This block accepts a bit sequence as input and yields its digitally modulated version as output. We define as the modulated symbol alphabet of order M. Now, let b ∈ [0, 1] ^K be the K-sized row input bit vector fed to the block, such that K ¯ = K log 2 M ∈ N . Consequently, we define d ¯ ∈ A K ¯ as the data row vector at the output of the constellation mapper, representing the digitally modulated version of b. We note that b can be either a binary file or a pseudo-random binary sequence, with the addition of an appropriate padding to satisfy the above size condition. Any mapping function can be implemented in this block to support the chosen digital modulation scheme.

This block prepares the modulated symbols for the frame generation in the frequency domain. Let us assume that only a central portion of the available spectrum may be used to obtain a smoother impulse response of the transmit/receive filters in the USRPs. In particular, we let N _o be the number of active subcarriers, i.e., occupied tones, out of the N available for the OFDM transmission. Accordingly, a check on the size of d ¯ is performed before the serial to parallel operation. If K ¯ N o ∉ N , then a padding vector of dummy symbols d p ∈ C N o 1 + ⌊ K ¯ N o ⌋ - K ¯ is appended to d ¯ , such that d = d ¯ d p , new padded data row vector of size K ~ = N o 1 + ⌊ K ¯ N o ⌋ , is obtained. Naturally, if K ¯ N o ∈ N , then d = d ¯ and K ~ = K ¯ . This block transforms the data vector d in a data matrix D ( O ) ∈ A N o × K ~ N o , mapping the mth element of d to D ( O ) m - N o ⌊ m N o ⌋ , ⌊ m N o ⌋ + 1 . Finally, we note that K, N _O and N are user-defined parameters known at both ends of the communication. These parameters are kept constant throughout all the duration of the tests. This comes without loss of generality and the consistency of the outcome of our tests persists over different system configurations.

The frame generation block accepts a data matrix D ^(O) as input and constructs an OFDM frame S, defined as

S = G P ( O ) D ( O ) ,

where G ∈ C N o × R g is a preamble matrix with pseudo-random entries and P ( O ) ∈ C N o × R p ( O ) is a deterministic pilot matrix, known a priori by the frame generator. Note that, R _g , R p ( O ) ∈ N .

We start by describing the preamble matrix G, adopted for time and frequency synchronization purposes at the receiver. We consider a preamble structure according to the classical procedure proposed by Schmidl and Cox (S-C) 21 . This approach makes use of the statistical properties of specially constructed sequences, characterized by interesting auto-correlation properties. In our implementation, we set R _g  = 1 and G degenerates into a N _o -sized vector g, obtained by alternating pseudo-random binary phase-shift keying (BPSK) symbols g _i , ∀ i ∈ 1 , N o 2 , and zeros such that g = g 1 , 0 , g 2 , 0 , … , g N o 2 T . The adopted pseudo-random sequence should be known at both ends of the communication, to allow for a more precise time synchronization at the receiver (detailed in the following). In this implementation, we achieve this situation by imposing the adoption of an identical user-defined algorithm and initial seed at both the OFDM transmitter and receiver. At this stage, we note that an inverse discrete Fourier transform (IDFT) over the N available subcarriers will be performed in the following block, to generate the OFDM symbols. Due to the properties of the IDFT, the time domain representation of g will consist of a repeated sequence over one full OFDM symbol, as in the S-C algorithm.

In principle, the knowledge of the preamble at the receiver could enable channel estimations at the latter (for equalization purposes) by evaluating the received instance of g, as done in classical pilot-based estimations. Nevertheless, the significant number of zeros in g may decrease the quality of said estimation, even if linear interpolation techniques were to be adopted. Therefore, the pilot matrix P ^(O) of size N o × R p ( O ) is appended to the frame after g, to provide a more reliable tool for channel estimation at the receiver. In particular, we let P ( O ) = p ( O ) 1 R p ( O ) T , with p ( O ) ∈ C N o deterministic vector known both at the transmitter and receiver. We remark that a bigger R p ( O ) could yield more accurate channel estimations at the receiver but reduces the spectral efficiency of the transmission. Thus, a careful adjustment of this parameter depending on the environment, e.g., perceived signal-to-noise ratio (SNR) at the receiver and coherence time of the channel, could become necessary during the field tests.

At this point, a power scaling may be performed to shape a desired power profile for S before the IDFT. Let α g ( O ) , α p ( O ) , α d ( O ) ∈ R be parameters adopted to scale independently the power of g, P ^(O) and D ^(O). We note that, the scaling parameters α g ( O ) , α p ( O ) and α d ( O ) are set empirically during the field tests, to achieve a more homogeneous power profile for the signal. The frame obtained at the output of the power scaling block can be written as S = α g ( O ) g α p ( O ) P ( O ) α d ( O ) D ( O ) .

The matrix S, input to the IDFT block, has size N o × 1 + R p ( O ) + K ~ N o , thus a further padding to S has to be appended to prepare the frame for the N-point IDFT. In fact, the number of occupied tones in the proposed scheme is lower than the number of available subcarriers, i.e., N _o  < N. Let N = 0 N - N o 2 × 1 + R p ( O ) + K ~ N o be a suitable zero padding matrix. The frequency domain representation of the full OFDM frame is defined as

S F = N T S T N T T ∈ C N × 1 + R p ( O ) + K ~ N o .

Then, S T , time domain representation of S F , is obtained by stacking the N-point IDFT of S T and an additional padding matrix Z = 0 N × R z , included for SNR estimation purposes at the OFDM receiver, as further detailed in Section 5.2. Then, S T reads

S T = F - 1 S F Z ∈ C ( N + L ) × 1 + R p ( O ) + K ~ N o + R z ,

with F unitary DFT matrix as defined in Section 2 and R z ∈ N . Note that, the matrix representation adopted so far has been provided only for the sake of compactness. In fact, in the operating framework provided by GNU Radio, algorithms based upon matrix-wise operations are not computationally efficient. Consequently, the N-point IDFTs (and DFTs) are implemented by means of the computationally efficient algorithms provided by the FFTW 22 C library, based on vector-wise operations. This choice has been made to decrease the overall required computational time.

The CP insertion can be modeled as a matrix operation as well, that is S T CP = A S T ∈ C ( N + L ) × 1 + R p ( O ) + K ~ N o + R z , with A CP insertion matrix as in Section 2. In practice, if we let S ¯ T ∈ C L × 1 + R p ( O ) + K ~ N o + R z be the matrix carrying the last L rows of S T , then the CP insertion operation can be implemented without matrix operations by constructing S T CP = S ¯ T T S T T T .

The output of this block is the serialized version of the input stream, ready to be fed to the USRP for transmission. This operation can be written as x ( O ) = vec S T CP T ∈ C ( N + L ) 1 + R p ( O ) + K ~ N o + R z , with x ^(O) a row vector.

Let us denote y as the signal obtained after the RF to baseband conversion performed by the USRP. After this operation, y is fed as input to the OFDM receiver baseband chain, as shown in Figure 5. The first operation performed by the latter on y is the time and frequency synchronization procedure. By construction, OFDM is based upon a large number of closely spaced orthogonal subcarrier signals, used to bear data on several parallel data streams or channels. In case of missed synchronization of the received frame, such carrier orthogonality is lost. Specifically, if the cyclic prefix L is not much larger than the delay spread of the channel, imperfect time synchronization of the frame may cause inter-block interference (IBI) and decrease the signal to interference plus noise ratio of the useful portion of the signal. Conversely, in case of imperfect frequency synchronization, issues such as inter-carrier interference (ICI) or phase noise may arise 23 , breaking the orthogonality between the subcarriers and impairing the decoder. Unfortunately, any communication system may experience a carrier frequency offset due to issues such as Doppler shifts, or imperfections in the phase lock loop responsible for the generation of the carrier frequency at the transmitter and receiver (used in the RF demodulation step to obtain the baseband representation of the received signal), just to name a few. Thus, an appropriate procedure to achieve time and frequency synchronization is required.

Herein, we exploit the special structure of the preamble, described in Section 5.1, and adopt the S-C method 21 to achieve both time and frequency synchronization. First, the timing of the first sample of the preamble is identified. Then, the carrier frequency offset is detected and corrected to achieve frequency synchronization.

In this implementation, the receiver disposes of the same seed adopted at the transmitter to generate the preamble, as explained in Section 5.1, thus is able to generate a copy of g T = F - 1 0 1 × N - N o 2 g T 0 1 × N - N o 2 T , time domain version of the N-sized preamble (CP excluded). Now, let us consider a window of N received samples. We define t as the time index corresponding to the first sample of the window. If we let the window slide along in time that we have, the receiver can search for the preamble by computing P _t , auto-correlation function of the received signal evaluated at t, ∀ t ∈ N , given by

P t = ∑ m = 0 N 2 - 1 y t + m ∗ y t + m + N 2 ,

with y _a  = y[a] for clarity in the notation. Let M t c be a timing metric, defined as

M t c = P t 2 R t 2 ∈ 0 , 1 ,

with R t = ∑ m = 1 N / 2 | y t + m + ( N / 2 ) | 2 received energy for the second half-window. The properties of the adopted preamble’s auto-correlation induce the formation of a plateau to M t c , whose length is equal to L - l, with l number of channel taps (excluding the line-of-sight component) as defined in Section 2. The starting sample of the preamble may be taken to be anywhere within this plateau 21 , leading to some uncertainty for the receiver. A two-step timing estimation is adopted to solve this issue. First, a coarse timing estimation is computed, i.e., t ̂ c , to identify the approximate position of the preamble within the received sequence by

t ̂ c = arg max t M t c .

Then, we select a fixed window of received samples of size N 2 + 2 L , including the sample at t ̂ c (as the (L + 1)-th sample), and compute its cross-correlation with g T as

P ~ t = ∑ m = 0 N / 2 + 2 L - 1 y d ̂ c - L + m ∗ g T , m .

Note that, (16) is feasible if L ≤ N 4 , condition usually verified in practical systems for matters of spectral efficiency 11 . Now, the fine estimation of the timing of the first sample of the preamble, i.e., t ̂ f , is obtained by exploiting the property of the peak of the cross-correlation P ~ t as

t ̂ f = t ̂ c + arg max t P ~ t - L - 1 .

From now on, for clarity, we will let y ~ be the received frame after the time synchronization, obtained by discarding the first t ̂ f - 1 samples of y. Once the best timing point t ̂ f has been identified, the carrier frequency offset (in subcarrier spacings) f _Δ can be directly estimated by evaluating ϕ ̂ , phase difference between the two halves of the received preamble, in radians, estimated at t ̂ f as

ϕ ̂ = ( P t , t ̂ f ) .

Accordingly, f _Δ can be computed as

f Δ ̂ = ϕ πN + 2 z N ,

with z = 0 for | ϕ ̂ | < π and z ∈ Z ∖ { 0 } otherwise. We note that in the set of preliminary experimental OFDM transmissions performed according to the parameters in Table 2, to assess the effectiveness of the synchronization algorithms, the condition | ϕ ̂ | < π was always satisfied. Consequently, no estimator for the integer part of f _Δ has been implemented in this block 21 . In this regard, the time history of the resulting f Δ ̂ , depicted in Figure 6, shows a very stable and consistent behavior across the 100 performed tests.

As a result of the procedure described so far, the synchronized version of the received frame carrying the first ( N + L ) ( 1 + R p ( O ) + K ~ N o + R z ) + N received samples after the t ̂ f th, defined as x ̂ ( O ) ∈ C ( N + L ) 1 + R p ( O ) + K ~ N o + R z + N , is obtained by taking

x ̂ t ( O ) = e - j 2 π t f ̂ Δ y ~ t .

Finally, the leading N samples of x ̂ ( O ) , i.e., the preamble, are discarded and the resulting x ̂ ( O ) ∈ C ( N + L ) 1 + R p ( O ) + K ~ N o + R z is fed to the serial to parallel block.

This block yields X ̂ T = H pp S T CP + W ( O ) ∈ C ( N + L ) × 1 + R p ( O ) + K ~ N o + R z , stream matrix ready for the CP removal operation, with W ( O ) ∈ C ( N + L ) × 1 + R p ( O ) + K ~ N o + R z matrix collecting the overall effect of both the thermal noise and the residual interference generated by the secondary transmission, if perfect CSI is not available at HT. In particular, the mth element of x ̂ ( O ) is mapped to [ X ̂ T ] m - ( N + L ) ⌊ m N + L ⌋ , ⌊ m N + L ⌋ .

The CP removal block discards the first L rows of the matrix X ̂ , to obtain a matrix X ̂ T , N , ready to be processed by the DFT block. We can represent this operation in matrix form by

X ̂ T , N = B X ,

with B cyclic prefix removal matrix as defined in Section 2.

The DFT block yields X ̂ F , N = F X ̂ T , N ∈ C N × 1 + R p ( O ) + K ~ N o + R z , representation of the received frame in the frequency domain. As for the transmitter, herein the matrix representation is adopted for the sake of compactness, whereas the actual N-point DFT is computed by means of vector-wise operations through the FFTW 22 C library.

At this stage, a channel equalization is performed to remove the effect of the channel on the received signal and proceed to the decoding. The orthogonality between the subcarriers 24 allow the adoption of a classical low-complexity ZF strategy to equalize the received frame, as typically done in OFDM receivers. First, the portion of the spectrum with no active subcarrier is discarded from X ̂ F , N , to recover the received noisy version of S. Accordingly, we remove both the first and the last N - N o 2 rows from the matrix X ̂ F , N , obtaining S ̂ = Q X ̂ F , N = [ g ̂ P ̂ ( O ) D ̂ ( O ) Z ̂ (O) ] , with Q = 0 N o × N - N o 2 I N o 0 N o × N - N o 2 . Note that, Z ̂ (O) = Q F B Z ∈ C N o × R z is the frequency domain representation of the received noisy version of the padding matrix Z.

Before the equalization, the receiver can have an approximate estimation of the average SNR experienced during the reception, i.e., SNR ̂ , by computing the ratio between the energy of the preamble g and the energy of the AWGN, obtaining

SNR ̂ = 10 log 10 g ̂ H g ̂ tr Z ̂ (O) Z ̂ (O)H .

Note that, this approximation is more suitable for medium and high SNR regime, due to the presence of a noise component in g. Thus, the precision of SNR ̂ depends on the size of g and Z, being more accurate for 1 < < R _z . Subsequently, the receiver can exploit the knowledge of P ^(O) and compute the equalizer matrix H ̂ eq = diag 1 ĥ 1 , … , 1 ĥ N o ∈ C N o × N o , with ĥ k given by

ĥ k = 1 R p ( O ) ∑ m = 1 R p ( O ) P ̂ ( O ) k , m P ( O ) k , m , ∀ k ∈ 1 , N o .

Then, the equalized version of the data matrix is obtained as D ̂ eq ( O ) = H ̂ eq D ̂ ( O ) , ending the equalization process.

This block yields d ̂ ∈ C K ~ N o = vec D ̂ eq ( O ) T , row vector carrying the received version of the digitally modulated symbol vector d, of size K ~ N o .

The constellation demapper implements the appropriate function to recover the received bit vector B ̂ , ending the receiver processing.

This block provides the same functions as its previously described OFDM counterpart. In this case, we let b ∈ [0, 1] ^J be the J-sized row input bit vector fed to the constellation mapper, such that J ¯ = J log 2 M ∈ N . Then, we let d ¯ ∈ A J ¯ be the data row vector at the output of the constellation mapper, representing the digitally modulated version of b.

This block provides the same functions as its previously described OFDM counterpart. Note that, the precoder E adopted in the following block operates on sequences of size L (i.e., dim ker H ~ sp d = L ), as detailed in Section 2. Then, as before, a preliminary check on the size of d ¯ is performed. If J ¯ L ∉ N , a padding vector of dummy symbols d p ∈ C L ( 1 + ⌊ J ¯ L ⌋ ) - L ¯ is appended to d ¯ , such that d = d ¯ d p , yielding a padded data row vector of size J ~ = L 1 + ⌊ J ¯ L ⌋ . Naturally, if J ¯ L ∈ N , then d = d ¯ and J ~ = J ¯ . Finally, the data vector d is transformed into a data matrix D ( C ) ∈ A L × J ~ L , by mapping the mth element of d to D ( C ) m - L ⌊ m L ⌋ , ⌊ m L ⌋ + 1 . As before, we note that L and J are user-defined parameters known at both ends of the communication and kept constant throughout the duration of the tests.

This block is responsible for both the CIA frame generation and linear precoding. The CIA frame includes four parts, namely a preamble g ∈ C N + L , a pilot matrix P ^(C) detailed in the following, the data matrix D ^(C) obtained as input after the serial to parallel conversion and a padding matrix Z = 0 ( N + L ) × R z , with g and Z obtained as described in Section 5.1. Note that, the sizes of the input symbol vector of CIA and OFDM and L and N, respectively, do not coincide. Thus, the structure of the pilot matrix for CIA and OFDM, the latter being described in Section 5.1, is different. In this case, we let P ( C ) ∈ C L × R p ( C ) , (with R p ( C ) ≥ L ) be a semi-unitary pilot matrix, such that P ^(C)P ^(C)H=I _L . In Section 5.4, we will see how this choice allows for a simpler channel estimation at CT.

Now, we recall that HT acts as an OFDM receiver during the uplink phase, as explained in Section 4. During this phase, a frequency domain estimation of the channel towards OT, i.e., h ̂ ps u = χ h ̂ sp d , is acquired and stored. The time domain version of χ h ̂ sp d , necessary to build the circulant channel matrix χ H ~ sp d ∈ C N × ( N + L ) as in (4), is then obtained by taking the IDFT of χ h ̂ sp d , and fed to the precoder block during the downlink phase, as shown in Figure 7. Subsequently, the efficient algorithms provided by the portable linear algebra library LAPACK 25 are exploited to compute the singular value decomposition (SVD) of χ H ~ sp d and select its right singular vectors generating ker ( H ~ sp d ) , to obtain the CIA precoder E satisfying (7), as detailed in 3 . Finally, the CIA frame is constructed as

C = g E P ( C ) E D ( C ) Z ∈ C ( N + L ) × 1 + R p ( C ) + J ~ L + R z ,

where only the pilot and data matrices are precoded with E. We note that the preamble g is not precoded in order to preserve its useful properties in the time domain for synchronization purposes. The padding matrix does not need to be precoded, being entirely composed of null entries.

At this stage, a power scaling may be applied to shape a desired power profile for C before the parallel to serial operation. Let α g ( C ) , α p ( C ) , α d ( C ) ∈ R be parameters adopted to scale independently the power of g, EP ^(C) and ED ^(C). In particular, the scaling parameters α g ( C ) , α p ( C ) and α d ( C ) are set such that the peak power of both the CIA and OFDM frames has the same order of magnitude. This choice has been made to guarantee that any interaction between the two signals at the receiver is due to their structure and not to favorable power levels of one signal w.r.t. the other. The frame obtained at the output of the power scaling block can be written as C = α g ( C ) g α p ( C ) E P ( C ) α d ( C ) E D ( C ) Z .

We denote the output of the parallel to serial block as x ∈ C ( N + L ) 1 + R p ( C ) + J ~ L + R z , serialized version of the stream, ready to be fed to the USRP for transmission. This operation can be written as x ^(C) = vec(C)^T, with x ^(C) being a row vector.

The synchronization block provides the same functions as its previously described OFDM counterpart. The output of this block is x ̂ (C) ∈ C ( N + L ) 1 + R p ( C ) + J ~ L + R z , synchronized and corrected vector carrying the first ( N + L ) 1 + R p ( C ) + J ~ L + R z samples after the t ̂ f + N -th sample of the received vector y.

A serial to parallel conversion is performed on x ̂ (C) to prepare the received stream for the channel estimation and equalization. The output of this block is the matrix C ̂ = g ̂ E ̂ P ̂ ( C ) E ̂ D ̂ ( C ) Z ̂ (C) ∈ C ( N + L ) × 1 + R p ( C ) + J ~ L + R z , such that the mth element of x ̂ (C) is mapped to C ̂ m - ( N + L ) ⌊ m N + L ⌋ , ⌊ m N + L ⌋ .

A channel estimation and a subsequent equalization are performed in this block, to remove the combined effect of channel and precoder on the received signal. We note that, an approximate estimation of the average SNR experienced during the reception, i.e., SNR ̂ , can be computed by the CIA receiver before the actual equalization, by means of (22) as explained in Section 5.2. The received frame can be rewritten as

C ̂ = g ̂ E ̂ P ̂ ( C ) E ̂ D ̂ ( C ) Z ̂ (C)

= H ss d g E P ( C ) E D ( C ) Z + W ( C ) ,

where the channel matrix Hssd has been isolated, for clarity. Note that, in (26), the matrix W ( C ) = g W E W P W ( C ) E W D W ( C ) Z W ∈ C ( N + L ) × 1 + R p ( C ) + J ~ L + R z collects the overall effect of both the thermal noise and the interference generated by the OFDM transmission, with g W ∈ C N + L , E W ∈ C ( N + L ) × L , P W ( C ) ∈ C ( N + L ) × R p ( C ) , D W ( C ) ∈ C ( N + L ) × J ~ L and Z W ∈ C ( N + L ) × R z .

Let us consider an equivalent representation of the channel faced by the pilot and data matrices, given by the contribution of the CIA precoder and the actual channel. Let H ( C ) = H ss d E ∈ C ( N + L ) × L be the equivalent channel matrix. Then, an estimation of H ^(C) is computed in this block by evaluating the received pilot matrix P ̂ ( C ) to obtain

H ̂ ( C ) = ( H ( C ) P ( C ) + P W ( C ) ) P ( C ) H

= H ( C ) + P W ( C ) P ( C ) H ︸ interference plus noise ,

where the properties of the semi-unitary pilot matrix P ^(C) have been exploited. Now, let H ̂ ( C ) = U ( C ) Σ ( C ) V ( C ) H be the SVD of H ̂ ( C ) , with U ( C ) ∈ C ( N + L ) × ( N + L ) and V ∈ C L × L unitary matrices and Σ = [ Σ ^σ Σ ⁰]^T, with Σ ^σ  = diag(σ ₁,…,σ _L ) diagonal matrix carrying the L ordered singular values of H ̂ ( C ) and Σ ⁰ = 0 _{L × (N - L)}. Then, we can obtain H ̂ eq ( C ) , ZF equalizer for the equivalent channel, as

H ̂ eq ( C ) = V ( C ) Σ ~ ( C ) U ( C ) H ∈ R L × ( N + L ) ,

with Σ ~ ( C ) = diag ( 1 σ 1 , … , 1 σ L ) Σ 0 T . The estimated version of the data matrix D ^(C) after the equalization is computed as

D ̂ eq ( C ) = H ̂ eq ( C ) ( H ̂ ( C ) D ( C ) + W ( C ) )

= U ( C ) Σ ( C ) V ( C ) H ( V ( C ) Σ ~ ( C ) U ( C ) H D ( C ) + W ( C ) )

= D ( C ) + U ( C ) Σ ( C ) V ( C ) H W ( C ) ︸ interference plus noise .

and this ends the equalization process.

A parallel-to-serial operation is performed on D ̂ eq ( C ) to yield d ̂ = vec D ̂ eq ( C ) T ∈ C J ~ L , row vector carrying the received version of the digitally modulated symbol vector d, of size J ~ L , ready to be fed to the constellation demapper.

The constellation demapper provides the same functions as its previously described OFDM counterpart. It implements the appropriate function to recover the received bit vector B ̂ , ending the receiver processing.

Let us consider a stand-alone OFDM transmission performed by HT and OT, according to the parameters in Table 2, as if the secondary link was not present. A BPSK modulation is adopted for simplicity. A straightforward way to evaluate how the performance of the OFDM transmission may vary in presence or absence of the CIA transmission, is discussed in the following. First, an upper bound on the achievable throughput of the considered OFDM transmission, i.e., the maximum number of information bits that HT can transmit per second to OT, can be computed according to the parameters in Table 2. In this regard, if we let be the transmit bandwidth at HT then the maximum achievable throughput of the OFDM transmission can be computed as

T o = N o B ( N + L ) ( R p ( O ) + R z (O) + K ¯ N o + 1 ) ,

that, in our case, corresponds to 8.13 kbps. We start noting that the value of T _o does not depend on the SNR. However, the same is not true for the experimental throughput, defined herein as T o ̂ for clarity. In this regard, let ρ ∈ R be the average SNR at the receiver, an estimation of which is given by SNR ̂ in (22). As a matter of fact, T o ̂ depends on ρ, given that T o ̂ = T o N o ̂ ( ρ ) N o , with N o ̂ ( ρ ) defined as the number of correct received bits. Consequently, the actual experimental throughput will always be lower or equal to T _o .

The experimental throughput achieved by the actual OFDM transmission is computed for several experiments performed for different values of the SNR at the receiver. During our tests, the SNR variations at the receiver to obtain different experimental throughput values are user-induced. In practice, the transmit gain of the transmitting USRP is modified by the user when necessary, such that the transmit power may vary between 1 and 20 mW, for a resulting SNR at the receiving antenna ranging between 10 and 30 dB. Accordingly, as a first step, we compute the experimental throughput of the aforementioned stand-alone OFDM transmission, to obtain a specific benchmark to evaluate the performance of the primary transmission, when coexisting with the secondary CIA transmission. Afterwards, the CIA frame is generated and added to the transmit signal at HT to assess its impact on the experimental throughput of the primary transmission.

Concerning the CIA frame, we aim at validating the interference cancelation (reduction) capabilities of the precoder E. As a consequence, in our tests, E is first computed from the estimation of h ̂ ps u performed by HT during each uplink transmission, then from a Rayleigh fading channel, randomly generated before each downlink transmission, according to the model described in Section 2. The rationale for this is that if the precoder built upon h ̂ ps u were not more effective than a randomly generated null-space precoder, then CIA would lose its attractiveness, and there would be no use in further pursuing the development. The three so-obtained throughput curves are depicted in Figure 11. As previously mentioned, our proof-of-concept was not optimized to achieve the best rates but rather to show that CIA provides some effective interference protection. Therefore, we focus on a comparative analysis, i.e., a comparison between the performance obtained in presence of CIA w.r.t. to the stand-alone OFDM vase.

We note that the throughput loss experienced by the OFDM transmission when coexisting with the CIA transmission diminishes as the SNR increases if E is built upon h ̂ ps u , whereas it increases with the SNR if E is computed using the random channel realization. For the latter, the throughput is clearly interference-limited. Furthermore, we notice that for high SNR, i.e., larger than >20 dB, the experimental throughput of the OFDM transmission is very close to (if not coinciding with) T _o . Thus, despite the imperfections due to the non-optimized practical implementation, these findings show the effectiveness of the CIA precoder built upon the actual channel estimation, as a mean to protect the primary receiver from undesired interference.

We now perform a last test w.r.t. the primary transmission and activate only the CIA transmitter chain at HT and switch our focus on the received power at OT after the CP removal operation and DFT. With this experiment, we aim at measuring the actual residual interference experienced by OT, to better characterize the previous results. Now, let M = Q F B ( H pp d E D (C) + W ) ∈ C N o × J ¯ L be the residual interference plus noise component at OT after the CP removal operation and DFT, with W ∈ C N o × J ¯ L matrix collecting the effect of the thermal noise, F, B and Hppd defined in Sec. 2, E and D ^(C) defined in Sec. 5.3 and Q defined in Sec. 5.2. Then, we introduce a metric called interference plus noise-to-noise ratio (INNR), as the ratio between the energy of the interference plus thermal noise component and the energy of the thermal noise, given by

INNR = 10 log 10 tr M M H tr Z ̂ (O) Z ̂ (O)H ,

with Z ̂ (O) as defined in Section 5.2. Note that, herein E is derived according to the two aforementioned strategies, i.e., first the precoder is built upon the actual channel estimation then upon a random channel realization. As shown in Figure 12, the INNR for the randomly derived E is significantly higher than the result for the actual CIA precoder, with the latter providing approximately 10 dB of interference isolation towards the OT, w.r.t. the former.

These findings confirm the previous results. However, we note that the INNR for the actual CIA precoder can reach up to 7 dB at high SNR. This shows the impact of both the lack of optimization in our implementation and possible hardware imperfections not properly compensated at software level on the quality of the acquired CSI, even for very favorable SNR values, i.e., SNR >20 dB.

As a final test, we focus on the link between HT and CT to evaluate the performance of the secondary transmission. We first perform a stand-alone CIA transmission using a previously built E, upon one of the many h ̂ ps u estimations, according to the parameters in Table 2. Subsequently, we follow an analogous approach to the test described in Section 6.2.1 and compute an upper bound on the achievable throughput of the considered CIA transmission, given the parameters in Table 2. Accordingly, we compute T _c , maximum throughput of the CIA transmission, i.e., the maximum number of information bits that HT can transmit per second to CT, as

T c = J B ( N + L ) R p (C) + R z (C) + J ¯ J + 1 ,

whose value is identical to the previous case, i.e., 8.13 kbps, due to the identical size of the OFDM and CIA frame by construction. Like before, we evaluate the experimental throughput achieved by the actual CIA transmission, i.e., T c ̂ , for several experiments performed for different values of the SNR at the receiver. In this regard, we recall the dependency of the experimental throughput on the average SNR at the receiver, as discussed in Section 6.2.1. After the computation of the performance of the stand-alone CIA transmission, the impact of the primary transmission on the experimental throughput at CT is assessed by activating the OFDM transmitter chain at HT. Therefore, the signal transmitted by HT for this test is the serialized version of the sum of the CIA and OFDM frame. The results of this test are provided in Figure 13.

The throughput of the secondary transmission is lower than the performance of the primary system, even though the difference is not large due to the adopted low modulation order, i.e., BPSK. We note that, this finding confirms the theoretical results in 5 , showing that the CIA transmission achieves a non-negligible throughput w.r.t. OFDM. On the other hand, the presence of the OFDM transmission induces interference limited performance of the secondary system. Once again the performance loss of around 5% is mitigated by the adopted low modulation order, but its trend is evident throughout the whole range of experienced SNR, confirming the findings in 5 .