Effect of changing the symbol rate of QAM modem on the performance of 32kb/s ADPCM system

Exhaustive work had been done to accommodate high speed voiceband data signal either by modifying the algorithm of ADPCM [15-25] or by modifying the model of data transmission [22, 26-27]. One way of modifying the model of data transmission is to use different constellations of Quadrature Amplitude Modulation (QAM) signal.

Structure of adpcm

The algorithm of 32 kb/s ADPCM which is described here is as in CCITT G.726 [15]. Fig. 1 shows simplified block diagram of ADPCM codec. Two major components form the algorithm: an adaptive quantizer and an adaptive predictor. The relation between the encoder and the decoder is also depicted. The difference between them is that the encoder has adaptive quantizer( Q ) and inverse adaptive quantizer( Q^-1 ) ,while, the decoder has inverse adaptive quantizer only. The decoder is simply a subset of the encoder and transmits r(n) as its output instead of c(n). The adaptive predictor, which is composed of two poles and six zeros, computes an input signal estimate ŝ(n) which is subtracted from input signal s(n) resulting in a difference signal d(n). The adaptive quantizer codes d(n) into 4-bit codeword c(n) which is sent over the transmission facility. At the receiving end, an ADPCM decoder uses c(n) to attempt to reconstruct the original signal s(n). Actually, only r(n) can be reconstructed which is related to the original input signal s(n) by

r(n) = s(n) + e(n)                                                                     (1)

where

e(n) = dq(n) – d(n) = r(n) – s(n)                                                  (2)

is the error introduced by the quantizer, and dq(n) is the output of inverse adaptive quantizer

A typical measure of the ADPCM performance is given by signal-to-noise ratio (SNR)

SNR= E[s²(n)]/E[e²(n)] = σ s ²/ σ e ²

Where E denotes expectation, σ s ² is the power (or variance) of input signal, &σ e ² is the power (or variance) of the error signal.

Qam modem

Computer simulation test

A series of computer simulation tests have been carried out on ADPCM codec using the three QAM modem signals at 16.8kb/s with constellations shown in Figs.2-4. The performance of ADPCM is measured by calculating SNR in equation 3.

Table 1 shows the results of testing ADPCM using modem-I. It seems that the performance of ADPCM with circular constellation is better than rectangular one by approximately 0.3dB.

Table 2 shows the results of testing ADPCM using modem-II. It seems that the performance of ADPCM with circular constellation is better than rectangular one by approximately 0.4dB.

(a) Rectangular                                            (b) (6,12,18,24,30,38)

о

(a) Rectangular

Fig. 3. 64-ary QAM constellations

(b) (6,12,19,27)

(c)(5,11,16)

Fig. 4. 32-ary QAM constellations

Table 3 shows the results of testing ADPCM using modem-III. It seems that the performance of ADPCM with circular constellation is better than rectangular one by approximately 0.5dB.

The comparison among the three modems shows that the performance of ADPCM with modem-III is better than its performance with modem-II by approximately 1.1dB and the later is better than modem-I by approximately 1.2dB .

Summary and conclusion

Three QAM modems operate at data rate of 16.8kb/s have been considered in order to reduce the nonlinear distortion of ADPCM. The simulation results show that the performance of ADPCM with – 201 –

Table 1. Performance of ADPCM

	Modem-I
SNR(dB)	Rect	(6,12,18,24,30,38)
	19.7	20

Table 2. Performance of ADPCM

	Modem-II
SNR(dB)	Rect	(6,12,19,27)
	20.9	21.3

Table 3. Performance of ADPCM

Modem-III SNR(dB) Rect (4,11,17) (5,11,16) 21.8 22.2 22.3 modem-III is better than modem-II and the later is better than modem-I. Also, the performance with circular constellation is better than rectangular one.

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