, it removes the need for robust channel estimation and subsequent equalisation is not required. It also delivers high performance data transfer while requiring only minor modification to the conventional OFDM receiver architecture.

In underwater acoustic communication systems (such as between remotely operated surveillance vehicles, underwater sensor networks, and in pipe networks for infrastructure monitoring), a transmitted signal can follow many different propagation paths before arriving at the receiver, each pathway having a different propagation delay. This causes multipath interference, where signals from different pathways interfere with each other due to the differences between the pathways. Multipath interference results in fluctuations in the received signal's amplitude, phase and angle of arrival resulting in multipath fading. In shallow water the acoustic channels available are particularly problematic because they exhibit large amounts of multipath interference. One technique used in under water acoustic wave communication systems is passive phase conjugation (PPC). This technique provides a simple low data rate receiver. PPC techniques have thus far been limited to underwater acoustics applications. A PPC system is shown in Fig. 2. Initially a source 210 transmits a signal which is used as a signal probe. After waiting for the multipath arrivals to clear, the source then transmits a data stream. At each element in the distant receiving array 230, the received probe is cross-correlated with the received data stream. Fig. 2 shows the transmitter 210 sending the signal Si and S₂ in sequence. These signals traverse through the channel H220 (assumed to be static over the transmission period of Si and S₂), and are observed by the receiver 230 as HSi and HS₂. The receiver cross-correlates HSi and HS₂, producing | H| ¾¾. This cross -correlation is done in parallel at each array element and the results are summed across the array to achieve the final communication suitable for demodulation. The autocorrelation of the channel impulse response | H| ² acts to reconcentrate, i.e., to focus coherently, the multipath arrivals. Whenever the propagation medium changes it is necessary to break up the data stream and insert new probe.

In all previously reported PPC systems, the message must be encoded in the correlation of the two consecutively transmitted waveforms Si and S2. To this end, two signalling schemes, namely pulse position modulation (PPM) and differential phase shift keying (DPSK) with Gold sequences are typically used.

The major shortcoming of these schemes is that they have low spectral efficiency

(i.e. they can only support low bit rates in the region of 0.02 bit/s/Hz in a typical case where the length of the employed Gold sequence is 32 bits. This is because multiple chips are required to represent a single information symbol.

Furthermore, the length of the chip sequence has to be large in order to achieve good cross-correlation properties. Figure 3A shows one possible example of a multipath communication system which combines OFDM and PPC (OFDM-PPC). The signal source 310 operates in a similar way to the conventional OFDM transmitter 1 10 described above and transmits a signal through a noisy shallow water channel 320. The channel comprises reflective boundaries such as the water's surface 321 and the sea / lake / river bed 323. The channel 320 also comprises a number of scattering objects 323. As shown in figure 3A, multiple paths for a transmitted signal exist between the transmitter 310 and the receiver 320. Each path has its own propagation time which will differ from the propagation time of another path. The system has R antennas 331 connected to R array elements. Of course, it is possible for a system in accordance with the present disclosure to have a single antenna connected to a single array element.

Figure 3B and Figure 3C are block diagrams of the transmitter and receiver respectively which are shown in figure 3A.

As shown in figure 3B and noted above, the transmitter 310 functions in a similar way to a conventional OFDM transmitter. At the transmitter 310, each group of two information bits {c„} is mapped into one of four Quadrature Phase-Shift Key (QPSK) symbols s„ by modulator 313. A set of N symbols is serial to parallel converted and imposed onto orthogonal sub-carriers by the means of an inverse fast Fourier transform (IFFT) module 314. The output from IFFT module 314 is then passed to a cyclic prefix (CP) module 315, where it is converted into serial data and a cyclic prefix (CP) is inserted to form one OFDM symbol for transmission. Each symbol is assigned to a subcarrier frequency and then transmitted at module 316 over a noisy channel (H) .

Optionally, as in this embodiment, the transmitter 310 can comprises a channel encoding module 31 1 and an interleaver 312. Channel encoding is used in conjunction with interleaving to improve bit error rate performance.

The signal is transmitted by module 316 as a data frame which contains an OFDM-PPC probe signal. Thus there is an agreed frame protocol which used by both the transmitter 310 and receiver 320 so that the receiver can extract the probe signal from the data frame. The frame protocol used should be selected based on channel conditions. For example, when the channel is slowly time-varying channel, such as an 802.1 1 based WLAN (Wireless Local Area Network) system, only one probe is needed for every 1000 OFDM symbols. In IEEE 802.1 1 a, each OFDM symbol has a duration of 4 με. Thus, a probe with duration of 4 με is used followed by data transmission of duration 4 ms. Thus, it is possible to specify that the first 0.1 % of data in a data frame is probe information. The transmitter 310 forms a frame by transmitting one probe symbol followed by nine hundred and ninety nine data symbols; after the receiver retrieves a frame of data, it treats the first symbol as a probe signal and the rest as information carrying signals.

In the LTE (Long Term Evolution) radio standard which is mostly concerned with mobile environments, one probe is needed for every 100 OFDM symbols. In LTE, each data frame is 10 ms in duration, the first 0.1 ms of which is allocated to the probe. The transmitter 310 forms a frame by transmitting one probe symbol followed by ninety nine data symbols; after the receiver retrieves a frame of data, it treats the first symbol as a probe signal and the rest as information carrying signals. Other frame formats are available, and the more stable the channel the greater the number of symbols that can be transmitted with a probe in a frame.

Unlike an OFDM probe signal, it is preferable that the OFDM-PPC probe signal does not have a complex component and is made up of a sequence of all real 1 s and 0s, i.e. positive real numbers. In this example the probe signal is an all-one sequence (i.e.

p2, -, PN] = [1 , 1, · · ·, 1])- Using such probe signals simplifies signal detection at receiver in the OFDM-PPC system.

As show in figure 3C, for this exemplary system the array elements of the receiver 330 operate in the same way as the conventional OFDM receiver 130 except that the equalization module 134 is replaced with a PPC module 334. Of course, other arrangements are possible such as, for example, a combination of equalization and PPC modules could be used.

After passing through channel 320, the symbols are received by receiver 330. The signals are initially picked up by the R antennas in a receiver array 331. CP is then removed by a remove CP modules 332.

Next a fast fourier transform (FFT) is performed on the signal by FFT modules 333. As described above when discussing a standard OFDM receiver the output of a FFT module 333 can be expressed as:

where H„ is the frequency response of the channel at the nth subcarrier.

Next the signal is passed to PPC modules 334 to detect the transmitted symbol from the signal received at the receiver. The first source signal Si can be represented by a sequence of N probes P = [pi, p₂, ..., PN] and which can be extracted from the received data frame and the second source signal S₂ can be represented by a transmitted sequence of N symbols S = [si, s₂, s_N].

The inputs corresponding to the probe P and data S to PPC module r connected to the rth (r = 1, 2, ... , R) receiver array 331 are represented as Y_P(r) and ¾τ) respectively. Y_P(r) and ¾(r) can be determined using the following equations:

Yp(r) =

and ¾(r) = [siHi{r) + &(r), s₂H₂{r) + ¾(r), ..., s II (r) + ξ^τ)], where: Sn(r) and ξ_η(τ) are zero mean AWGN with variance V₀ (i.e. s„(r), ξ_η(τ) ~ Ct (0, V₀). H_m( ) is the frequency response of the mth subcarrier corresponding to the channel between the source and the rth (r = 1, 2, ...,R) receiver array 331 element. H_m(r) can be expressed as

represents the magnitude of H_m(r) and <^(r) represents its phase.

Performing phase conjugation (element-wise cross-correlation of the above two sequences) and summing up the phase conjugation outputs of individual branches, we obtain the following equation 3:

/> ∑ // (r)^" · ) (r). p s.∑ //.(r)^" · ).(r). 1/ r) ^{' ■} e> (r)

Where p_n represents the complex conjugate of p_n; and

z is a vector, each element of which is the decision statistic corresponds to each subcarrier.

The noise term co_n(r) can be expressed in the following equation 4:

(o_n(r) =

ξ_η(τ), where n = 1, 2, ...,N.

In this embodiment, as probe is set to 1 (i.e. Si =1), \ H| ²Si*S₂= \ H| ²S₂. As phase modulation is used (such as for example phase-shift keying (PSK) modulation), I Η 1² does not affect the phase of the received signal. Therefore, | Η | ² can be considered merely a scaling factor and ignored during symbol decision. Thus, S2 can be recovered without an equaliser. Thus, when the probe is chosen to be an all-one sequence (i.e. [p_}, p_2, P_N] = [1, I, 1]) equation 3 can be simplified to give the following equation 5: z =

Γ R R R

s ∑ // . ( /· ) · ) (r ). s .∑ II Ar ) ^■ o Ar ). s_N∑ \H _N (r)| ² + ω_Ν (r)

_ r=\ r=\ r=\

The nth entry in equation 5 represents the decision statistics for the nth symbol, and is expressed below in equation 6:

^R 2 ^R

substituting G_Kfor∑|H„(r)| and c7_Kfor ^ co„(r) gives:

r=l r=l

^Zn = S„G„ + n

where m_n ~ C (0,F_ffl).

Equation 3 shows that the multipath induced phase shifts, §_m(r), have been removed by the passive phase conjugation operation. Consequently, the transmitted symbols can be recovered without the need for channel estimation (using standard OFDM pilot carrier methods) and subsequent equalisation.

The OFDM symbols output from the PPC modules are the summed together by an adder 335 and the symbols are then passed to a demodulator 336 where they are demodulated from QPSK. The demodulator 336 is coupled to a de- interleaver 337 and decoder 338 which convert the demodulated signal back to groups of two information bits {c„} . In this example, the PPC modules remove the need for explicit recovery of the channel and its subsequent equalisation. This follows from the fact that PPC implicitly recombines the multipath arrival signals instead of trying to invert the channel as required by direct channel equalisation methods. Thus OFDM-PPC mainly involves complex multiplication operations.

In contrast, direct channel equalisation methods require the channel be inverted. For example, as discussed above the equaliser coefficient (<¾) for conventional OFDM systems is derived as 1 1 H„ for a ZF equaliser or H„^* / ( | H„ | ² + δ_ν ²) for a MMSE equaliser. Thus, the equalisation process in conventional OFDM systems requires complex division operations due to the inversion of the channel.

Generally speaking, a complex divider requires three times more logic resources than a complex multiplier. In addition complex multiplication is a faster operation than complex division. For example, a 16-bit complex multiplier takes about three clock cycles to complete a multiplication, while a 16-bit complex divider could take up to twenty clock cycles to complete a division. Therefore, the computational load and latency is drastically reduced when compared to conventional OFDM schemes.

The only restriction of the proposed system is that the employed modulation scheme has to be M-ary Phase Shift Keying (PSK) for which information is carried by the phase. Consequently, symbol decision only depends on phase and amplitude scaling (due to the scaling factor ( | H„(r) | ²) does not impact on the symbol decision making process.

The scaling factor ( | H„(r) | ²) will affect the decision for a QAM system. For a PSK system, by passing the receiver output through a limiter (not shown) all amplitude variation is removed, thus removing | H„(r) | ². It is also evident from equation 3 that the signals from different branches are automatically and constructively added up. Consequently, a spatial diversity gain can be achieved by using multiple receiver array elements in the proposed OFDM-PPC system without additional computational overhead.

In addition, a method is provided for predicting the average bit error rate (BER) performance of an OFDM-PPC system with multiple array elements. For simplicity, the method assumes multipath channels with uniform power delay profile (PDP) and without mutual coupling.

Based on equation 4, we can derive the variance of the Gaussian random variable <¾(/") as

F<¾(r) = E[ I <%(r) | ²]

H_n(r) I ²EsE[ I s_n(r) \ ²] + \ H_n(r) \ ² E[ \ ξ_η(τ) \ ²]

= \ H_n(r) \ ²E_sVo + \ H_n(r) \ ²Vo] which gives the following equation 7: Fc„(r) = | H„(r) | V₀(^ + l) where E_s = E[ \ s„ \ ²] and is the average symbol energy.

The channel frequency response at the nth subcarrier is given by the nth discrete Fourier transform (DFT) coefficient of the channel impulse response. According to DFT definition, we get following equation 8:

where h(r) is the /th channel coefficient from the transmitter to the rth receiver array element and is assumed to be a zero mean complex Gaussian random variable with variance Pi(r) = E[ \ hif) \ Thus, the Gaussian random variable hi(r) can be denoted as hi(r) ~ CX(0, Pi(r)).

Since hi{x) is a complex Gaussian random variable, H„(r) is also a complex Gaussian random variable. Based on equation 8, its variance can be computed as

L-l

∑?i (r).

1=0

The above equation holds since | exp( co) | = 1 for any value of ω. We can now denote H»(r) as

Without loss of generality, we assume the variance of H_n (r) is normalized such that

Based on equation 7, the variance of ω_η is

V_m = E[ I ω_η I ²] = X V_→) = (E_s + l)V₀ X |H„ (rf substituting G or∑|H„(r , this gives (E_s + l)V₀G,

The signal-to-noise ratio (SNR) for the decision statistic z„ in equation 6 can be calculated as

G E_S _ G E_S G_nE_s

V_a (E_s + l)V₀G„ (E_s + l)V₀

In the case of QPSK modulation, one symbol corresponds to 2 bits, the relation between symbol energy and bit energy is £_s = 2E_b, therefore

2G E_h

SNR

(2E_b + l)V₀

The bit error probability is denoted as P_b and is a measure of the bit error rate (BER) uniquely determined by the SNR, more specifically (and as described in the text book "Digital Communications" by J. Proakis), P_b = Q( sNR), where Q(x) is the complementary Gaussian cumulative distribution function and is explained below in more detail. Therefore, the bit error probability conditioned on the random variable G„ can be expressed as:

as described in "Digital Communications" by J. Proakis, the complementary Gaussian cumulative distribution function Q is given by

In order to obtain the average bit error probability, we need to average Pb(G„) over the distribution of the random variable G„, as shown in equation 8:

where f(G„) is the probability density function (PDF) of G„. Since H_n(r) is a Gaussian random variable, | H„(r) | ² is a Chi-square random variable. From "Digital Communications" by J. Proakis, a Chi-square random variable has the following characteristic function:

L-l

where y_r = ^ P, (r) and r

Considering the multipath having uniform power delay profile (PDP), i.e., interference is assumed to be identically distributed with the same interference parameter, we have y_r = /for all r. Since | H„(l) | ², | H„(2) | ², | H„{R) \ ² are statistically independent random variables, the characteristic function of G_n can be expressed as :

G„ =

Where ]^~[ denotes the product operation. Taking the inverse Fourier transform of equation 9, we obtain the PDF of G as shown: j{G_n) = (f(R - 1)!)-^/- ^;exp(-G„/7), G„≥ 0.

Substituting/(G„) into equation 8 p_b (G_n )f(G_n )dG_n gives equation 10:

This equation for Φ above is an e uation having the following form:

where μ = and Γ(Ζ) is the Gamma function of Z, i.e.

r(z) = jt^i_1 exp(- t)dt, where Z > 0. If Z is a positive integer, Γ(Ζ)

Thus, by assigning a can calculate Φ as

shown below:

Therefore, the closed-form expression for the average bit error probability for the OFDM-PPC system can be as shown below in equation 1 1 :

The analytical results from equation 1 1 for different numbers of array elements are compared with the simulation results in Figs. 4 and 5. Here the FFT size is 512 PSK symbols, the length of cyclic prefix (CP) is 16 samples, the channel has 13 taps with uniform PDP. It can be seen from Figs. 4 and 5 that equation 1 1 provides results which are in close agreement with the simulation results, while providing further insights into the behaviour of an OFDM-PPC system and a prediction of its BER performance.

Fig. 6 shows the performance of an OFDM-PPC system predicted by equation 1 1 for different number of array elements. These results suggest that BER of 10^"6 can be achieved a E_bIV₀ of 20 dB for ? = 5 in an OFDM-PPC system without channel coding.

Fig. 7 shows a comparison between an OFDM system comprising a PPC module (OFDM-PPC) and both the conventional PPC approach and the conventional OFDM approach for systems with a single array element. To obtain the data shown in figure 7 simulations were run. For simulation of the multipath channels, the SUI-3 channel model used for the 802.16d fixed WiMAX systems as described in the article entitled "Channel models for fixed wireless applications" by V. Erceg et al. was used. This has a tap spacing of 500ns, and maximum tap delay of 1000ns. For the conventional PPC system, we use DPSK modulation and Gold codes of length 31 , the data rate is 64.5 Kbps; for the OFDM based systems, the modulation scheme is QPSK, the FFT size is chosen to be N = 64, the length of CP is 4, the data rate is 4 Mbps.

Fig. 7 shows that for a single input single output situation, an OFDM-PPC system is superior to a conventional PPC system in terms of bit error rate (BER) performance. Note that DPSK with PPC is superior to DPSK without PPC because PPC can focus the multipath arrivals and remove phase ambiguity.

The OFDM-PPC system is also much more spectrally efficient than a

conventional PPC system. In the conventional PPC system, one Gold sequence (which occupies L time slots, where L is the length of the Gold sequence) only carries one information bit; whereas in an OFDM-PPC system each time slot carries two information bits with QPSK modulation. If we assume the channel remains static during the transmission of M OFDM symbols (meaning that only one OFDM probe needs to be transmitted for every M OFDM data symbols), the spectral gain with respect to the Gold sequence approach is 2LM/(M + 1 ). The length of Gold sequence L needs to be increased in order to decrease cross- correlations and improve the performance of the DPSK-PPC system. In Fig. 7 we also compare an OFDM-PPC system with a conventional OFDM system having:

i) imperfect channel estimation (real CE); and

ii) perfect knowledge of the channel information (perfect CE).

In the first case, we estimate the channel with the probe; in the latter case, we assume the channel frequency response H„ is perfectly known to the receiver, this serves as a performance lower bound for the OFDM system.

Fig. 7 shows that OFDM-PPC yields almost identical performance to the conventional OFDM system employing ZF equaliser with real CE. However, this is achieved at a much lower complexity since channel estimation and

equalisation are not needed. In addition, the complex multiplication involved in PPC module of the OFDM-PPC system is much easier to implement than the complex division involved in equalisation. The price paid for this is a loss of spectral efficiency (transmission rate) of a factor of 1/M, but it should be noted that the conventional OFDM systems also lose spectral efficiency through needing pilots for channel estimation. One can also observe from Fig. 7 that both systems are 3 dB above the performance lower bound obtained by assuming the perfect channel estimate.

In IEEE 802.1 1 a, each OFDM symbol has a duration of 4με (Ο.δμε for CP and 3.2με for data). Channel estimation is carried out for each burst which has a duration of 4 ms for indoor environment. In this case, M = 1000, i.e. only one probe is needed for every 1000 OFDM symbols. In the LTE radio standard which is mostly concerned with mobile environments, channel coherence time is equal to 9 ms at 30 km/h, and LTE frames are 10 ms in duration. These are divided into 10 subframes, each subframe being 1 .0 ms long. Each subframe is further divided into two slots, each of 0.5 ms duration. Slots consist of either 6 or 7 OFDM symbols, depending on whether the normal or extended cyclic prefix is employed. In this case, M « 100, i.e., only one probe is needed for every 100 OFDM symbols. Consequently, in either of these cases a spectrum loss of MM = 0.01 or 0.001 is not significant.

Turning to systems having a plurality of array elements (i.e. R > 1 ), figure 8 shows that for the conventional OFDM system the MMSE equaliser generally performs much better than the ZF equaliser for systems with multiple array elements, therefore the MMSE equaliser will be used for the purpose of the comparisons to follow.

Figure 9 shows the array diversity gain for plots corresponding to R = 1 , 2, 3, and 4 respectively. Here it can be seen that the performances of all the configurations simulated improve significantly as the number of array elements R increases.

When R > 1 , the performance of an OFDM-PPC system becomes superior to the conventional OFDM system with real CE and converges to that of the

conventional OFDM system with perfect CE estimate at SNR greater than 15 dB. This is due to the fact that the OFDM-PPC system achieves array diversity gain by automatic maximum ratio combining and automatic constructive signals summation from different array elements.

In contrast, the FFT-Equalisation process in the conventional OFDM system leads to equal gain combining when multiple array elements are employed, therefore, the achievable diversity gain is smaller.

In real propagation environments, source to receiver array channels are correlated to a certain extent due to their finite separation, geometry of array and effect of surrounding objects in the near field of the receiving antenna elements. For the purpose of evaluating the effect that mutual coupling between receiver elements has on PPC-OFDM system behaviour, the mutual coupling is defined, as the envelope correlation coefficient (p) between signals received at each array element, i.e.

_ E{(^ (/) - E{^ (/)})(^ (/) - E{^ (/)})^*}

E{|(A,- (0 - E{h_t (/)}|² }E{\h_m (/) - E{h_m (/)}|} ²

where: il) denotes the channel coefficient corresponding to the /th tap of the impulse response of the channel between the source and the /th/mth receiver array element; E{x} denotes the entropy of x (where entropy is a measure of the amount information in a random variable); and var( ) and COV(JC) are the statistical variance and covariance functions respectively. As described in the article entitled "Signal correlation including antenna coupling" by A. Derneryd et al., the value of p for practical half-wave dipole antennas is in the range of 0.2 and 0.3 for the antenna separation of half a wavelength.

In Fig. 10, we show the impact of mutual coupling on the performance of different systems. Here the number of array element R = 2, and the correlation factor p is set to be 0.0, 0.2, 0.4, and 0.6 respectively. This shows that mutual coupling has a detrimental effect on all the configurations simulated. As the value of p increases, the difference between the conventional OFDM with perfect CE and OFDM-PPC remain relatively similar for 0.2 < p < 0.6, and still outperform the conventional OFDM with real CE in the presence of strong mutual coupling (p = 0.6). The impact of the mutual coupling is further examined for the OFDM-PPC system in Fig. 1 1 for ? = 4. It is evident from this figure that the array diversity gradually diminishes as the correlation factor increases. One can also see that small mutual couplings (e.g. p = 0.2) do not have noticeable effect on system

performance.

The OFDM technique is widely used in the practical radio communication systems to combat frequency selective fading. On the other hand, PPC has been adopted within the underwater acoustic communications community in order to constructively combine multipath arrivals. We have introduced a novel OFDM- PPC scheme which utilizes the desired properties of both OFDM and PPC, and which requires only minor modification to the classic OFDM system.

The results we obtained show that the proposed system outperforms both the conventional PPC (higher power and spectral efficiencies) and the conventional OFDM systems (no need for sophisticated channel estimation and equalisation methods) while preserving reduced computational complexity. OFDM-PPC is shown to be more advantageous in systems with multiple receiver array elements by facilitating automatic and constructive combining of the signals received, this is in contrast to the equal gain combining experienced in the conventional OFDM system.

The OFDM-PPC system described herein has applications in any situation where the propagation environment is unknown or cannot be accurately estimated. Embodiments of the OFDM-PPC system are advantageous in that they enable autocorrelation of the channel response, making it possible to refocus multipath signals and obviating the need for channel inversion.

Improvements and modifications may be made without departing from the scope of the invention which is defined by the appended claims.

Claims

Claims

1. A receiver for retrieving OFDM symbols from a received signal, wherein the receiver comprises a passive phase conjugation module.

2. The receiver of claim 1 wherein the passive phase conjugation module is adapted to cross-correlate a received data signal with a complex conjugate of a received probe signal.

3. The receiver of any preceding claim wherein the receiver comprises an antenna for receiving signals and a demodulator for decoding the retrieved OFDM symbols and the passive phase conjugation module is connected to the signal path between the antenna and the demodulator.

4. The receiver of claim 3 further comprising a plurality of antennas.

5. The receiver of claim 4 further comprising a plurality of passive phase conjugation modules, wherein each passive phase conjugation module is connected to at least one antenna and the receiver comprises an adder to add the outputs from the passive phase conjugation modules together.

6. The receiver of claim 5 wherein the output from the adder is provided to the demodulator.

7. The receiver of any one of claims 3 to 6 wherein the output from the demodulator is provided to a de-interleaver and the output of the de-interleaver is provided to a decoder.

8. The receiver of any preceding claim, further comprising memory coupled to the passive phase conjugation module, whereby in use the memory stores the received probe signal and provides the probe signal to the passive phase conjugation module.

9. The receiver of claim 8, further comprising decision module for extracting a probe signal from a received signal and providing the received probe signal to memory.

10. The receiver of claim 9, wherein the decision module extracts the probe signal from a data frame in the received signal.

1 1. The receiver of any preceding claim further comprising a fast Fourier transform (FFT) module.

12. The receiver of claim 1 1 , wherein the passive phase conjugation module is located on the signal path between the FFT module and the demodulator.

13. The receiver of any preceding claim further comprising a cyclic prefix removal module for removing a cyclic prefix from a received signal.

14. A firmware module for use with an OFDM receiver, wherein the firmware module comprises means for performing passive phase conjugation.

15. The firmware module of claim 14 wherein the firmware module is adapted to cross -correlate a received data signal with a complex conjugate of a received probe signal.

16. The firmware module of claim 14 or claim 15 wherein the firmware module is adapted to perform a plurality of parallel passive phase conjugation operations in use, each passive phase conjugation operation being associated with at least one antenna of a plurality of antennas.

17. The firmware module of any one of claims 14 to 16 wherein the firmware module comprises an adder to add the results of the parallel passive phase conjugation operations together.

18. The firmware module of any one of claims 14 to 17 wherein the firmware comprises firmware for demodulating OFDM symbols.

19. The firmware module of claim 18 when dependent upon claim 17 wherein the firmware for demodulating OFDM symbols is coupled to the output of the adder.

20. The firmware module of claim 19 wherein the firmware comprises a de- interleaver coupled to the output from the demodulator and a decoder coupled to the output from the de-interleaver.

21. The firmware module of any one of claims 14 to 20 further comprising memory, whereby in use the memory stores the received probe signal for use in performing passive phase conjugation .

22. The firmware module of claim 21 comprising firmware for extracting a probe signal from a received signal and providing the received probe signal to memory.

23. The firmware module of claim 22 wherein the firmware for extracting a probe signal extracts the probe signal from a data frame in the received signal.

24. The firmware module of any one of claims 14 to 23 comprising firmware for performing a fast Fourier transform (FFT).

25. The firmware module of claim 24 wherein the FFT is performed prior to passive phase conjugation.

26. The firmware module of any one of claims 14 to 26 comprising firmware for removing a cyclic prefix from a received signal.

27. A method for extracting OFDM symbols from a received signal, the method comprising performing passive phase conjugation on the received signal.

28. The method of claim 27, wherein cross-correlation is performed between a received data signal and a complex conjugate of a received probe signal.

29. The method of claim 27 or claim 28 wherein the method includes

demodulating the retrieved OFDM symbols after passive phase conjugation has been performed.

30. The method of any one of claims 27 to 29 wherein a plurality of parallel passive phase conjugation operations are performed, each passive phase conjugation operation being associated with the signal received by at least one antenna of a plurality of antennas.

31. The method of claim 30 further comprising the step of adding the results of the plurality of parallel passive phase conjugation operations together.

32. The method of claim 31 , wherein the sum of the results of the plurality of parallel passive phase conjugation operations is demodulated.

33. The method of claim 32, wherein the demodulated signal is de-interleaved and decoded.

34. The method of any one of claims 27 to 33, wherein the method includes storing the received probe signal and providing the probe signal in order to perform passive phase conjugation.

35. The method of any one of claims 27 to 34 wherein the method includes extracting the probe signal from a received signal.

36. The method of claim 35 wherein the probe signal is extracted from a data frame in the received signal.

37. The method of any one of claims 27 to 36, wherein the method includes performing a fast Fourier transform (FFT) on a received signal.

38. The method of claim 37, wherein passive phase conjugation is performed after the FFT and before demodulation.

39. The method of any one of claim 27 to 38, wherein the method includes the step of removing a cyclic prefix from a received signal.

40. A transmitter for transmitting an OFDM signal, wherein the transmitter comprises a module for generating a passive phase conjugation probe signal for transmission.

41. The transmitter of claim 40 comprising a control module for controlling how frequently passive phase conjugation probe signals are transmitted.

42. The transmitter of claim 41 wherein passive phase conjugation probe signals are sent at intervals of around 4 ms or at intervals of around 10 ms.

43. The transmitter of claim 41 or claim 42 wherein the rate at which passive phase conjugation probe signals are sent by the control module is based on the rate of change of the channel and increases when the rate of change of the channel increases.

44. The transmitter of any one of claims 40 to 43 wherein the transmitter is adapted to send the PPC probe as part of a data frame comprising a plurality of OFDM symbols.

45. The transmitter of claim 44 wherein the data frame corresponds to an OFDM data frame with a PPC probe.

46. The transmitter of any one of claims 40 to 45 wherein the module for generating the PPC probe signal generates a probe signal which does not comprise a complex element.

47. A method of transmitting an OFDM signal, wherein the method comprises the step of generating a passive phase conjugation probe signal for transmission.

48. The method of claim 47 comprising determining the rate at which passive phase conjugation probe signals are sent.

49. The method of claim 48 wherein passive phase conjugation probe signals are sent at intervals of around 4 ms or at intervals of around 10 ms.

50. The method of claim 48 or claim 49, wherein the rate at which passive phase conjugation probe signals are sent is dependent upon on the rate of change of the channel and increases when the rate of change of the channel increases.

51 . The method of any one of claims 47 to 50, wherein the passive phase conjugation probe is sent as part of a data frame comprising a plurality of OFDM symbols.

52. The method of claim 51 wherein the data frame corresponds to an OFDM data frame with a passive phase conjugation probe.

53. The method of any one of claims 47 to 52, wherein the PPC probe does not comprise a complex element.

54. A transmission firmware module for an OFDM system, wherein the transmission firmware module is adapted to generate a passive phase

conjugation probe signal for transmission.

55. The transmission firmware module of claim 54, wherein the transmission firmware determines the rate at which passive phase conjugation probe signals are sent.

56. The transmission firmware module of claim 55, wherein the transmission firmware sends passive phase conjugation probe signals at intervals of around 4 ms or at intervals of around 10 ms.

57. The transmission firmware module of claim 54 or 55 wherein the rate at which passive phase conjugation probe signals are sent by the transmission firmware is dependent upon on the rate of change of the channel and increases when the rate of change of the channel increases.

58. The transmission firmware module of any one of claims 54 to 57 wherein the transmission firmware module is adapted to insert the PPC probe into a data frame for transmission, the data frame comprising a plurality of OFDM symbols.

59. The transmission firmware module of 58 wherein the data frame corresponds to an OFDM data frame with a PPC probe.

60. The transmission firmware module of any one of claims 54 to 59 wherein the transmission firmware module generates a probe signal which does not comprise a complex element.