Abstract:
A system for doing BLAST with fewer receive antennas or even only one receiving antenna is provided. A system implementation architecture is provided together with a detailed analysis on its principle and theory behind this engineering solution to reduce the MIMO technology cost by using fewer antennas whilst achieving high spectrum efficiency. Examples are provided on how to implement this idea in a CDMA platform and in a OFDM platform. For the CDMA system, the code space is automatically doubled or tripled and therefore a significant system capacity increase is realized. For OFDM systems, the throughput is doubled similar as 2×2 blasting. The system complexity is minimum and full standards backward compatibility can be achieved.

Description:
FIELD OF THE INVENTION  
       [0001]     The invention relates to MIMO (multiple input, multiple output) transmitters and receivers, systems and methods, and more specifically to such systems designed to have fewer antennas or only one antenna in the receiver.  
       BACKGROUND OF THE INVENTION  
       [0002]     Over the past decade, there has been a revolution in the ways in which we communicate. The Internet has created the demand for high information transfer rates, while cell phones and other mobile wireless devices have fueled the desire for ubiquitous connectivity. A significant hurdle on the road toward achieving high data rate transmission is the limit on the amount of reliable information exchange between two ends, which is known as the channel capacity C. Channel capacity is the maximum value of the so called mutual information between the transmitter and the receiver that is given by Claude Shannon&#39;s famous formula:  
       C   =     W   ⁢           ⁢     log   ⁡     (     1   +     S     W   ×   No         )             
 
 or a normalized version  
             C   =         log   2     ⁡     (     1   +     S   N       )       ⁢           ⁢   bps   ⁢     /     ⁢   Hz             (   1   )             
 
 where, S is the received signal power, N=W×No is the noise power, and information is measured in bits per second per Hertz. W is the available bandwidth. 
 
         [0005]     With the transmission maximum power limited and the frequency spectrum overcrowded, Shannon&#39;s expression does not seem to leave much room for increasing the information capacity. It shows a logarithmic increase in capacity as SNR (signal-to-noise ratio) increases. Roughly speaking, the channel can reliably deliver one extra bit per 5 dB SNR increase.  
         [0006]     A careful review of Shannon&#39;s capacity formula derivation (refer to C. E. Shannon, a Mathematical theory of communication, Bell Systems Technical Journal, Vol.27, (1948), pp 379-423.) reveals that Shannon made the following three key assumptions: 
        1) the communication channel is point-to-point;     2) the-communication channel is memoryless; and     3) the communication channel is stationary and flat and only AWGN (additive white Gaussian noise) is present.        
 
         [0010]     However, in many real wireless communication environments (i.e. channels), wireless transmissions with wavelengths of roughly 10-30 cm are readily scattered by surrounding objects such as buildings, mountains, trees, desks, cars, and so on. In the presence of such scattering objects, there are a number of paths from the transmitter to the receiver which collectively form the actual wireless communication channel. These real environments do not strictly satisfy Shannon&#39;s assumptions and therefore the question has been posed as to whether one can go beyond Shannon&#39;s capacity limit. Many researchers have claimed a ‘Yes’ answer to this question. However, the theories proposed thus far have been lacking of convincing proofs and/or are based upon a misleading assumption.  
         [0011]     Over the past several years, multiple transmitting antennae and multiple receiving antennae systems (usually referred to as MIMO systems) have increasingly been investigated to surpass Shannon&#39;s limit. In 1996, Gerry Foschini at Bell Labs theorized that the key to beating the logarithmic nature of (1) is to exploit the scattering inherently present in the wireless communication environment [G. J. Foschini, M. Cans, on limits of wireless communications in a fading environment when using multiple antennas, Personal Communications 6, 311 (1998)]. The plurality of paths in a wireless communication environment, while appearing to only complicate matters, turns out to be a more reliable information transfer pipe. Roughly speaking, a different signal message (or a different bit stream) can be sent over each distinct path between the transmitting and receiving antenna arrays, thus increasing the information transfer rate as many times as the number of distinct channels. Foschini came up with a coding and decoding scheme, known now as BLAST (Bell Labs Space Time Architecture) that obtains these higher information-transfer rates even when the details of the scattering environment are not known to the transmitter. Generally, the idea of sending multiple distinct signals between multiple antenna arrays is known as MIMO.  
         [0012]     To increase the information rate, M T  different bit streams are sent via the same physical channel from each of M T  transmitting antennas, respectively. The channel can be defined in frequency, time or by an orthogonal code. If the bit streams can be decoded at the receiver array, the information transfer rate can become roughly M T  times as large as that for single-antenna transmission with the same resource. More precisely, Shannon&#39;s capacity formula can be reproduced as  
             C   =       M   T     ⁢           ⁢     log   ⁡     (     1   +         M   R     ⁡     (     S   /     M   T       )       N       )       ⁢           ⁢   bps   ⁢     /     ⁢   Hz             (   2   )             
 
 Note that in order to decode the M T  separate transmitted signals, the number of receiver antennas, M R , must be at least as many as the number of transmitter antennas, M T  according to the state of the art of BLAST technology today. The above expression assumes that the total transmitted power is kept constant regardless of the number of transmitting antennas M T . In other words, each of the M T  bit streams is transmitted with power S/M T . Sending M T  different bit streams is advantageous, because it results in an increased information transfer rate by a factor of M T , as compared to beam steering approaches that only increase the information transfer rate logarithmically. In fact, when the system is configured as M×1 (M transmitters transmitting the same bit stream and 1 receiver) or 1×M (1 transmitter and M receivers), the capacity formula is  
             C   =       log   ⁡     (     1   +     M   ⁢           ⁢     S   N         )       ⁢           ⁢   bps   ⁢     /     ⁢   Hz             (   3   )             
 
 Theoretically MIMO has a higher spectrum efficiency gain over the conventional diversity configuration. Unfortunately, this promising approach only works if the M T  original signals can be separated from the M R  received signals. 
 
         [0015]     A practical case in which it does not work is when the number of receiving antennas M R  is significantly less than the number of transmitting antennas M T  or when only one receiving antenna is deployed.  
         [0016]     Another case in which it dramatically fails is when the propagating wireless signals do not scatter off any obstacles, the so-called LOS (line-of-sight) case. The problem here is that, in some practical scenarios, all M R  antennas in the receiving antenna array receive essentially the same combination of the M T  different transmitted signals (up to a global phase shift). That is, there is little or no diversity between the M R  received signals. It is then extremely difficult if not impossible to distinguish the M T  individual transmitted signals from one another. Thus, beam steering remains the best approach in the line-of-sight case.  
         [0017]     For the MIMO system to function properly, there is an eigen condition on the channel matrix H. The requirement is that the matrix H*H is “well conditioned”, where H* is the complex conjugate of the channel matrix H. A well conditioned matrix has full rank and has eigen values which are not extremely separated. The actual amount of separation between the eigen values that can be tolerated in a given system will be a function of the noise conditions. In the various practical scenarios mentioned above, this condition fails for the eigen values to be satisfied.  
         [0018]     This situation can be understood by simple optics. In order for the receiver to “see” that distinct signals are being transmitted from the M T  distinct transmitting antennas, it must be able to resolve a geometric angle of less than α=L T /d, where L T  is the size of the transmitting array and d is the distance between the transmitting and receiving arrays. However, if one thinks of the receiver as a lens whose aperture is its size L R , its diffraction-limited angular resolution is α=λ/L R , where λ is the wavelength. Thus, if λL R &gt;&gt;L T /d, which is almost always true for cell-phone systems, it is impossible for the receiver to resolve the individual transmitted signals. Another case that is well observed in the real environment is the so called “Keyhole” phenomenon that will collapse the MIMO capacity into a diversity capacity.  
         [0019]     The presence of scattering objects in the environment effectively increases the aperture of the receiver lens that looks at the transmitting array. In other words, the scattering objects act as a large complex lens that allows the receiving array to distinguish the several different signals from a relatively small transmitter array. It is critical that, in the presence of scattering, the receiver receives power from a wide range of directions, so that the finite angular resolution of the receiver is not a limiting factor.  
         [0020]     As a simple example consider the case shown in  FIG. 1  where there are two distinct paths  14 , 16  from a transmitter array  10  having two antennas to a receiver array  12  having two antennas: one of the paths  14  is along the line of sight and the other path  16  bounces off a scattering object  18 . Generically speaking, the outputs of the two receiving antennas in array  12  are two different linear combinations of the signals arriving from the two directions. Similarly, the signals from the two directions are two different linear combinations of the inputs to the two transmitting antennas. Thus the outputs are independent linear combinations of the inputs and can be deduced from the outputs. Therefore, if two different bit streams are sent by the transmitting antennas, the receiver will be able to recover them.  
         [0021]     As discussed above, being able to receive two distinguishable bit streams essentially doubles the transferred information capacity. More generally, if there are M distinct paths from the transmitting to the receiving array, and there are at least M transmitters and M receivers, then the capacity may be increased M times. The maximum number of fully independent paths that can exist in a scattering environment turns out to be related to the length of time the radiation remains confined in that environment before escaping or being absorbed.  
         [0022]     Another way to understand this capacity increase is to think in terms of phased-array techniques. With appropriately phased inputs to the transmitting antennas, the transmitter can beam steer one bit stream in one direction (along the line-of-sight path), or beam steer another bit stream in a different direction (toward the scattering object). By summing the inputs for these two cases (by the superposition principle), the transmitter will simultaneously send one bit stream along one direction and the other bit stream in the other direction. Similarly, two different combinations of the received outputs with appropriate phases will give the incoming signals from the two different directions. Thus each of the two bit streams can literally be sent over each of the two different paths and be independently received.  
         [0023]     MIMO systems have become very attractive since the previously mention paper by Foshini defining the BLAST technique. However, MIMO systems usually need the number of receiver antennas to be greater or equal to the number of independent data transmission chains. When the number of receiving antennas is less than the number of independent data transmission chains, the MIMO service cannot always be guaranteed. This practical limitation makes it difficult to apply MIMO technology to terminal designs because one RF (radio frequency) chain contributes a significant part of the whole terminal cost, and multiple RF chains will result in too large of an expense. Particularly, most of the wireless terminals on the market, if not all of them, have a single receiving antenna which means that the MIMO technology cannot be applied to these wireless terminals including TDMA, CDMA, WCDMA, 802.11 a/b and 802.16 etc.  
         [0024]     An example of a current transmitter and receiver for 3GPP/UMTS is shown in  FIG. 2 . The transmitter is generally indicated at  501  and the receiver at  503 . The transmitter has two generic channels P-SCH  500  and S-SCH  502  which are not user specific. Channel P-SCH  500  undergoes gain G P    510  and channel S-SCH  502  undergoes gain G S    512 . The two generic channels are combined in adder  514 . Channels  504 ,  506 ,  508  are the channels which are sent to a specific user. There would be multiple sets of these channels for different users. Shown is the pilot channel PICH  504  and dedicated channels DDCH  1   506  . . . DDCH N  508 . The pilot channel  504  is multiplied by spreading code C PICH    504  and undergoes gain G PICH    517 . Each of the channels  506  . . .  508  is spread by a respective code C D1    516  . . . , C DN    518  and undergoes respective gain G D1    519  . . . G DN    520 . Each of the user specific channels are combined at adder  522  and is scrambled by the same scrambling code at  524 . The generic channels are then combined with the user specific channels at adder  526 , lowpass filtered at  528  and digital-to-analog converted at  530  before being transmitted through antenna  532 .  
         [0025]     In the receiver, the receive antenna is indicated at  540 . The signal received through the receive antenna  540  is converted back to digital form in ADC  542 . The output of the ADC  542  is processed by synchronization block  544  which performs synchronization in both time and frequency. A frequency control output  545  is fed back to the ADC  542 . The output of the synchronization block  544  is fed to finger detection block  546  which processes the synchronized signal to determine finger locations. Finger control block  548  receives the finger locations from the finger detection block  546  and controls the de-scrambling operation  550 . The output of the de-scrambler  550  goes to de-spreader  552  which in turn goes to a RAKE combiner  554  which outputs soft bits for decoding indicated at  555 .  
         [0026]     In conventional OFDM (orthogonal frequency division multiplexing) systems, the subcarrier pulse used for transmission is chosen to be rectangular. This has the advantage that the task of pulse forming and modulation can be performed by a simple Inverse Discrete Fourier Transform (IDFT) which can be implemented very efficiently as an Inverse Fast Fourier Transform (IFFT). Advantageously in a receiver only a Fast Fourier Transform (FFT) operation is required to reverse this operation. According to the theorem of the Fourier transform, the rectangular pulse shape will lead to a sin(x)/x type of spectrum of the subcarriers.  
         [0027]     The frequency spectrums of the OFDM subcarriers are not separate, but in fact they overlap. The reason why the information transmitted over the carriers can still be separated is the so-called orthogonality relationship giving the method its name. By using an IFFT for modulation the spacing of the subcarriers is implicitly chosen in such a way that at the frequency where a particular received subcarrier signal is evaluated all other received subcarrier signals are very close to zero. In order for this orthogonality to be preserved the following must be true: 
        a) the receiver and the transmitter must be perfectly synchronized. This means they both must assume exactly the same modulation frequency and the same time-scale for transmission;     b) the analog components, both in the transmitter and receiver, must be of very high quality; and     c) there should be no multipath channel.        
 
         [0031]     To deal with the multipath channel constraint the OFDM symbols are artificially prolonged by periodically repeating the ‘tail’ of the symbol and preceding the symbol with it. At the receiver, this guard interval is removed. As long as the length of this guard interval Δ is longer than the maximum channel delay τ max , all reflections of previous symbols are removed and the orthogonality is preserved. By preceding the useful information, of length T u , by the guard interval some parts of the signal are lost since the guard interval is not being used to transmit useful information. Taking all this into account the signal model for the OFDM transmission over a multipath channel becomes very simple: The transmitted symbols at time-slot l and subcarrier k are only disturbed by a factor H l,k  which is the channel transfer function (the Fourier transform of the multipath channel) at the subcarrier frequency, and by AWGN n(l,k) 
 
 z   l,k =α l,k   H   l,k   +n (l,k)   (4) 
 
 The influence of the channel can easily be removed by dividing by H l,k . 
 
         [0033]     The general structures of the traditional OFDM transmitter and receiver are symbolically illustrated in  FIG. 3 . The transmitter, generally indicated by  100 , performs channel coding  104  on input bits  102 , followed by symbol mapping  106 . Serial-to-parallel conversion is indicated at  108 . The parallel output is processed by the IFFT function  110 . The output of the IFFT function is fed through a parallel-to-serial function  112 . Next, the guard banding and or cyclic extension and windowing etc. are performed as indicated at  114 . Digital-to-analog conversion is then performed at  116  followed by RF transmission  118  over antenna  120 . Similarly, at the receiver, generally indicated at  122 , processing generally follows the reverse of that which occurred in the transmitter beginning with RF reception  126  occurring via receive antenna  124 . Analog-to-digital conversion  128  precedes time frequency synchronization  130 . At  132 , the cyclic extension is removed. Serial-to-parallel conversion  134  is followed by FFT  136 , parallel-to-serial conversion  138 , symbol demapping  140  and decoding  142  to produce the received bit stream  144 .  
       SUMMARY OF THE INVENTION  
       [0034]     According to one broad aspect, the invention provides a transmitter comprising: N transmit antennas, where N&gt;=2; wherein the transmitter is adapted to transmit a respective one of N transmit signals from each of the N antennas, the N transmit signals collectively containing a plurality N of main signals and a plurality of delayed main signals each delayed main signal being a delayed version of one of the main signals, wherein each transmit signal comprises a combination of a respective main signal of the plurality of main signals and at least one respective delayed main signal of the N delayed main signals.  
         [0035]     In some embodiments, the N transmit signals comprise a Jth transmit signal Transmit J  from antenna J=1, . . . , N, and wherein Transmit J  comprises:  
         Transmit   J     =         α   J     ⁢       T   J     ⁡     (     S   J     )         +       ∑     i   =   1       K   J       ⁢       α     i   ⁢           ⁢   J       ⁢       T     i   ,   J       ⁡     (       S     i   ⁢           ⁢   J       ⁡     (     t   -     D   iJ       )       )                 
 
 S J =is the Jth main signal of the plurality of main signals; α J =is a virtual spatial reflector applied to the Jth main signal; T J =is a transformation applied to the Jth main signal; K J  is a number of delayed signals included in the Jth transmit signal; α iJ =is a virtual spatial reflector applied to the ith delayed signal included in the Jth transmit signal; S iJ , i=1, . . . , K J  are the signals which are to be delayed and included in the Jth transmit signal where each iJ ε 1, . . . , N; D iJ =is a delay applied to signal S iJ ; T iJ =is a transformation applied to the ith delayed signal included in the Jth transmit signal. 
 
         [0037]     In some embodiments, each transmit signal comprises a CDMA signal.  
         [0038]     In some embodiments, each main signal comprises a respective combined set of at least one code separated channel.  
         [0039]     In some embodiments, each transmit signal further comprises at least one additional code separated channel not included in any main signal.  
         [0040]     According to another broad aspect, the invention provides a transmitter for transmitting a first main signal S A (t) and a second main signal S B (t), the transmitter comprising: a first antenna and a second antenna; a first delay element for delaying the first main signal S A (t) to produce a first delayed signal S A (t-D 1 ) where D 1  is a first delay; a second delay element for delaying the second main signal S B (t) to produce a second delayed signal S B (t-D 2 ) where D 2  is a second delay; wherein a first linear combination of one of the main signals and one of the delayed signals is transmitted from the first antenna and a second linear combination of the other of the main signals and the other of the delayed signals is transmitted from the second antenna.  
         [0041]     In some embodiments, the first main signal and the second main signal are each CDMA signals.  
         [0042]     In some embodiments, the first linear combination comprises: 
 
 X   A ( t )=α A1   S   A ( t )+α A2   S   A ( t - D   1 ) 
 
 and the second linear combination comprises: 
 
 X   B ( t )=α B1   S   B ( t )+α B2   S   B ( t - D   2 ) 
 
 wherein α A1 , α A2 , α B1 , α B2  form a set of virtual spatial reflectors chosen such that a resulting channel matrix H yields a well conditioned H*H for a particular noise environment where D 1  and D 2  are delays. 
 
         [0045]     In some embodiments, the transmitter further comprises: a scrambling circuit for scrambling a first signal to produce the first main signal and for scrambling a second signal to produce the second main signal, the first signal and the second signal being scrambled with an identical scrambling code.  
         [0046]     In some embodiments, the transmitter further comprises: a scrambling circuit for scrambling a first signal to produce the first main signal and for scrambling a second signal to produce the second main signal, the first signal and the second signal being scrambled with different scrambling codes.  
         [0047]     In some embodiments, each delay implemented in one of the delay elements is selected to provide enough separation between the scrambling code and a version of the scrambling code delayed by the delay such that the scrambling code and the scrambling code delayed by the delay are substantially orthogonal to each other.  
         [0048]     In some embodiments, the transmitter further comprises: a demultiplexer for splitting a symbol stream into symbols included in said first signal and said second signal.  
         [0049]     In some embodiments, the transmitter adapts to transmit from each antenna a respective CDMA signal containing a plurality of code separated channels, the plurality of code separated channels comprising: a respective first set of at least one channels which are generic to multiple users; a respective second set of at least one channels which are user specific; and a respective third set of channels which are user specific and which function as one of said main signals.  
         [0050]     In some embodiments, the first main signal and the second main signal are each OFDM signals.  
         [0051]     In some embodiments, the first linear combination comprises: 
 
 X   A ( t )=α A1   S   A ( t )+α B2   S   B ( t - D   1 ) 
 
 and the second linear combination comprises: 
 
 X   B ( t )=α B1   S   B ( t )+α A2   S   A ( t - D   2 ) 
 
 wherein α A1 , α A2 , α B1 , α B2  form a set of virtual spatial reflectors chosen such that a resulting channel matrix H yields a well conditioned H*H for a particular noise environment, where H* is the complex conjuguate of the chemical matrix H. 
 
         [0054]     In some embodiments, the transmitter further comprises: a forward error correction block for performing forward error correction on an incoming bit stream to generate a coded bit stream; a symbol mapping function for mapping the coded bit stream to a first modulation symbol stream; a demultiplexing function adapted to divide the modulation symbol stream into second and third modulation symbol streams; a first IFFT function, first prefix adding function and first windowing filter adapted to process the second modulation symbol stream to generate the first main signal; a second IFFT function, second prefix adding function and second windowing filter adapted to process the third modulation symbol stream to generate the second main signal.  
         [0055]     In some embodiments, α A1 , α A2 , α B1 , α B2  are chosen to optimize at least one of the following constraints: a) balanced energy: |α A1 | 2 +|α A2 | 2 +|α A1 +α A2 | 2 =|α B1 | 2 +|α B2 | 2 +|α B1 +α B2 | 2 ; b) there is no large notch in frequency domain; c) maximize capacity; and d) meet a specified spectrum mask.  
         [0056]     According to another broad aspect, the invention provides a receiver for receiving a signal transmitted over a wireless channel from a transmitter having a plurality N of transmit antennas, wherein the transmitter is adapted to transmit a respective one of N transmit signals from each of the N antennas, the N transmit signals collectively containing a plurality N of main signals and a plurality of delayed main signals each delayed main signal being a delayed version of one of the main signals, wherein each transmit signal comprises a combination of a respective main signal of the plurality of main signals and at least one respective delayed main signal of the N delayed main signals, the receiver comprising: at least one receive antenna, each receive antenna receiving a respective receive signal over the wireless channel from the transmitter; receive signal processing circuitry adapted to perform receive processing for each of the N main signals and each of the N delayed main signals.  
         [0057]     In some embodiments, there are less than N receive antennas.  
         [0058]     In some embodiments, there is only one receive antenna.  
         [0059]     In some embodiments, all signals are CDMA signals.  
         [0060]     In some embodiments, the receive signal processing circuitry comprises: a finger detector configured to process each receive signal to identify multi-path components transmitted by each antenna, the multi-path components comprising at least one pair of multi-path components comprising a first multi-path component and a second multi-path component which is later than the first multi-path component by the delay introduced at the transmitter.  
         [0061]     In some embodiments, the receive signal processing circuitry comprises de-scrambling and de-spreading functions which produce de-spread signals for each multi-path component, the receiver further comprising: a virtual array processor for performing combining of the de-spread signals.  
         [0062]     According to another broad aspect, the invention provides a receiver for receiving a signal transmitted over a wireless channel from a transmitter having a plurality N of transmit antennas, wherein the transmitter is adapted to transmit a respective one of N transmit signals from each of the N antennas, the N transmit signals collectively containing a plurality N of main signals and a plurality of delayed main signals each delayed main signal being a delayed version of one of the main signals, wherein each transmit signal comprises a combination of a respective main signal of the plurality of main signals and at least one respective delayed main signal of the N delayed main signals, the receiver comprising: at least one receive antenna, each receive antenna receiving a respective receive signal over the wireless channel from the transmitter; for each receive antenna, a respective over-sampling analog to digital converter which samples the respective receive signal and a respective sample selector adapted to produce a respective plurality of sample streams; signal processing circuitry adapted to perform receive processing for each of the sample streams to produce pre-combined signals; a MIMO decoder adapted to perform MIMO processing on the pre-combined signals.  
         [0063]     In some embodiments, each transmit signal comprises a main signal and N- 1  delayed signals, and wherein each over-sampling analog to digital converter performs N times over-sampling.  
         [0064]     In some embodiments, each transmit signal comprises one main signal and one delayed main signal, wherein two-times over-sampling is performed, and wherein the sample selector takes all even samples to generate a first of the sample streams, and takes all odd samples to generate a second of the sample streams.  
         [0065]     According to another broad aspect, the invention provides a system comprising: a transmitter; a receiver comprising: at least one receive antenna, each receive antenna receiving a respective receive signal over the wireless channel from the transmitter; receive signal processing circuitry adapted to process the receive signals.  
         [0066]     In some embodiments, the receive signal processing circuitry is adapted to perform receive processing for each of the N main signals and each of the N delayed main signals.  
         [0067]     In some embodiments, the system adapts to transmit and receive CDMA signals.  
         [0068]     In some embodiments, each main signal comprises a respective combined set of at least one code separated channel.  
         [0069]     In some embodiments, there are two transmit signals, and the main signals comprise a first main signal S A (t) and a second main signal S B (t), the transmitter further comprising: a first antenna and a second antenna; a first delay element for delaying the first main signal S A (t) to produce a first delayed signal S A (t-D 1 ) where D 1  is a first delay; a second delay element for delaying the second main signal S B (t) to produce a second delayed signal S B (t-D 2 ) where D 2  is a second delay; wherein a first linear combination of one of the main signals and one of the delayed signals is transmitted from the first antenna and a second linear combination of the other of the main signals and the other of the delayed signals is transmitted from the second antenna.  
         [0070]     In some embodiments, the receive signal processing circuitry comprises: a finger detector configured to process each receive signal to identify multi-path components transmitted by each antenna, the multi-path components comprising at least one pair of multi-path components comprising a first multi-path component and a second multi-path component which is later than the first multi-path component by the delay introduced at the transmitter.  
         [0071]     In some embodiments, the receive signal processing circuitry comprises de-scrambling and de-spreading functions which produce de-spread signals for each multi-path component the receiver further comprising: a virtual array processor for performing combining of the de-spread signals.  
         [0072]     In some embodiments, the system adapts to transmit and receive OFDM signals.  
         [0073]     In some embodiments, the system adapts to transmit and receive OFDM signals wherein the transmitter further comprises: a forward error correction block for performing forward error correction on an incoming bit stream to generate a coded bit stream; a symbol mapping function for mapping the coded bit stream to a first modulation symbol stream; a demultiplexing function adapted to divide the modulation symbol stream into second and third modulation symbol streams; a first IFFT function, first prefix adding function and first windowing filter adapted to process the second modulation symbol stream to generate the first main signal; a second IFFT function, second prefix adding function and second windowing filter adapted to process the third modulation symbol stream to generate the second main signal.  
         [0074]     In some embodiments, the receiver comprises: at least one receive antenna, each receive antenna receiving a respective receive signal over the wireless channel from the transmitter; for each receive antenna, a respective over-sampling analog to digital converter which samples the respective signal and a respective sample selector adapted to produce a respective plurality of sample streams; signal processing circuitry adapted to perform receive processing for each of the sample streams to produce pre-combined signals; a MIMO decoder adapted to perform MIMO processing on the pre-combined signals.  
         [0075]     In some embodiments, each transmit signal comprises a main signal and N- 1  delayed signals, and wherein each over-sampling analog to digital converter performs N times over-sampling.  
         [0076]     In some embodiments, each transmit signal comprises one main signal and one delayed main signal, wherein two-times over-sampling is performed, and wherein the sample selector takes all even samples to generate a first of the sample streams, and takes all odd samples to generate a second of sample streams.  
         [0077]     According to another broad aspect, the invention provides a method of transmitting comprising: delaying each of N main signals by each of at least one respective delay to produce at least one respective delayed main signal; transmitting from each of N&gt;=2 antennas a respective signal comprising one of the main signals combined with at least one of the delayed main signals.  
         [0078]     According to another broad aspect, the invention provides a method of receiving comprising: at a single receive antenna, receiving over a wireless channel a received signal produced in accordance with one of the above methods; processing the received signal to produce at least two signals which are mathematically equivalent to two signals-which would be received over two different receive antennas; processing the two signals as if they were received over two different antennas. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0079]     Preferred embodiments of the invention will now be described with reference to the attached drawings in which:  
         [0080]      FIG. 1  is a schematic illustration of typical communication link existing in a scattering environment;  
         [0081]      FIG. 2  is a block diagram of a typical conventional typical CDMA (Code Division Multiple Access) transmitter;  
         [0082]      FIG. 3  is a block diagram of a traditional OFDM (orthogonal Frequency Division Modulation) transceiver;  
         [0083]      FIG. 4A  is a schematic of a downlink transmitter for a CDMA based transmitter provided by an embodiment of the invention;  
         [0084]      FIG. 4B  is a block diagram of a generic spatial reflector function provided by an embodiment of the invention;  
         [0085]      FIG. 4C  is a block diagram of a CDMA transmitter similar to that of  FIG. 2 , but adapted to employ the spatial reflector function of  FIG. 4B , in accordance with an embodiment of the invention;  
         [0086]      FIG. 5  is schematic of a downlink transmitter for a CDMA based transmitter provided by another embodiment of the invention;  
         [0087]      FIG. 6  is a schematic of a CDMA receiver provided by an embodiment of the invention, for use with the embodiment of  FIG. 4 ;  
         [0088]      FIG. 7  is a code tree to demonstrate that using the CDMA embodiment of  FIG. 4  or  5  enlarges the code space over traditional CDMA;  
         [0089]      FIG. 8  is a block diagram of an OFDM based transmitter provided by an embodiment of the invention;  
         [0090]      FIG. 9  is a block diagram of another OFDM based transmitter provided by another embodiment of the invention;  
         [0091]      FIG. 10A  is a plot of the impulse response sampling of a rectangular channel;  
         [0092]      FIG. 10B  is a plot of the impulse response sampling of a channel Ch A (t)=rect(t)+rec(t-T/2) for use with some embodiments of the invention;  
         [0093]      FIG. 10C  is a plot of the impulse response sampling of a channel Ch B (t)=rect(t)−2rect(t-T/2) for use with some embodiments of the invention;  
         [0094]      FIG. 11  is a schematic illustration of a communication link consisting of a transmitter section and a virtual spatial antenna configuration representing a single receiver antenna, as provided by an embodiment of the invention;  
         [0095]      FIG. 12  is a block diagram of an OFDM virtual antenna receiver provided by an embodiment of the invention, useable with the transmitters of  FIGS. 6 and 7 ;  
         [0096]      FIG. 13  is a schematic illustration of the keyhole phenomenon as it relates to a communication link;  
         [0097]      FIG. 14  is a block diagram of an embodiment of the invention employing two receive antennas; and  
         [0098]      FIG. 15  shows simulated performance results in terms of SNR (Signal-To-Noise) versus BER (Bit-Error-Rate) for QSPK and QAM-16 modulation techniques of various BLAST, and STTD (Space-Time Transmit Diversity) transmission schemes, and for embodiments of the invention.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [heading-0099]     Channel Interception via Designed Reflectors  
         [0100]     According to an embodiment of the invention, a method, herein referred to as “channel interception” is provided which pre-sets a propagation environment either in a deterministic way or quasi-random way to guarantee a satisfactory MIMO (Multiple Input Multiple Output) eigen condition of the channel matrix H.  
         [0101]     The propagation environment adds further channel variations on top of the pre-set environment but the pre-set environment will exist even if the random environment causes a destruction of the MIMO channel structure. It is noted that the conventional pre-distortion concept and constellation rotation concept may be considered types of channel interception. Both these conventional techniques use channel impulse response information (usually by feedback) and reverse the channel before transmission in order to cancel the multipath effect in the receiver end.  
         [0102]     In contrast, the channel interception provided in this embodiment of the invention, rather than attempting to remove the multipath effect, intentionally creates a multipath effect. The basic concept is to form a set of wave reflectors in baseband before transmission so that the received channel matrix favours MIMO transmission. Using this method, the MIMO channel can always be setup whether the channel is scattering or not.  
         [0103]     Furthermore, it has been noted above that with conventional MIMO applications, MIMO needs more than one receiver antenna and this proves to be a very stringent requirement for conventional mobile terminals which typically only have one receiver RF chain. To add another RF chain almost doubles the mobile terminal cost and increases power consumption significantly. With the channel interception technology provided by the invention, one receiving antenna is enough in most applications to receive and then to distinguish the multiple transmitted data streams.  
         [0104]     The invention has very general applications. Two very specific implementations will be presented, namely CDMA (Code Division Multiple Access) and OFDM (Orthogonal Frequency Division Modulation) implementations. The very specific examples will involve two transmit antennas and one receive antenna. However, it is to be understood that larger numbers of transmit antennas can be employed in alternative embodiments. Furthermore, additional receive antennas can be employed. Each receive antenna in such an application will behave as if it were multiple receive antennas. In the case of multiple receive antennas, ‘virtual antennas’ provided by the invention can be used together with the physical antennas to form an enlarged antenna array.  
         [heading-0105]     CDMA Embodiment  
         [0106]     This embodiment of the invention provides a system and method for performing parallel transmission (or BLAST) with only one receiving antenna in a CDMA context. For this very specific example, the 3GPP/UMTS standard is assumed as an example but the concept is very generic and can be applied to other systems such as, but not limited to, CDMA2000 or TD-SCDMA or even GSM.  
         [0107]      FIG. 4A  illustrates the main transmitter baseband processing blocks for an example implementation. In the diagram, the coded bits  30  are first mapped to constellation symbols with constellation mapping  32 , and the symbol sequence is de-muxed with demultiplexer  36  into two parallel streams which are output at  35  and  37 . More generally, any number of parallel streams may be generated at this point. Each data stream, say the upper output  35 , is first spread and scrambled. More specifically, for the upper output  35 , spreading code A  34  is applied, and the output of this is multiplied with a scrambling code  44  in multiplier  40 . Similar processing for output  37  is applied with spreading code A  38  and multiplier  42 . Scrambling occurs at the chip rate. A low pass filtering operation, for example using a RRC (Root Raised Cosine) filter, indicated at  46 , 48  is applied to the outputs of the two multipliers  40 , 42 . This might for example realize a shaping filter function and an interpolation filter function to convert the chip level data into a quantized signal suitable for Digital-to-Analog Conversion (DAC). Up conversion will start after applying the channel Gain GA 1  and GB 1  and combining with other channels such as a pilot channel and/or other data channels if present.  
         [0108]     The output of the first lowpass filter  46  is signal s A (t), while the output of the second lowpass filter  48  is signal s B (t). The signal s A (t) is processed by functional block  47  whose purpose is to process the signal such that single antenna reception can be performed as described below. Similarly, the signal s B (t) is processed by functional block  49 .  
         [0109]     In functional block  47 , signal s A (t) is multiplied by a virtual spatial reflector α A1    56 . The signal s A (t) is also delayed in delay block  50 , and then multiplied by a second virtual spatial reflector α A2    54 . The outputs of the two virtual reflectors  54 , 56  are combined in adder  58 . A channel gain G A1  is applied at  60  and the data stream is then combined with other users channels or common signaling channels such as pilot channel (PICH) or primary synchronization channel (PSCH) etc., and is transmitted via antenna A  70 .  
         [0110]     Similarly, in functional block  49 , the signal S B (t) is multiplied by a virtual spatial reflector α B1    64 . The signal s B (t) is also delayed in delay block  52 , and then multiplied by a second virtual spatial reflector α B2    62 . The outputs of the two virtual reflectors  62 , 64  are combined in adder  66 . A channel gain G B1  is applied at  68  and the data stream is then combined with other users channels or common signaling channels such as pilot channel (PICH) etc., and is transmitted via antenna B  72 .  
         [0111]     Note that the reflectors α A1 , α A2 , α B1 , α B2  and the delay introduced in delay blocks  50 , 52  are design parameters. In some embodiments, the reflectors are constant over time and might be complex numbers for example. In other embodiments, the reflectors are functions of time. For example, in one embodiment the reflectors are pseudo-random functions of time. When this is the case, the reflectors still need to satisfy the constraints introduced below at any given instant. Preferably the reflectors will have a unit gain and will result in a balanced power dissipation and balanced eigen values of the matrix defined by the following:  
                     H   *   H     =       ⁢         [           α   A1           α   B1               α   A2           α   B2           ]     *     ⁡     [           α   A1           α   B1               α   A2           α   B2           ]                   =       ⁢     [                    α   A1          2     +            α   A2          2                 conj   ⁡     (     α   A1     )       ⁢     α   B1       +       conj   ⁡     (     α   A2     )       ⁢     α   B2                       conj   ⁡     (     α   B1     )       ⁢     α   A1       +       conj   ⁡     (     α   B2     )       ⁢     α   A2                        α   B1          2     +            α   B2          2             ]                   (   5   )             
 
         [0112]     The delays implemented in delay blocks  50 , 52  are to be selected to provide enough separation between the scrambling code and the delayed version of the same scrambling code, subject to the constraint that the processing delay is tolerable. The design of the delays is a matter of tradeoff between the scrambling code auto correlation property and the hardware processing delay.  
         [0113]     One simple set of ‘reflector’ values are α A1 =1; α A2 =1; α B1 =1; α B2 =−1 or −2. This set of reflectors results in a unit gain in the two paths over a 1.5 chip duration. It can be verified easily that the corresponding two eigen values are identical. The delay may be determined by the scrambling code auto-correlation property. Using 3GPP/UMTS scrambling code a delay=4.5 chips is a good choice in experience but other values can be used.  
         [0114]     Note that the traditional MIMO baseband signals that would be transmitted, respectively, from antenna A  70  and B  72  (in  FIG. 4 ) in the absence of functional blocks  47 , 49  are  
                 S   A     ⁡     (   t   )       =       ∑   k     ⁢         s   A     ⁡     (   k   )       ⁢           ⁢       ∑     l   =   0       L   -   1       ⁢       c   ⁡     (   l   )       ⁢           ⁢     h   ⁡     (     t   -   lT   -       (     k   -   1     )     ⁢   LT       )       ⁢           ⁢     pn   ⁡     (     l   +       (     k   -   1     )     ⁢   L       )                       (   6   )                   S   B     ⁡     (   t   )       =       ∑   k     ⁢         s   B     ⁡     (   k   )       ⁢           ⁢       ∑     l   =   0       L   -   1       ⁢       c   ⁡     (   l   )       ⁢           ⁢     h   ⁡     (     t   -   lT   -       (     k   -   1     )     ⁢   LT       )       ⁢           ⁢     pn   ⁡     (     l   +       (     k   -   1     )     ⁢   L       )                       (   7   )             
 
 where s A (k) and s B (k) are mapped symbols, c( 1 ) is the lth chip wave-form of the OVSF (Orthogonal Variable Spreading Factor) code, h(t) is the RRC filter with rollover 0.2, L is the length of the OVSF code and pn(t) is the corresponding downlink scrambling code. By comparison, the waveforms being transmitted from antenna A  70  and antenna B  72  for the new systems are for the example delay value of 4.5 T, respectively, expressed as 
 
 X   A ( t )=α A1   S   A ( t )+α A2   S   A ( t -4.5  T )   (8) 
 
 X   B ( t )=α B1   S   B ( t )+α B2   S   B ( t -4.5  T )   (9) 
 
         [0116]     More generally, delays D 1  and D 2  may be applied instead of the equal delays 4.5 T.  
         [0117]     It is noted that the other channels such as PICH (pilot channel), SCH (synchronous channel), DDCH (dedicated data channel) etc. have been omitted in the diagram and in the equations.  
         [0118]     Functional block  47  of  FIG. 4A  is a very specific way of implementing a spatial reflector function, as provided by an embodiment of the invention. More generally, this function can be implemented as shown in  FIG. 4B . Here, the incoming main signal S A (t) is shown being processed along N parallel paths. The first path has no delay. Each of the other paths has a respective delay D 2    630  through D N    632  which produces a respective delayed signal. Each of the paths is also shown being processed by a respective transformation block. The transformation block for: the first path is indicated at T 1    634 . The transformation block for the second and Nth paths is shown as blocks T 2    636  and T N    638 . This transformation is any path specific processing of the signal which is to be implemented. For example, one path might perform a complex conjugation operation. The paths might include delay specific filtering functions. In the most basic embodiment, the signals pass through the transformations  634 , 636  . . .  638  unchanged. Each of the paths is then multiplied by a respective virtual spatial reflector α A1    640 , α A2    642  through α AN    644 . The paths are then combined in adder  646 . Each of the delays is different and subject to the same constraints as the single delay embodiment of  FIG. 4A . In the most simple implementation, there are only two paths one of which has the delay.  
         [0119]      FIG. 4C  is a block diagram of how the embodiment of  FIG. 4A , using the generic functionality of  FIG. 4B  can be applied to the CDMA transmitter of  FIG. 2 . Here, the functionality in respect of the generic channels is indicated at  601  and only shows them being combined in combiner  614 . The functionality for one or more user specific channels which are not to be processed by the spatial reflector function is indicated generally at  603 . Again all that is shown here is a summer  608  which combines the various channels after having being spread by their respective spreading code, and the scrambling function  610 . All of the channels which are not to be processed by the spatial reflector function are combined as  616 . The functionality for all of the channels to be processed by the spatial reflector function is generally indicated at  605 . Here, all of the channels to be processed are combined at  600 , scrambled with scrambling code at  602 , and then processed by the spatial reflector function  604 . This function can be any appropriate implementation of the generic figure shown in  FIG. 4B . The channels which were processed by the spatial reflector function  604  are combined at  612  with the other channels and the result is lowpass filtered at  620  and digital-to-analog converted at  622  and output through the transmit antenna  624 . This functionality would be implemented for each of the transmit antennas.  
         [0120]     In the example of  FIG. 4A , the delayed versions of signals are transmitted by the same antenna as the non-delayed signals. Thus, the signal transmitted by one antenna contains two versions of the same signal. In another embodiment, the delayed signals are transmitted from different antennas than the non-delayed signals. For example, shown in  FIG. 5  is a modified version of  FIG. 4A  adapted to achieve this alternate embodiment. The signal produced by virtual spatial reflector  54  is combined at  66  with the signal produced by virtual spatial reflector  64  and output by antenna B  72 . The outputs of the other two virtual spatial reflectors  56 , 62  are combined and output by the remaining antenna A  70 . This changes the transmitted signals to have the following form: 
 
 X   A ( t )=α A1   S   A ( t )+α B2   S   B ( t - 4 . 5   T )   (10) 
 
 X   B ( t )=α B1   S   B ( t )+α A2   S   A ( t - 4 . 5   T )   (11) 
 
 As in the previous case, more generally two delays D 1 ,D 2  may be applied. In either case, one antenna transmits a combination of one of the main signals and one of the delayed signals, and the other antenna transmits a combination of the other of the main signals and the other of the delayed signals. 
 
         [0122]     Thus, a general way to think of the transmitter of  FIGS. 4A , or  5  is that the transmitter can be configured to transmit a respective one of N transmit signals from each of the N antennas, the N transmit signals collectively containing a plurality N of main signals and a plurality of delayed main signals, wherein each transmit signal contains a combination of a respective main signal of the plurality of main signals and at least one respective delayed main signal of the N delayed main signals. In this context, “combination” has a broad interpretation. It is meant that there may or may not be a non-identity transformation applied to a given main signal or delayed main signal and there may or may not be non-unity virtual spatial reflectors applied. In this general context, the delayed main signals which are used to generate a given transmit signal may be delayed versions of any of the main signals. The embodiment shown in  FIG. 4A  had a given antenna transmitting a main signal and a delayed version of the main signal, while the  FIG. 5  embodiment had a given antenna transmitting a main signal and a delayed version of another main signal.  
         [0123]     In another embodiment, the N transmit signals comprise a Jth transmit signal Transmit J  transmitted from antenna J, where J=1, . . . , N, and wherein Transmit J  comprises:  
         Transmit   J     =         α   J     ⁢       T   J     ⁡     (     S   J     )         +       ∑     i   =   1       K   J       ⁢       α     i   ⁢           ⁢   J       ⁢       T     i   ,   J       ⁡     (       S     i   ⁢           ⁢   J       ⁡     (     t   -     D     i   ⁢           ⁢   J         )       )                 
        S J =is the Jth main signal of the plurality of main signals;     α J =is a virtual spatial reflector applied to the Jth main signal;     T J =is a transformation applied to the Jth main signal;     K J  is a number of delayed signals included in the Jth transmit signal as said respective at least one delayed main signal;     α iJ =is a virtual spatial reflector applied to the ith delayed signal included in the Jth transmit signal;     S iJ , i=1, . . . , K J  are the signals which are to be delayed and included in the Jth transmit signal where each iJ ε 1, . . . , N as said respective at least one delayed main signal;     D ij =is a delay applied to signal S ij ;     T iJ =is a transformation applied to the ith delayed signal included in the Jth transmit signal. Any or all of these transformations may be identity functions (f(x)=x) in which case in a physical implementation they would not exist as a separate function.        
 
         [0132]     As mentioned previously, the transmitter design is easily generalized to more than two transmit antennas. Furthermore, before the physical transmission of-the signals mentioned above, any necessary processing for transmission needs to occur. This is system specific and outside the scope of the invention. Depending on the application, this might involve digital-to-analog conversion, RF up-conversion, channel gain, filtering, and/or other functions.  
         [0133]     Furthermore, while a specific transmitter design has been shown, any CDMA transmitter equipped with two or more parallel processing paths each generating main and delayed signals can be employed.  
         [heading-0134]     Receiver Design with Virtual Antennas  
         [0135]     According to the transmitter diagram ( FIG. 4A ), the received continuous baseband signal will be:  
                     y   ⁡     (   t   )       =       ⁢         ∑     i   =   1     I     ⁢       β   Ai     ⁢       x   A     ⁡     (     t   -     τ   i       )           +       ∑     i   =   1     I     ⁢       β   Bi     ⁢       x   B     ⁡     (     t   -     τ   i       )           +     N   ⁡     (   t   )                     =       ⁢         ∑     i   =   1     I     ⁢       β   Ai     ⁡     (         α   A1     ⁢       S   A     ⁡     (     t   -     τ   i       )         +       α   A2     ⁢       S   A     ⁡     (     t   -     τ   i     -     4.5   ⁢   T       )           )         +                     ⁢       ∑     i   =   1     I     ⁢       β   Bi     ⁡     (         α   B1     ⁢       S   B     ⁡     (     t   -     τ   i       )         +       α   B2     ⁢       S   B     ⁡     (     t   -     τ   i     -     4.5   ⁢   T       )           )                       (   12   )             
 
 where τ i  is the ith significant multipath with Rayleigh fading coefficients β Ai  and β Bi , respectively, I is the number of significant multipaths, and N(t) is a combination of thermal noise, interferences and some ignored multipaths. 
 
         [0137]     Inside the receiver, each multipath component, commonly referred to as a “finger” is detected usually by a pilot correlator. According to the transmitter configuration, statistically the fingers should pop up in pairs with a separation of 4.5 T (or whatever the separation was at the transmitter), in the case of this example, or as pre-defined, i.e. (τ i , τ i +4.5 T) and both paths associated with the finger pair experience the same Rayleigh fading β A1  or β Bi .  
         [0138]     For this particular configuration, the finger detection module will identify 2I fingers. Typically, a different pilot will be transmitted by each of the antennas and this pilot is used in searching for multipaths. A separate searching process is conducted for each pilot and a series of multipaths or fingers are identified. In a perfect world, at one receive antenna the fingers detected with the two different pilots will be perfectly aligned. However, due to the actual channel over which the signals are transmitted, they may not be perfectly aligned. When fingers are aligned, they can be treated as pairs. Otherwise, where one significant finger is detected on one pilot but not on the other, it can still be treated as a pair, but with a zero gain on the other pilot. A special case occurs when the signals propagate only along line of sight. Then only two fingers are detected, that is (τ 1 , τ 1 +4.5 T).  
         [0139]     Each finger is treated independently, similar to a RAKE receiver. After de-scrambling and de-spreading, the ith finger pair (τ i , τ i +4.5 T) processing will output the kth data symbol as 
 
 r   i1 ( k )=β Ai α A1   S   A ( k )+β Bi α B1   s   B ( k )+ n   i1 ( k ) 
 
 r   i2 ( k )=β Ai α A2   s   A ( k )+β Bi α B2   s   B ( k )+ n   i2 ( k ) 
 
 By putting these data pairs into an array, the following matrix equation can be formulated:  
               [             r   i1     ⁡     (   k   )                   r   i2     ⁡     (   k   )               M               r   I1     ⁡     (   k   )                   r   I2     ⁡     (   k   )             ]     =         [             β   A1     ⁢     α   A1               β   B1     ⁢     α   B1                   β   A1     ⁢     α   A2               β   B1     ⁢     β   B2               M       M               β   AI     ⁢     α   A1               β   BI     ⁢     α   B2                   β   AI     ⁢     α   A2               β   BI     ⁢     α   B2             ]     ⁡     [             s   A     ⁡     (   k   )                   s   B     ⁡     (   k   )             ]       +     [             n   i1     ⁡     (   k   )                   n   i2     ⁡     (   k   )               M               n   I1     ⁡     (   k   )                   n   I2     ⁡     (   k   )             ]               (   13   )             
 
 In this configuration, there are two unknowns s A (k) and s B (k) and 2I (≧2) equations. More importantly, the coefficient matrix is always rank-2 whenever β A1 ≠0 and β B1 ≠0. So the waveform coding first expands the channel matrix rank and the multipath-rich environment experienced by the signal will further enhance this rank property to favour the MIMO decoder. By using the equation (13), either hard-decision or soft-decision methods can be applied to infer the bits information of s A (k) and s B (k). For example, a simple Least-Mean-Square solution (LMS) can be derived as  
               [             s   A     ⁡     (   k   )                   s   B     ⁡     (   k   )             ]     =           Λ     -   1       ⁡     [             β   A1     ⁢     α   A1               β   B1     ⁢     α   B1                   β   A1     ⁢     α   A2               β   B1     ⁢     β   B2               M       M               β   AI     ⁢     α   A1               β   BI     ⁢     α   B2                   β   AI     ⁢     α   A2               β   BI     ⁢     α   B2             ]       T     ⁢           [             r   i1     ⁡     (   k   )                   r   i2     ⁡     (   k   )               M               r   I1     ⁡     (   k   )                   r   I2     ⁡     (   k   )             ]             (   14   )               Λ   =     [           2   ⁢           ⁢       ∑     i   =   1     I     ⁢            β   Ai          2                         ∑     i   =   1     I     ⁢       β   Ai     ⁢     α   A1     ⁢     conj   ⁡     (       β   Bi     ⁢     α   B1       )           +                 β   Ai     ⁢     α   A2     ⁢     conj   ⁡     (       β   Bi     ⁢     α   B2       )                                   ∑     i   =   1     I     ⁢       conj   ⁡     (       β   Ai     ⁢     α   A1       )       ⁢     β   Bi     ⁢     α   B1         +                 conj   ⁡     (       β   Ai     ⁢     α   A2       )       ⁢     β   Bi     ⁢     α   B2                   2   ⁢           ⁢       ∑     i   =   1     I     ⁢            β   Bi          2               ]             (   15   )             
 
 with 
 
 A more sophisticated method such as MLD (Maximum Likelihood Detection) can also be implemented. Equation (13) is very similar to the output of an antenna array and is denoted as a ‘Virtual Antenna Array’. 
 
         [0144]     An example of a receiver design is shown in  FIG. 6 . A single antenna  80  is shown, although the design can be generalized to handle multiple antennas as described further below. It is to be understood a complete receiver would include additional functions not shown in  FIG. 6 , and these are omitted to simplify the figure. The received signal is digitized in an ADC (Analog-to-Digital Converter)  82 . Finger detection occurs in Finger Detector  84  which passes the finger locations thus detected to the Finger Control Function  90 . The Finger Control Function  90  controls the de-scrambling operation.  86  and in some cases de-spreading operation  88 . Whether or not the Finger Control Function  90  controls both the De-Scrambling Operation  86  and the De-Spreading Operation  88  depends upon a given implementation. The Finger Control Function  90  therefore will also control the overall de-spreading time and data buffer time, but this will vary depending upon whether the implementation is done serially or in parallel. The output signals are fed to a “virtual array processor”  92 , i.e. using the above derived array virtual array equations which in turn generates soft bits  94  as the overall output of the circuit of  FIG. 4 . It is noted that in some designs, de-scrambling and de-spreading operations are done sequentially for the various finger locations by a single hardware implementation. Furthermore, it is noted that for the processing performed in the receiver, once the multiple fingers are identified (twice as many fingers as would be found in the absence of waveform coding) the remainder of the receiver can for the most part be designed according to any otherwise conventional approach.  
         [0145]     Advantageously, for the CDMA embodiment, the network capacity is automatically doubled as all the services can be fulfilled by doubling the spreading length compared to the traditional system configuration. Longer spreading not only doubles the code space, but also relaxes the interference level in the whole system. Capacity for a 2×1 system can be written as  
             C   =       log   2     ⁢           ⁢     det   ⁡     (       (         1       0           0       1         )     +         E   ⁢     {   s   }       2     ⁢           ⁢   Λ       )       ⁢           ⁢   bps   ⁢     /     ⁢   Hz             (   16   )             
 
 Where Λ is defined by equation (15). 
 
         [0147]     The downlink signals of each sector/cell are scrambled using the same scrambling code. The same scrambling code with different offsets can be regarded as different orthogonal scrambling codes. Therefore, different fingers can be regarded as different signals carried by different orthogonal scrambling codes (this is similar to OFDM where different tones are used for parallel transmission). Conventional CDMA uses the environment to form a diversity path for different scrambling code offsets. This embodiment actively creates different paths inside the transmitter. Similar to MIMO, those different paths can be either used as diversity paths to increase the receiver SNR as a RAKE receiver does, or used as virtual antenna to gain spectrum efficiency. From equation (15) it can be seen that Λ is a compromise between the cross correlation noise and the eigen mode.  
         [0148]     In fact, only half of the fingers are employed to build up a virtual rank-2 channel matrix so that the blasted data stream can be recovered. The limiting factor is still the reception of the cross correlation noise when increasing the number of parallel transmissions. However, there will always be a gain when the network is code space limited. In that situation, the code space is automatically doubled by parallel transmission.  
         [0149]     For instance, if a service needs a spreading factor of 4 in the conventional CDMA system the CDMA embodiment only needs to use a spreading factor of 8, which releases half of the OVSF code branch and relaxes the overall interference level to other users.  
         [0150]     An example of this is shown in  FIG. 7 . Channels with a spreading factor  4  are indicated at  91 . A single user typically occupies one such channel in conventional 3GPP/UMTS. Spreading factor  8  channels are indicated at  93 . Each spreading factor  8  channel takes up half-the code space of spreading factor  4  channel. One user with the CDMA embodiment only needs one spreading factor  8  channel.  
         [heading-0151]     OFDM Embodiment  
         [0152]     Similar to the CDMA embodiment described above, the OFDM channel can be intercepted before hand to guarantee a suitable channel for MIMO operation. However the interception criteria are different.  
         [0153]     An embodiment of the invention provides an OFDM system that will first force the propagation channel to effectively behave like a multipath channel even if it is not. The provision of the pre-designed multipath channel will allow the employment of terminals that have only one receiver antenna provided the MIMO channel matrix embedded in the transmitted signal in frequency domain is full rank. This property of the channel matrix will be further enhanced by the real environment which may also be a multipath-rich environment.  
         [0154]     A first example of an OFDM transmitter provided by an embodiment of the invention is illustrated in  FIG. 8 . Input bits  140  are processed by FEC (Forward Error Correction) coding block  142 . This is followed by QAM quadrature amplitude modulation) mapping  144 . Other symbol mappings may alternatively be employed. This is followed by a serial-to-parallel conversion function  146  which converts the symbol stream into a parallel stream, and divides the parallel stream into two parallel streams S a (k) and S b (k). The first stream S a (k) is processed by path  147  and the second stream S b (k) is processed by path  148 .  
         [0155]     Path  147  begins with an IFFT function  148  followed by a parallel-to-serial function  150 . Block  152  adds the conventional cyclic prefix  152  to produce a signal I a (k). Windowing is performed by the windowing filter  154 . In this diagram, the windowing filter  154  can be any shaping filter satisfying any provided out-of-band emission specifications. The commonly used window functions are raised cosine, Hamming or Hanning windows. The output of the windowing filter  154  is then processed by block  155 , which is very similar to block  47  of  FIG. 3  for the CDMA embodiment.  
         [0156]     In functional block  155 , the output of the windowing filter  154  is multiplied by a virtual spatial reflector α A1    158 . The windowing filter output is also delayed in delay block  156  having a delay of T/2 in the illustrated embodiment where T is the OFDM symbol duration. Other delay values may be used. The delayed signal is then multiplied by a second virtual spatial reflector, α A2    162 . The outputs of the two virtual reflectors  158 , 162  are combined in adder  160 . The output is then converted to analog form with DAC  164  that is connected to RF transmitter  166  which outputs the signal,to transmit through the antenna  168 .  
         [0157]     The processing in the second path  148  is the same as in the first path except that in processing block  170  different virtual spatial reflectors α B1  and α B2  are employed.  
         [0158]     One simple set of reflectors that can be used with the embodiment of  FIG. 8  is α A1 =1, α A2 =1, α B1 =1, α B2 =−2.  
         [0159]     In another embodiment, the delayed versions can also be transmitted from different transmitters as illustrated in  FIG. 9 .  FIG. 9  is the same as  FIG. 8  with the exception of the fact that each output signal is generated from a combination of the output of one spatial reflector in the first path  147  and the output of one spatial reflect in the second path  148  similar to the CDMA embodiment of  FIG. 5  described previously.  
         [heading-0160]     OFDM Multi-Path Propagation  
         [0161]     In this section and the forthcoming sections, analysis is presented for the embodiment of  FIG. 8  only. The analysis for the embodiment of  FIG. 9  is similar. Furthermore, for embodiments with more than two transmitters, the analysis is the same with a little bit more effort on optimizing the delays and interception parameters.  
         [0162]     In conventional systems, the shaped OFDM symbol is transmitted after DAC and PA (power amplification) and is propagated to the receiver via the environmental multipath channels  
                 ch   A     ⁡     (   t   )       =       ∑     k   =   1       K   A       ⁢         α   A     ⁡     (   k   )       ⁢           ⁢     rect   ⁡     (     t   -     τ   A   k       )                   (   17   )                   ch   B     ⁡     (   t   )       =       ∑     k   =   1       K   B       ⁢         α   B     ⁡     (   k   )       ⁢           ⁢     rect   ⁡     (     t   -     τ   B   k       )                   (   18   )             
 
 where rect(t) is the rectangular shaping function which is defined as rect(t)=1 when t is between -T/2 and T/2 and 0 elsewhere. 
 
         [0164]     Note that the impulse responses of both channels are time limited in theory and therefore sampling the channels at the Nyquist rate can only provide partial channel information or the sampled channel spectrum will be affected by aliasing. In other words, over sampling these channels will always provide more information on the multipath channels compared to Nyquist rate sampling. To illustrate the multipath channel over sampling concept using the example transmitter configuration (with α A1 =1, α A2 =1, α B1 =1, α B2 =−2) suppose the channels are LOS (line of sight) with a channel gain equal to one, i.e. the ideal non-scattering environment. This is a special case in which the conventional MIMO blast technique does not work properly. In this case, 
 
 ch   A ( t )=rect( t )+rect( t - T/ 2)   (19) 
 
 is the channel output at antenna A and 
 
 ch   B ( t )=rect( t )−2rect( t - T /2)   (20) 
 
 is the channel output at antenna B. 
 
         [0167]     The conventional channel is shown in  FIG. 10A . The channel represented by equation 19 is shown in  FIG. 10B , and the channel represented by equation 20 is shown in  FIG. 10C . The dotted arrows indicate the sampling instants, which are T/2 apart. With this simple waveform coding, the odd and even samples of channels are quite different for the channels shown in  FIGS. 10B and 10C  compared to conventional OFDM that goes through the rectangular channel of  FIG. 10A . For the channel of  FIG. 10B , for instance, the odd and even channel samples are Ch Ao =[1 1 0 . . . 0] and Ch Ae =[2 0 0 . . . 0] while for the channel of  FIG. 10C  Ch Bo =[1 −2 0 . . . 0] and Ch Ae =[−1 0 0 . . . 0]. This odd and even channel difference will cause their frequency domain impulse responses to vary and therefore a full rank channel matrix with high probability is generated in the frequency domain. In fact, for the above simple case, the channel gains for the kth tone can be calculated respectively as F Ao (k)=1+exp(−j2π/1024)2k, F Bo (k)=1−2exp(−j2π/1024)2k, F Ae (k)=2 and F Be (k)=−1. They form the kth tone channel matrix:  
         [             F   Ao     ⁡     (   k   )               F   Bo     ⁡     (   k   )               2         -   1           ]             
 
 which always has a full rank. 
 
         [0169]     Note that for this example, the powers from two different antennas are balanced within a 1.5T time interval, and the signal spectrum stays the same as the conventional OFDM system.  
         [0170]     It is noted that in the transmitters of  FIGS. 8 and 9 , each path of the transmitters are similar to conventional transmitters except for splitting the QAM mapped signal between the-two paths, and the waveform coding performed by functional blocks  155 , 170 . Thus, where a particular implementation for the remainder of the transmitter is shown, more generally an embodiment of the invention provides any transmitter equipped to perform the described waveform coding for two or more transmit signals.  
         [heading-0171]     OFDM Receiver  
         [0172]     In general, the blasted signals {I a (k)} and {I b (k)} (refer to  FIG. 8 ) will propagate along the multipath channels ch A (t) and ch B (t) respectively that have been defined in equations (17) and (18). With the new waveform coding, they will propagate with the intercepted multipath channels which can be expressed respectively as  
                 ch   AI     ⁡     (   t   )       =       ∑     k   =   1       K   A       ⁢         α   A     ⁡     (   k   )       ⁡     [         α   A1     ⁢     rect   ⁡     (     t   -     τ   A   k       )         +       α   A2     ⁢     rect   ⁡     (     t   -     T   2     -     τ   A   k       )           ]                 (   21   )                   ch   BI     ⁡     (   t   )       =       ∑     k   =   1       K   B       ⁢         α   B     ⁡     (   k   )       ⁡     [         α   B1     ⁢     rect   ⁡     (     t   -     τ   B   k       )         +       α   B2     ⁢     rect   ⁡     (     t   -     T   2     -     τ   B   k       )           ]                 (   22   )             
 
 The received baseband signal (for one antenna) can be modeled as  
               y   ⁡     (   t   )       =         ∑   k     ⁢         I   a     ⁡     (   k   )       ⁢           ⁢       ch   AI     ⁡     (     t   -   kT     )           +       ∑   k     ⁢         I   b     ⁡     (   k   )       ⁢           ⁢       ch   BI     ⁡     (     t   -   kT     )           +     n   ⁡     (   t   )                 (   23   )             
 
 Discretizing y(t) will simultaneously sample the multipath channels. Suppose y(t) is sampled at two times the Nyquist rate, i.e. y(t) is discretized as  
             {       y   ⁡     (     m   ⁢           ⁢     T   2       )       =         ∑   k     ⁢         I   a     ⁡     (   k   )       ⁢           ⁢       ch   AI     ⁡     (       m   ⁢           ⁢     T   2       -   kT     )           +               (   24   )                       ⁢               ∑   k     ⁢         I   b     ⁡     (   k   )       ⁢           ⁢       ch   BI     ⁡     (       m   ⁢           ⁢     T   2       -   kT     )           +     n   ⁡     (     m   ⁢           ⁢     T   2       )         |   m     =   0     ,   1   ,   2   ,   …     ⁢           }                         
 
 These samples can be classified by odd or even indexed samples, i.e.  
             {         y   o     ⁡     (   l   )       =         ∑   k     ⁢         I   a     ⁡     (   k   )       ⁢           ⁢       ch   AI     ⁡     (     lT   +     T   2     -   kT     )           +       ∑   k     ⁢       I   b     ⁢     (   k   )     ⁢           ⁢       ch   BI     ⁡     (     lT   +     T   2     -   kT     )           +               (   25   )                       ⁢           n   ⁡     (     lT   +     T   2       )       |   l     =       2   ⁢   m     +   1       ,     m   =   0     ,   1   ,   2   ,   …     ⁢           }                         and                         {         y   e     ⁡     (   p   )       =         ∑   k     ⁢         I   a     ⁡     (   k   )       ⁢           ⁢       ch   AI     ⁡     (     pT   -   kT     )           +               (   26   )                       ⁢               ∑   k     ⁢         I   b     ⁡     (   k   )       ⁢           ⁢       ch   BI     ⁡     (     pT   -   kT     )           +     n   ⁡     (   pT   )         |   p     =     2   ⁢   m       ,     m   =   0     ,   1   ,   2   ,   …     ⁢           }                         
 
 The odd samples can be regarded as the acquisition of a signal that equals the transmitted data symbols transmitted on the odd multipath channel whilst the even samples can be regarded as the acquisition of a signal that equals the same transmitted data symbols transmitted on the even multipath channel. Note that for conventional OFDM, these odd and even samples are the same when in a LOS environment as the odd and even paths are the same. 
 
         [0177]     As has been shown for the new waveform coding, odd multipath channels 
 
{ ch   Ao ( m )= ch   A ( mT + 0 . 5   T )| m= 0, 1, 2 . . . }
 
and 
 
{ ch   Bo ( m )= ch   B ( mT + 0 . 5   T )| m= 0, 1, 2 . . . }
 
 are always quite different from even channels 
 
{ ch   Ae ( m )= ch   A ( mT )| m =0, 1, 2, . . . }
 
and 
 
{ ch   Be ( m )= ch   B ( mT )| m =0, 1, 2, . . . }. 
 
 Their corresponding frequency contents are forced to change at each delay instant and are also modulated with the natural Rayleigh fading coefficients. Odd and even samples of y(t) can be regarded as coming from two different imaginary receiver antennae RxA and RxB which take samples at T-space. This is illustrated diagrammatically in  FIG. 11 , which shows a virtual spatial antenna configuration. This shows a transmitter generally indicated at 200 having two transmit antennae TxA  202  and TxB  204 . Also shown is a receiver generally indicated at  201  having a single receive antenna  214 . By performing the above discussed division between even and odd samples taken at the receiver  201 , effectively there is a first virtual RxA  216  which receives odd samples and a second virtual RxB  218  which receives even samples. Then, there are the four channels shown, namely ch Ao    206  between TxA and RxA, ch Ae    208  between TxA and RxB, ch Be    212  between TxB and RxB, and ch Bo    210  between TxB and RxA. This results in the same effective number of channels as in the conventional MIMO scenario requiring two receive antennas. 
 
         [0180]     A block diagram of an example OFDM receiver is provided in  FIG. 12 . Reception begins at the single receive antenna  220  through the RF front end  222 . Analog to digital conversion occurs with ADC  224 . Next sample collector  226  extracts the odd samples produced by the ADC  224  to produce an odd sample stream  227  and extracts the even samples produced by the ADC  224  to create even sample stream  229 . Virtual antennae  228 , 230  are shown which effectively receive the odd sample stream  227  and the even sample stream  229  respectively but no such physical antennae exist, rather only the single receive antenna  220  is provided. Processing of the odd sample stream  227  and the even sample stream  229  then progresses basically in the conventional manner described previously with reference to  FIG. 3 . The prefix is extracted at  232 . Serial-to-parallel conversion takes place at  235 . FFT occurs at  236  followed by parallel-to-serial conversion  237  which produces a pre-combined output. The outputs of functions  232 , 236  are used by channel estimation function  234  to develop a channel estimate for the odd channel. The output of the parallel-to-serial converter  237  and output of the channel estimator function  234  are input to a MIMO decoding function  250 . Similarly, for the even sample stream  229 , the cyclic extension is removed at  238  followed by serial-to-parallel conversion  239 , FFT  242  and parallel-to-serial conversion  243  which is another pre-combined output. Channel estimation takes place as indicated at  240 . The output of the parallel-to-serial converter  243  and output of the channel estimator function  240  are input to a MIMO decoding function  250 .  
         [0181]     The MIMO decoding function  250  performs MIMO decoding/combination of the pre-combined outputs using any technique, conventional or otherwise. The output of MIMO decoding  250  is processed by the QAM de-mapping function  252  and this is followed by FEC decoding  254 . It is important to realize that after the splitting of the input samples into even and odd streams  227 , 229 , the remainder of the receiver can be built identically to any two antenna MIMO receiver. For example, in one embodiment, the MIMO decoding might be MRC (maximum ratio combining) combining, in which the outputs of the FFTs are simply weighted by the channel estimates and combined. Other decoding approaches might alternatively be employed, and this may change the manner in which the even and odd sample streams are processed.  
         [0182]     Theoretically, the correlation between the odd samples channel and even samples channel depends on the bandwidth of the multipath channel (not to be confused with the signal bandwidth). Their mutual dependency reduces as the Multipath-Channel-Bandwidth increases. The odd samples channel and even samples channel may be partially correlated with each other in time. However, they always have quite different frequency responses, which enables the virtual antenna setup in the receiving end though only one physical antenna exists. This phenomenon is true for every wireless system and is well suited for an OFDM system-as the shaping function of OFDM system is a rectangular pulse.  
         [0183]     It is possible to return to the frequency domain by performing a FFT on both the odd samples channel and the even samples channel. The receiver model for the nth tone can be expressed as  
               [             Y   o     ⁡     (   n   )                   Y   e     ⁡     (   n   )             ]     =         [             H   ao     ⁡     (   n   )               H   bo     ⁡     (   n   )                   H   ae     ⁡     (   n   )               H   ae     ⁡     (   n   )             ]     ⁡     [             s   a     ⁡     (   n   )                   s   b     ⁡     (   n   )             ]       +     [             N   e     ⁡     (   n   )                   N   o     ⁡     (   n   )             ]               (   27   )             
 
 where, H ae (n), H be (n), H ao (n) and H bo (n) are the frequency domain channel responses for the nth tone. Therefore MIMO decoding techniques can be applied whenever the channel matrix is full rank. The capacity of this embodiment will solely depend on the eigen condition of the channel matrix. 
 
 OFDM Transmitter Parameters Optimization 
 
         [0186]     For the above example 2×1  FIG. 8  embodiment, α A1 =1; α A2 =1; α B1 =1; α B2 =−2 were the values used. These four parameters can be optimized in terms of capacity or frequency domain channel conditions. The following are several rules/constraints which may be employed alone or in any combination to optimize these parameters. 
        a) balanced energy: |α A1 | 2 +|α A2 | 2 +|α A1 +α A2 | 2 =|α B1 | 2 =|α B2 | 2 +|α B1 +α B2 | 2 ;     b) there is no large notch in frequency domain;     c) the capacity is maximized; and     d) meet the spectrum mask i.e. the signal stays within a required band.        
 
         [0191]     Odd and even channel taps will make frequency domain channel response vary significantly. In fact, the odd and even channels absorb different multipaths and are therefore helpful when a set of multipaths form a destructive signal or when multipaths are formed by a wide scattering environment. To precisely describe this statement, one can classify the random delays by the following index classification  
                 I   A1     ⁡     (   n   )       =     {     k   |         (     n   -   1     )     ⁢   T     &lt;     τ   A   k     ≤   nT       }             (   28   )                   I   A2     ⁡     (   n   )       =     {     k   |       nT   -     T   2       &lt;     τ   A   k     ≤     nT   +     T   2           }             (   29   )                   I   A3     ⁡     (   n   )       =     {     k   |     nT   &lt;     τ   A   k     ≤       (     n   +   1     )     ⁢   T         }             (   30   )             
 
 Then the channels sampled at even (2nT/2) and odd ((2n+1)T/2) intervals can be explicitly expressed as:  
                 ch   A   e     ⁡     (   n   )       =         ch   A     ⁡     (     2   ⁢     nT   /   2       )       =         α   A2     ⁢       ∑     k   ∈     I   A1         ⁢           ⁢       α   A     ⁡     (   k   )           +       α   A1     ⁢       ∑     k   ∈     I   A2         ⁢       α   A     ⁡     (   k   )                       (   31   )                   ch   A   o     ⁡     (   n   )       =         ch   A     ⁡     (       2   ⁢     nT   /   2       +     T   /   2       )       =         α   A1     ⁢       ∑     k   ∈     I   A3         ⁢           ⁢       α   A     ⁡     (   k   )           +       α   A2     ⁢       ∑     k   ∈     I   A2         ⁢       α   A     ⁡     (   k   )                       (   32   )             
 
 Similarly for channel B:  
                 ch   B   e     ⁡     (   n   )       =         ch   B     ⁡     (     2   ⁢     nT   /   2       )       =         α   B2     ⁢       ∑     k   ∈     I   B1         ⁢           ⁢       α   B     ⁡     (   k   )           +       α   B1     ⁢       ∑     k   ∈     I   B2         ⁢       α   B     ⁡     (   k   )                       (   33   )                   ch   B   o     ⁡     (   n   )       =         ch   B     ⁡     (       2   ⁢     nT   /   2       +     T   /   2       )       =         α   B1     ⁢       ∑     k   ∈     I   B3         ⁢           ⁢       α   B     ⁡     (   k   )           +       α   B2     ⁢       ∑     k   ∈     I   B2         ⁢       α   B     ⁡     (   k   )                       (   34   )             
 
 Hence it can be seen that that the index sets I A1 (n), I A2 (n), I A3 (n) (also I B1 (n), I B2 (n), I B3 (n)) are functions of the random delays which are environmentally determined factors. More importantly, I A1 (n) and I A3 (n) are disjoint. Along with the channel interception parameters and Rayleigh fading, the even and odd samples of the channel do have a significant variation that will provide frequency diversity and build up the channel rank of a MIMO decoder with only one receiver antenna. 
 
         [0195]     Particularly, when I A2 (n) and I B2 (n) are empty, the corresponding odd and even channel responses are independent.  
         [0196]     It is noted that CDMA pioneers also considered the selection of multipaths to form each individual finger by controlling the chip rate [J. Shapira and C. E. Wheatley, Channel based optimum bandwidth for spread spectrum land cellular radio, Qualcomm, 1992.]. In practice, it is very difficult to control the amount of ambiguity of a designated finger to have a large amount of mutual information. Unfortunately, the theoretical results show that CDMA systems tends to diminish the mutual information when all the multipaths are resolvable. This occurs when the chip rate is large enough. OFDM seems not to have that issue as it always considers the multipaths together. This might be another advantage of an OFDM system over a CDMA system with a RAKE receiver.  
         [0197]     Conventional MIMO passively exploits the spatial channels and therefore requires the environment must be rich scattering and a non-keyhole environment. Keyhole environments are elaborated upon below. When the real environment is LOS (this situation comprises 15% of the cases in urban areas) or keyhole, MIMO does not work properly. The embodiment is different in the sense that it intercepts the channels first to make the spatial channel a type having wide and rich scattering even if it would otherwise not.  
         [0198]     Advantageously, embodiments of the invention do not suffer a loss in Keyhole Environments. A keyhole environment is one that will force waves propagating along multiple paths to recombine and then continue propagating with the appearance of a single wave. In  FIG. 13  there are two transmitting antennae  300 , 302  and two receiving antennae  304 , 306 . Transmission waves start to propagate from the two transmitting antennae  300 , 302 . When the signals hit surrounding obstacles  310 , 312 , 314 , they get scattered and multiple waves are generated by reflection or diffraction. If a large shielding wall  308  is considered between the transmitters and receivers the keyhole phenomenon acts as a small hole  316  in the wall that transmission of the multiple paths is directed towards and the signals can pass through.  
         [0199]     The combined electric field incident on the keyhole can be expressed as 
 
 E   inc =α 1   s   1 +α 2   s   2    (43) 
 
 Where α 1  and α 2  are caused by the multiple scattering objects  310 , 312 , 314  surrounding the transmitters  300 , 302 . After passing through the keyhole, the electric intensity becomes ρE inc  due to the scaling effect of the keyhole ρ. So the received electric field vector of the two receiver antennae can be written as  
               E   r     =           [           β   1               β   2           ]     ⁢   ρ   ⁢           ⁢     E   inc       +   N     =           ρ   ⁡     [           β   1               β   2           ]       ⁡     [           α   1           α   2           ]       ⁡     [           s   1               s   2           ]       +   N               (   44   )             
 
 where β 1  and β 2  are caused by the scattering objects  318 , 320 , 322  surrounding the receiving antennae. 
 
         [0202]     The Keyhole phenomenon was first noticed by Lucent [Dmitry, Chizhik, G. J. Foschini, M. J. Gans and R. A. Valenzuela, Keyholes, correlations, and capacities of multi-element transmit and receive antennas, IEEE Transactions on Wireless Communications, Vol. 1, No. 2, 2002, pp 361-368.]. In particular roof edge diffraction is perceived as creating a keyhole effect as is the indoor hallway environment. It has been observed by Lucent that the keyhole effect significantly reduces the MIMO BLAST capacity. As a matter of fact, the channel matrix (ref. equation (44)) is always a rank-1 matrix and therefore MIMO blasting capacity collapses to a single transmit and single receive system channel capacity. With the embodiments of the invention, due to the waveform coding transmission technique the keyhole effect will not pose a problem in the statistical sense.  
         [heading-0203]     Multiple Receiver Embodiment  
         [0204]     In the previous section, only multiple transmitter and single receiver systems have been discussed. However, more generally, embodiments can be used either in single receiver antenna systems or multiple receiver antennae system. In fact, the technology can be fully exploited in MIMO systems to produce a robust transceiver system while maintaining a low cost. For example, 2×4 MIMO system performance can be achieved with 2×2 MIMO systems with the invented technology built in.  FIG. 14  illustrates a 2×2 MIMO receiver diagram provided by an embodiment of the invention that has similar performance to a MIMO 2×4 system.  
         [0205]     Two antennae  400 , 402  are used to receive the incoming signals. A RF receiver  404  accepts the signal from antenna  400  and from there it proceeds to the ADC  406 . The stream is split into even and odd paths with sample collector  408  and then framed  410  before undergoing prefix treatment  412 , 416 . The processing done in combining the received signals is somewhat different. The virtual array processing is conducted instead of the RAKE receiver processing. This amounts to a software change in a receiver. The two paths undergo respective serial-to-parallel conversion  451 , 453 , FFT  414 , 418 , parallel-to-serial conversion  459 , 461  the outputs of which are fed to MIMO decoding function  436 . Similarly, the other antenna  402  receives a signal and it proceeds to the RF receiver  420  before the bits continue on to the ADC  422 . The bit stream is split at  424 . The two bit streams are then processed by prefix treatments functions  428 , 432 , serial-to-parallel converters  455 , 457 , FFT functions  430 , 434  and parallel-to-serial converters  463 , 465  the outputs of which are fed to the MIMO decoding function  436 . Also shown in the figure are the four virtual antennas  411 , 415 , 417 , 419 , but as in previous embodiments these virtual antennas do not exist in the physical sense. The outputs of the four FFT stages  414 , 418 , 430 , 434  are combined in the MIMO processing engine which results in an output being sent to the QAM de-mapping function  438 . At this point the bit stream undergoes FEC decoding  440 .  
         [0206]     It can be seen that a 2×2 MIMO system is equivalent to the 2×4 MIMO system with a significant cost reduction. The  FIG. 14  embodiment includes functionality after separating the two received signals into four streams which is basically equivalent to a four antenna system. Any four antenna processing approach can be followed. The figure shows only one example. In general, M r  receive antennas can achieve pM r  receive antennas performance with p times over sampling along with the pre-channel interception. P times over sampling would be required in a system implementing the general virtual spatial reflector of  FIG. 4B  with p paths.  
         [heading-0207]     Simulation Setup and Link Performance  
         [0208]     Simulations were performed using a well developed OFDM Prototype Simulator. The results were obtained by simultaneously running the prototype 2×2 system configurations and 2×1 system configuration side by side. All the simulation parameters were kept the same except that the implementation of the invention uses only a single receiver antenna output and two times over sampling. The simulation results show that the performance of a 2×1 embodiment (using either. QAM or QPSK) is comparable to that of a MIMO 2×2 system (again using either QAM or QPSK). The 2×1 embodiment is also shown to outperform the conventional 2×1 BLAST with MLD or 2×1 STTD when they are restricted to the same throughput. An additional simulation was run for a 2×2 embodiment and a BLAST 2×4 system. It can be seen that the 2×2 embodiment again has comparable performance to the more elaborate BLAST 2×4 system. In  FIG. 14  the two groups of curves have been plotted. The first group represents the simulation on QPSK modulation  510  with the six transmission-reception schemes (i.e. 2×1 embodiment  518 , BLAST 2×1  520 , BLAST 2×2  516 , STTD 2×1  522 , 2×2 embodiment  214  and BLAST 2×4  512 ). The second group  500  represents the simulation applying QAM-16 to four of the same transmission-reception schemes (2×1 embodiment  504 , BLAST 2×1  508 , BLAST 2×2  502 , STTD 2×1  506 . Note that BLAST 2×1 is new and has been simulated with an advanced MLD decoder that best suits the system in order to provide a fair comparison of the systems.